Accord.Math
Base class for parallel learning algorithms.
Gets or sets the parallelization options for this algorithm.
Gets or sets a cancellation token that can be used
to cancel the algorithm while it is running.
Initializes a new instance of the class.
Called when the object is being deserialized.
Methods for operating with categorical data.
Calculates the prevalence of a class for each variable.
An array of counts detailing the occurrence of the first class.
An array of counts detailing the occurrence of the second class.
An array containing the proportion of the first class over the total of occurrences.
Calculates the prevalence of a class.
A matrix containing counted, grouped data.
The index for the column which contains counts for occurrence of the first class.
The index for the column which contains counts for occurrence of the second class.
An array containing the proportion of the first class over the total of occurrences.
Groups the occurrences contained in data matrix of binary (dichotomous) data.
This operation can be reversed using the method.
A data matrix containing at least a column of binary data.
Index of the column which contains the group label name.
Index of the column which contains the binary [0,1] data.
A matrix containing the group label in the first column, the number of occurrences of the first class
in the second column and the number of occurrences of the second class in the third column.
Divides values into groups given a vector
containing the group labels for every value.
The type of the values.
The values to be separated into groups.
A vector containing the class label associated with each of the
values. The labels must begin on 0 and its maximum value should
be the number of groups - 1.
The original values divided into groups.
double[,] matrix =
{
{ 2, -1.0, 5 },
{ 7, 0.5, 9 },
};
// column means are equal to (4.5, -0.25, 7.0)
double[] colMeans = Stats.Mean(matrix, 0);
// row means are equal to (2.0, 5.5)
double[] rowMeans = Stats.Mean(matrix, 1);
Calculates the matrix Mean vector.
A matrix whose means will be calculated.
The dimension along which the means will be calculated. Pass
0 to compute a row vector containing the mean of each column,
or 1 to compute a column vector containing the mean of each row.
Default value is 0.
Returns a vector containing the means of the given matrix.
double[][] matrix =
{
new double[] { 2, -1.0, 5 },
new double[] { 7, 0.5, 9 },
};
// column means are equal to (4.5, -0.25, 7.0)
double[] colMeans = Stats.Mean(matrix, 0);
// row means are equal to (2.0, 5.5)
double[] rowMeans = Stats.Mean(matrix, 1);
Calculates the matrix Mean vector.
A matrix whose means will be calculated.
The sum vector containing already calculated sums for each column of the matrix.
Returns a vector containing the means of the given matrix.
Calculates the matrix Mean vector.
A matrix whose means will be calculated.
The sum vector containing already calculated sums for each column of the matrix.
Returns a vector containing the means of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
The mean vector containing already calculated means for each column of the matrix.
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
The mean vector containing already calculated means for each column of the matrix.
Pass true to compute the standard deviation using the sample variance.
Pass false to compute it using the population variance. See remarks
for more details.
Setting to true will make this method
compute the standard deviation σ using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true will
thus compute σ using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
Pass true to compute the standard deviation using the sample variance.
Pass false to compute it using the population variance. See remarks
for more details.
Setting to true will make this method
compute the standard deviation σ using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true will
thus compute σ using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Variance vector.
A matrix whose variances will be calculated.
Returns a vector containing the variances of the given matrix.
Calculates the matrix Variance vector.
A matrix whose variances will be calculated.
The mean vector containing already
calculated means for each column of the matrix.
Returns a vector containing the variances of the given matrix.
Calculates the matrix Variance vector.
A matrix whose variances will be calculated.
Returns a vector containing the variances of the given matrix.
Calculates the matrix Variance vector.
A matrix whose variances will be calculated.
The mean vector containing already calculated means for each column of the matrix.
Pass true to compute the sample variance; or pass false to compute
the population variance. See remarks for more details.
Setting to true will make this method
compute the variance σ² using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true
will thus compute σ² using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
Returns a vector containing the variances of the given matrix.
Calculates the matrix Medians vector.
A matrix whose medians will be calculated.
The quartile definition that should be used. See for datails.
Returns a vector containing the medians of the given matrix.
Calculates the matrix Medians vector.
A matrix whose medians will be calculated.
The quartile definition that should be used. See for datails.
Returns a vector containing the medians of the given matrix.
Computes the Quartiles of the given values.
A matrix whose medians and quartiles will be calculated.
The inter-quartile range for the values.
The quartile definition that should be used. See for datails.
The second quartile, the median of the given data.
Computes the Quartiles of the given values.
A matrix whose medians and quartiles will be calculated.
The inter-quartile range for the values.
The quartile definition that should be used. See for datails.
The second quartile, the median of the given data.
Computes the Quartiles of the given values.
A matrix whose medians and quartiles will be calculated.
The first quartile for each column.
The third quartile for each column.
The quartile definition that should be used. See for datails.
The second quartile, the median of the given data.
Computes the Quartiles of the given values.
A matrix whose medians and quartiles will be calculated.
The first quartile for each column.
The third quartile for each column.
The quartile definition that should be used. See for datails.
The second quartile, the median of the given data.
Calculates the matrix Modes vector.
A matrix whose modes will be calculated.
Returns a vector containing the modes of the given matrix.
Calculates the matrix Modes vector.
A matrix whose modes will be calculated.
Returns a vector containing the modes of the given matrix.
Computes the Skewness for the given values.
Skewness characterizes the degree of asymmetry of a distribution
around its mean. Positive skewness indicates a distribution with
an asymmetric tail extending towards more positive values. Negative
skewness indicates a distribution with an asymmetric tail extending
towards more negative values.
A number matrix containing the matrix values.
True to compute the unbiased estimate of the population
skewness, false otherwise. Default is true (compute the
unbiased estimator).
The skewness of the given data.
Computes the Skewness vector for the given matrix.
Skewness characterizes the degree of asymmetry of a distribution
around its mean. Positive skewness indicates a distribution with
an asymmetric tail extending towards more positive values. Negative
skewness indicates a distribution with an asymmetric tail extending
towards more negative values.
A number array containing the vector values.
The mean value for the given values, if already known.
True to compute the unbiased estimate of the population
skewness, false otherwise. Default is true (compute the
unbiased estimator).
The skewness of the given data.
Computes the Skewness for the given values.
Skewness characterizes the degree of asymmetry of a distribution
around its mean. Positive skewness indicates a distribution with
an asymmetric tail extending towards more positive values. Negative
skewness indicates a distribution with an asymmetric tail extending
towards more negative values.
A number matrix containing the matrix values.
True to compute the unbiased estimate of the population
skewness, false otherwise. Default is true (compute the
unbiased estimator).
The skewness of the given data.
Computes the Skewness vector for the given matrix.
Skewness characterizes the degree of asymmetry of a distribution
around its mean. Positive skewness indicates a distribution with
an asymmetric tail extending towards more positive values. Negative
skewness indicates a distribution with an asymmetric tail extending
towards more negative values.
A number array containing the vector values.
The column means, if known.
True to compute the unbiased estimate of the population
skewness, false otherwise. Default is true (compute the
unbiased estimator).
The skewness of the given data.
Computes the Kurtosis vector for the given matrix.
The framework uses the same definition used by default in SAS and SPSS.
A number multi-dimensional array containing the matrix values.
True to compute the unbiased estimate of the population
kurtosis, false otherwise. Default is true (compute the
unbiased estimator).
The kurtosis vector of the given data.
Computes the sample Kurtosis vector for the given matrix.
The framework uses the same definition used by default in SAS and SPSS.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
True to compute the unbiased estimate of the population
kurtosis, false otherwise. Default is true (compute the
unbiased estimator).
The sample kurtosis vector of the given data.
Computes the Kurtosis vector for the given matrix.
The framework uses the same definition used by default in SAS and SPSS.
A number multi-dimensional array containing the matrix values.
True to compute the unbiased estimate of the population
kurtosis, false otherwise. Default is true (compute the
unbiased estimator).
The kurtosis vector of the given data.
Computes the Kurtosis vector for the given matrix.
The framework uses the same definition used by default in SAS and SPSS.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
True to compute the unbiased estimate of the population
kurtosis, false otherwise. Default is true (compute the
unbiased estimator).
The kurtosis vector of the given data.
Computes the Standard Error vector for a given matrix.
A number multi-dimensional array containing the matrix values.
Returns the standard error vector for the matrix.
Computes the Standard Error vector for a given matrix.
The number of samples in the matrix.
The values' standard deviation vector, if already known.
Returns the standard error vector for the matrix.
Calculates the covariance matrix of a sample matrix.
In statistics and probability theory, the covariance matrix is a matrix of
covariances between elements of a vector. It is the natural generalization
to higher dimensions of the concept of the variance of a scalar-valued
random variable.
A number multi-dimensional array containing the matrix values.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
In statistics and probability theory, the covariance matrix is a matrix of
covariances between elements of a vector. It is the natural generalization
to higher dimensions of the concept of the variance of a scalar-valued
random variable.
A number multi-dimensional array containing the matrix values.
The dimension of the matrix to consider as observations. Pass 0 if the matrix has
observations as rows and variables as columns, pass 1 otherwise. Default is 0.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
In statistics and probability theory, the covariance matrix is a matrix of
covariances between elements of a vector. It is the natural generalization
to higher dimensions of the concept of the variance of a scalar-valued
random variable.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
A real number to divide each member of the matrix.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
A real number to divide each member of the matrix.
Pass 0 if the mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
In statistics and probability theory, the covariance matrix is a matrix of
covariances between elements of a vector. It is the natural generalization
to higher dimensions of the concept of the variance of a scalar-valued
random variable.
A number multi-dimensional array containing the matrix values.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
In statistics and probability theory, the covariance matrix is a matrix of
covariances between elements of a vector. It is the natural generalization
to higher dimensions of the concept of the variance of a scalar-valued
random variable.
A number multi-dimensional array containing the matrix values.
The dimension of the matrix to consider as observations. Pass 0 if the matrix has
observations as rows and variables as columns, pass 1 otherwise. Default is 0.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
In statistics and probability theory, the covariance matrix is a matrix of
covariances between elements of a vector. It is the natural generalization
to higher dimensions of the concept of the variance of a scalar-valued
random variable.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
A real number to divide each member of the matrix.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
A real number to divide each member of the matrix.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
A real number to divide each member of the matrix.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the weighted pooled covariance matrix from a set of covariance matrices.
Calculates the correlation matrix for a matrix of samples.
In statistics and probability theory, the correlation matrix is the same
as the covariance matrix of the standardized random variables.
A multi-dimensional array containing the matrix values.
The correlation matrix.
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
Pass true to compute the standard deviation using the sample variance.
Pass false to compute it using the population variance. See remarks
for more details.
The number of times each sample should be repeated.
Setting to true will make this method
compute the standard deviation σ using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true will
thus compute σ using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
The number of times each sample should be repeated.
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
The mean vector containing already calculated means for each column of the matrix.
The number of times each sample should be repeated.
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
The mean vector containing already calculated means for each column of the matrix.
Pass true to compute the standard deviation using the sample variance.
Pass false to compute it using the population variance. See remarks
for more details.
The number of times each sample should be repeated.
Setting to true will make this method
compute the standard deviation σ using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true will
thus compute σ using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
Returns a vector containing the standard deviations of the given matrix.
Calculates the matrix Standard Deviations vector.
A matrix whose deviations will be calculated.
Pass true to compute the standard deviation using the sample variance.
Pass false to compute it using the population variance. See remarks
for more details.
The number of times each sample should be repeated.
Setting to true will make this method
compute the standard deviation σ using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true will
thus compute σ using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
Returns a vector containing the standard deviations of the given matrix.
Calculates the covariance matrix of a sample matrix.
A number multi-dimensional array containing the matrix values.
An unit vector containing the importance of each sample
in . The sum of this array elements should add up to 1.
The mean value of the given values, if already known.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
A number multi-dimensional array containing the matrix values.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
An unit vector containing the importance of each sample
in . The sum of this array elements should add up to 1.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
A number multi-dimensional array containing the matrix values.
The number of times each sample should be repeated.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
A number multi-dimensional array containing the matrix values.
An unit vector containing the importance of each sample
in . The sum of this array elements should add up to 1.
The mean value of the given values, if already known.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the covariance matrix of a sample matrix.
A number multi-dimensional array containing the matrix values.
The number of times each sample should be repeated.
The mean value of the given values, if already known.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
A number multi-dimensional array containing the matrix values.
An unit vector containing the importance of each sample
in . The sum of this array elements should add up to 1.
The mean value of the given values, if already known.
A real number to multiply each member of the matrix.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Calculates the scatter matrix of a sample matrix.
By dividing the Scatter matrix by the sample size, we get the population
Covariance matrix. By dividing by the sample size minus one, we get the
sample Covariance matrix.
The number of times each sample should be repeated.
A number multi-dimensional array containing the matrix values.
The mean value of the given values, if already known.
A real number to multiply each member of the matrix.
Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.
The covariance matrix.
Computes the Median of the given values.
An integer array containing the vector members.
A boolean parameter informing if the given values have already been sorted.
The quartile definition that should be used. See for datails.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
The median of the given data.
Computes the Median of the given values.
An integer array containing the vector members.
A boolean parameter informing if the given values have already been sorted.
The quartile definition that should be used. See for datails.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
The median of the given data.
Computes the Quartiles of the given values.
An integer array containing the vector members.
A boolean parameter informing if the given values have already been sorted.
The inter-quartile range for the values.
The quartile definition that should be used. See for datails.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
The second quartile, the median of the given data.
Computes the Quartiles of the given values.
An integer array containing the vector members.
The first quartile.
The third quartile.
A boolean parameter informing if the given values have already been sorted.
The quartile definition that should be used. See for datails.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
The second quartile, the median of the given data.
Computes the lower quartile (Q1) for the given data.
An integer array containing the vector members.
A boolean parameter informing if the given values have already been sorted.
The quartile definition that should be used. See for datails.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
The first quartile of the given data.
Computes the upper quartile (Q3) for the given data.
An integer array containing the vector members.
A boolean parameter informing if the given values have already been sorted.
The quartile definition that should be used. See for datails.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
The third quartile of the given data.
Computes single quantile for the given sequence.
The sequence of observations.
The quantile type, 1...9.
The auantile probability.
A boolean parameter informing if the given values have already been sorted.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
Quantile value.
Computes multiple quantiles for the given sequence.
The sequence of observations.
The sequence of quantile probabilities.
The quantile type, 1...9.
A boolean parameter informing if the given values have already been sorted.
Pass true if the method is allowed to sort in place, overwriting the
its original order.
Quantile value.
Computes the mean of the given values.
A double array containing the vector members.
The mean of the given data.
Computes the mean of the given values.
An integer array containing the vector members.
The mean of the given data.
Computes the Geometric mean of the given values.
A double array containing the vector members.
The geometric mean of the given data.
Computes the log geometric mean of the given values.
A double array containing the vector members.
The log geometric mean of the given data.
Computes the geometric mean of the given values.
A double array containing the vector members.
The geometric mean of the given data.
Computes the log geometric mean of the given values.
A double array containing the vector members.
The log geometric mean of the given data.
Computes the (weighted) grand mean of a set of samples.
A double array containing the sample means.
A integer array containing the sample's sizes.
The grand mean of the samples.
Computes the mean of the given values.
A unsigned short array containing the vector members.
The mean of the given data.
Computes the mean of the given values.
A float array containing the vector members.
The mean of the given data.
Computes the truncated (trimmed) mean of the given values.
A double array containing the vector members.
Whether to perform operations in place, overwriting the original vector.
A boolean parameter informing if the given values have already been sorted.
The percentage of observations to drop from the sample.
The mean of the given data.
Computes the contraharmonic mean of the given values.
A unsigned short array containing the vector members.
The order of the harmonic mean. Default is 1.
The contraharmonic mean of the given data.
Computes the contraharmonic mean of the given values.
A unsigned short array containing the vector members.
The contraharmonic mean of the given data.
Computes the Standard Deviation of the given values.
A double array containing the vector members.
Pass true to compute the standard deviation using the sample variance.
Pass false to compute it using the population variance. See remarks
for more details.
Setting to true will make this method
compute the standard deviation σ using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true will
thus compute σ using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The standard deviation of the given data.
Computes the Standard Deviation of the given values.
A double array containing the vector members.
The standard deviation of the given data.
Computes the Standard Deviation of the given values.
A double array containing the vector members.
The mean of the vector, if already known.
Pass true to compute the standard deviation using the sample variance.
Pass false to compute it using the population variance. See remarks
for more details.
Setting to true will make this method
compute the standard deviation σ using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true will
thus compute σ using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The standard deviation of the given data.
Computes the Standard Deviation of the given values.
A float array containing the vector members.
The mean of the vector, if already known.
The standard deviation of the given data.
Computes the Standard Deviation of the given values.
An integer array containing the vector members.
The mean of the vector, if already known.
The standard deviation of the given data.
Computes the Standard Error for a sample size, which estimates the
standard deviation of the sample mean based on the population mean.
The sample size.
The sample standard deviation.
The standard error for the sample.
Computes the Standard Error for a sample size, which estimates the
standard deviation of the sample mean based on the population mean.
A double array containing the samples.
The standard error for the sample.
Computes the Variance of the given values.
A double precision number array containing the vector members.
The variance of the given data.
Computes the Variance of the given values.
A double precision number array containing the vector members.
Pass true to compute the sample variance; or pass false to compute
the population variance. See remarks for more details.
Setting to true will make this method
compute the variance σ² using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true
will thus compute σ² using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The variance of the given data.
Computes the Variance of the given values.
An integer number array containing the vector members.
The variance of the given data.
Computes the Variance of the given values.
An integer number array containing the vector members.
Pass true to compute the sample variance; or pass false to compute
the population variance. See remarks for more details.
Setting to true will make this method
compute the variance σ² using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true
will thus compute σ² using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The variance of the given data.
Computes the Variance of the given values.
A single precision number array containing the vector members.
The variance of the given data.
Computes the Variance of the given values.
A number array containing the vector members.
The mean of the array, if already known.
The variance of the given data.
Computes the Variance of the given values.
A number array containing the vector members.
The mean of the array, if already known.
Pass true to compute the sample variance; or pass false to compute
the population variance. See remarks for more details.
Setting to true will make this method
compute the variance σ² using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true
will thus compute σ² using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The variance of the given data.
Computes the Variance of the given values.
A number array containing the vector members.
The mean of the array, if already known.
Pass true to compute the sample variance; or pass false to compute
the population variance. See remarks for more details.
Setting to true will make this method
compute the variance σ² using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true
will thus compute σ² using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The variance of the given data.
Computes the Variance of the given values.
A number array containing the vector members.
The mean of the array, if already known.
The variance of the given data.
Computes the pooled standard deviation of the given values.
The grouped samples.
True to compute a pooled standard deviation using unbiased estimates
of the population variance; false otherwise. Default is true.
Computes the pooled standard deviation of the given values.
The grouped samples.
Computes the pooled standard deviation of the given values.
The number of samples used to compute the .
The unbiased variances for the samples.
True to compute a pooled standard deviation using unbiased estimates
of the population variance; false otherwise. Default is true.
Computes the pooled variance of the given values.
The grouped samples.
Computes the pooled variance of the given values.
True to obtain an unbiased estimate of the population
variance; false otherwise. Default is true.
The grouped samples.
Computes the pooled variance of the given values.
The number of samples used to compute the .
The unbiased variances for the samples.
True to obtain an unbiased estimate of the population
variance; false otherwise. Default is true.
Computes the Mode of the given values.
A number array containing the vector values.
The most common value in the given data.
Computes the Mode of the given values.
A number array containing the vector values.
Returns how many times the detected mode happens in the values.
The most common value in the given data.
Computes the Mode of the given values.
A number array containing the vector values.
True to perform the operation in place, altering the original input vector.
Pass true if the list of values is already sorted.
The most common value in the given data.
Computes the Mode of the given values.
A number array containing the vector values.
True to perform the operation in place, altering the original input vector.
Pass true if the list of values is already sorted.
Returns how many times the detected mode happens in the values.
The most common value in the given data.
Computes the Covariance between two arrays of values.
A number array containing the first vector elements.
A number array containing the second vector elements.
Pass true to compute the sample variance; or pass false to compute
the population variance. See remarks for more details.
Setting to true will make this method
compute the variance σ² using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true
will thus compute σ² using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The variance of the given data.
Computes the Covariance between two arrays of values.
A number array containing the first vector elements.
A number array containing the second vector elements.
The mean value of , if known.
The mean value of , if known.
Pass true to compute the sample variance; or pass false to compute
the population variance. See remarks for more details.
Setting to true will make this method
compute the variance σ² using the sample variance, which is an unbiased
estimator of the true population variance. Setting this parameter to true
will thus compute σ² using the following formula:
N
σ² = 1 / (N - 1) ∑ (x_i − μ)²
i=1
Setting to false will assume the given values
already represent the whole population, and will compute the population variance
using the formula:
N
σ² = (1 / N) ∑ (x_i − μ)²
i=1
The variance of the given data.
Computes the Skewness for the given values.
Skewness characterizes the degree of asymmetry of a distribution
around its mean. Positive skewness indicates a distribution with
an asymmetric tail extending towards more positive values. Negative
skewness indicates a distribution with an asymmetric tail extending
towards more negative values.
A number array containing the vector values.
True to compute the unbiased estimate of the population
skewness, false otherwise. Default is true (compute the
unbiased estimator).
The skewness of the given data.
Computes the Skewness for the given values.
Skewness characterizes the degree of asymmetry of a distribution
around its mean. Positive skewness indicates a distribution with
an asymmetric tail extending towards more positive values. Negative
skewness indicates a distribution with an asymmetric tail extending
towards more negative values.
A number array containing the vector values.
The values' mean, if already known.
True to compute the unbiased estimate of the population
skewness, false otherwise. Default is true (compute the
unbiased estimator).
The skewness of the given data.
Computes the Kurtosis for the given values.
The framework uses the same definition used by default in SAS and SPSS.
A number array containing the vector values.
True to compute the unbiased estimate of the population
kurtosis, false otherwise. Default is true (compute the
unbiased estimator).
The kurtosis of the given data.
Computes the Kurtosis for the given values.
The framework uses the same definition used by default in SAS and SPSS.
A number array containing the vector values.
The values' mean, if already known.
True to compute the unbiased estimate of the population
kurtosis, false otherwise. Default is true (compute the
unbiased estimator).
The kurtosis of the given data.
Computes the entropy function for a set of numerical values in a
given Probability Density Function (pdf).
A number array containing the vector values.
A probability distribution function.
The importance for each sample.
The distribution's entropy for the given values.
Computes the entropy function for a set of numerical values in a
given Probability Density Function (pdf).
A number array containing the vector values.
A probability distribution function.
The distribution's entropy for the given values.
Computes the entropy function between an expected value
and a predicted value between 0 and 1.
Computes the entropy function between an expected value
and a predicted value.
Computes the entropy function for a set of numerical values in a
given Probability Density Function (pdf).
A number array containing the vector values.
A probability distribution function.
The importance for each sample.
The distribution's entropy for the given values.
Computes the entropy function for a set of numerical values in a
given Probability Density Function (pdf).
A number array containing the vector values.
A probability distribution function.
The repetition counts for each sample.
The distribution's entropy for the given values.
Computes the entropy for the given values.
A number array containing the vector values.
The calculated entropy for the given values.
Computes the entropy for the given values.
A number array containing the vector values.
A small constant to avoid s in
case the there is a zero between the given .
The calculated entropy for the given values.
Computes the entropy for the given values.
A number matrix containing the matrix values.
A small constant to avoid s in
case the there is a zero between the given .
The calculated entropy for the given values.
Computes the entropy for the given values.
A number matrix containing the matrix values.
The calculated entropy for the given values.
Computes the entropy for the given values.
An array of integer symbols.
The starting symbol.
The ending symbol.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The starting symbol.
The ending symbol.
The importance for each sample.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The starting symbol.
The ending symbol.
The importance for each sample.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The starting symbol.
The ending symbol.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The starting symbol.
The ending symbol.
The importance for each sample.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The range of symbols.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The number of distinct classes.
The importance for each sample.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The number of distinct classes.
The importance for each sample.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The number of distinct classes.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The number of distinct classes.
The evaluated entropy.
Computes the entropy for the given values.
An array of integer symbols.
The number of distinct classes.
The importance for each sample.
The evaluated entropy.
Calculates the exponentially weighted mean.
A vector of observations whose EW mean will be calculated. It is assumed that
the vector is ordered with the most recent observations at the end of
the vector (and the oldest observations at the start).
The weighting to be applied to the calculation. A higher alpha discounts
older observations faster. Alpha must be between 0 and 1 (inclusive).
Returns a giving the exponentially weighted average of the
vector.
The following example shows how to compute the EW mean.
-
Wikipedia contributors. Quantile. Wikipedia, The Free Encyclopedia. July 25, 2017, 21:56 UTC.
Available at: https://en.wikipedia.org/wiki/Quantile.
The default quantile method in the framework (6).
The default method in R (7).
The dafault method in Maple (8).
Inverse of empirical distribution function.
Equivalent types in other packages: R: 1, SAS: 3, Maple: 1.
The same as R-1, but with averaging at discontinuities.
Equivalent types in other packages: R: 2, SAS: 5, Maple: 2.
The observation numbered closest to Np.
Equivalent types in other packages: R: 3, SAS: 2.
Linear interpolation of the empirical distribution function.
Equivalent types in other packages: R: 4, SAS: 1, SciPy: (0,1), Maple: 3.
Piecewise linear function where the knots are the values midway through the steps of the empirical distribution function. R-5, SciPy-(.5,.5), Maple-4.
Linear interpolation of the expectations for the order statistics for the uniform distribution on [0,1].
That is, it is the linear interpolation between points (ph, xh), where ph = h / (N + 1) is the probability
that the last of (N+1) randomly drawn values will not exceed the h-th smallest of the first N randomly drawn
values. Equivalence to other packages: R-6, Excel, SAS-4, SciPy-(0,0), Maple-5.
Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1].
Equivalence to other packages: R: 7, Excel, SciPy: (1,1), Maple: 6.
Linear interpolation of the approximate medians for order statistics. Equivalence to other packages:
R: 8, SciPy: (1/3,1/3), Maple: 7.
The resulting quantile estimates are approximately unbiased for the expected order statistics if x is normally
distributed. Equivalence to other packages: R: 9, SciPy: (3/8,3/8), Maple: 8.
Histogram for continuous random values.
The class wraps histogram for continuous stochastic function, which is represented
by integer array and range of the function. Values of the integer array are treated
as total amount of hits on the corresponding subranges, which are calculated by splitting the
specified range into required amount of consequent ranges.
For example, if the integer array is equal to { 1, 2, 4, 8, 16 } and the range is set
to [0, 1], then the histogram consists of next subranges:
- [0.0, 0.2] - 1 hit;
- [0.2, 0.4] - 2 hits;
- [0.4, 0.6] - 4 hits;
- [0.6, 0.8] - 8 hits;
- [0.8, 1.0] - 16 hits.
Sample usage:
// create histogram
ContinuousHistogram histogram = new ContinuousHistogram(
new int[] { 0, 0, 8, 4, 2, 4, 7, 1, 0 }, new Range( 0.0f, 1.0f ) );
// get mean and standard deviation values
Console.WriteLine( "mean = " + histogram.Mean + ", std.dev = " + histogram.StdDev );
Values of the histogram.
Range of random values.
Mean value.
The property allows to retrieve mean value of the histogram.
Sample usage:
// create histogram
ContinuousHistogram histogram = new ContinuousHistogram(
new int[] { 0, 0, 8, 4, 2, 4, 7, 1, 0 }, new Range( 0.0f, 1.0f ) );
// get mean value (= 0.505 )
Console.WriteLine( "mean = " + histogram.Mean.ToString( "F3" ) );
Standard deviation.
The property allows to retrieve standard deviation value of the histogram.
Sample usage:
// create histogram
ContinuousHistogram histogram = new ContinuousHistogram(
new int[] { 0, 0, 8, 4, 2, 4, 7, 1, 0 }, new Range( 0.0f, 1.0f ) );
// get std.dev. value (= 0.215)
Console.WriteLine( "std.dev. = " + histogram.StdDev.ToString( "F3" ) );
Median value.
The property allows to retrieve median value of the histogram.
Sample usage:
// create histogram
ContinuousHistogram histogram = new ContinuousHistogram(
new int[] { 0, 0, 8, 4, 2, 4, 7, 1, 0 }, new Range( 0.0f, 1.0f ) );
// get median value (= 0.500)
Console.WriteLine( "median = " + histogram.Median.ToString( "F3" ) );
Minimum value.
The property allows to retrieve minimum value of the histogram with non zero
hits count.
Sample usage:
// create histogram
ContinuousHistogram histogram = new ContinuousHistogram(
new int[] { 0, 0, 8, 4, 2, 4, 7, 1, 0 }, new Range( 0.0f, 1.0f ) );
// get min value (= 0.250)
Console.WriteLine( "min = " + histogram.Min.ToString( "F3" ) );
Maximum value.
The property allows to retrieve maximum value of the histogram with non zero
hits count.
Sample usage:
// create histogram
ContinuousHistogram histogram = new ContinuousHistogram(
new int[] { 0, 0, 8, 4, 2, 4, 7, 1, 0 }, new Range( 0.0f, 1.0f ) );
// get max value (= 0.875)
Console.WriteLine( "max = " + histogram.Max.ToString( "F3" ) );
Initializes a new instance of the class.
Values of the histogram.
Range of random values.
Values of the integer array are treated as total amount of hits on the
corresponding subranges, which are calculated by splitting the specified range into
required amount of consequent ranges (see class
description for more information).
Get range around median containing specified percentage of values.
Values percentage around median.
Returns the range which containes specifies percentage of values.
The method calculates range of stochastic variable, which summary probability
comprises the specified percentage of histogram's hits.
Sample usage:
// create histogram
ContinuousHistogram histogram = new ContinuousHistogram(
new int[] { 0, 0, 8, 4, 2, 4, 7, 1, 0 }, new Range( 0.0f, 1.0f ) );
// get 50% range
Range range = histogram.GetRange( 0.5f );
// show the range ([0.25, 0.75])
Console.WriteLine( "50% range = [" + range.Min + ", " + range.Max + "]" );
Update statistical value of the histogram.
The method recalculates statistical values of the histogram, like mean,
standard deviation, etc. The method should be called only in the case if histogram
values were retrieved through property and updated after that.
Original Fourier transform from AForge.NET. If possible,
please use instead.
The class implements one dimensional and two dimensional Discrete and Fast Fourier
Transformation. However, this class works only with square matrices with sizes that
are power of 2, and implements a different form of the transform that differs from
the implementations in other packages such as Octave and Matlab. For a more general
transform that should produce the same results as Octave, see .
This class may be deprecated (marked as obsolete) in the future.
Fourier transformation direction.
Forward direction of Fourier transformation.
Backward direction of Fourier transformation.
One dimensional Discrete Fourier Transform.
Data to transform.
Transformation direction.
Two dimensional Discrete Fourier Transform.
Data to transform.
Transformation direction.
One dimensional Fast Fourier Transform.
Data to transform.
Transformation direction.
The method accepts array of 2n size
only, where n may vary in the [1, 14] range.
Incorrect data length.
Two dimensional Fast Fourier Transform.
Data to transform.
Transformation direction.
The method accepts array of 2n size
only in each dimension, where n may vary in the [1, 14] range. For example, 16x16 array
is valid, but 15x15 is not.
Incorrect data length.
Shape optimizer, which merges points within close distance to each other.
This shape optimizing algorithm checks all points of a shape
and merges any two points which are within specified distance
to each other. Two close points are replaced by a single point, which has
mean coordinates of the removed points.
Because of the fact that the algorithm performs points merging
while it goes through a shape, it may merge several points (more than 2) into a
single point, where distance between extreme points may be bigger
than the specified limit. For example, suppose
a case with 3 points, where 1st and 2nd points are close enough to be merged, but the
3rd point is a little bit further. During merging of 1st and 2nd points, it may
happen that the new point with mean coordinates will get closer to the 3rd point,
so they will be merged also on next iteration of the algorithm.
For example, the below circle shape comprised of 65 points, can be optimized to 8 points
by setting to 28.
Maximum allowed distance between points, which are merged during optimization, [0, ∞).
The property sets maximum allowed distance between two points of
a shape, which are replaced by single point with mean coordinates.
Default value is set to 10.
Initializes a new instance of the class.
Initializes a new instance of the class.
Maximum allowed distance between points, which are
merged during optimization (see ).
Optimize specified shape.
Shape to be optimized.
Returns final optimized shape, which may have reduced amount of points.
3D pose estimation algorithm (coplanar case).
The class implements an algorithm for 3D object's pose estimation from it's
2D coordinates obtained by perspective projection, when the object is described coplanar points.
The idea of the implemented math and algorithm is described in "Iterative Pose Estimation using
Coplanar Feature Points" paper written by Oberkampf, Daniel DeMenthon and Larry Davis
(the implementation of the algorithm is very close translation of the pseudo code given by the
paper, so should be easy to follow).
At this point the implementation works only with models described by 4 points, which is
the minimum number of points enough for 3D pose estimation.
The 4 model's point are supposed to be coplanar, i.e. supposed to reside all within
same planer. See for none coplanar case.
Read 3D Pose Estimation article for
additional information and samples.
Sample usage:
// points of real object - model
Vector3[] copositObject = new Vector3[4]
{
new Vector3( -56.5f, 0, 56.5f ),
new Vector3( 56.5f, 0, 56.5f ),
new Vector3( 56.5f, 0, -56.5f ),
new Vector3( -56.5f, 0, -56.5f ),
};
// focal length of camera used to capture the object
float focalLength = 640; // depends on your camera or projection system
// initialize CoPOSIT object
CoplanarPosit coposit = new CoplanarPosit( copositObject, focalLength );
// 2D points of te object - projection
Accord.Point[] projectedPoints = new Accord.Point[4]
{
new Accord.Point( -77, 48 ),
new Accord.Point( 44, 66 ),
new Accord.Point( 75, -36 ),
new Accord.Point( -61, -58 ),
};
// estimate pose
Matrix3x3 rotationMatrix;
Vector3 translationVector;
coposit.EstimatePose( projectedPoints,
out rotationMatrix, out translationVector );
Best estimated pose recently found.
The property keeps best estimated pose found by the latest call to .
The same estimated pose is provided by that method also and can be accessed through this property
for convenience.
See also and .
Best estimated translation recently found.
The property keeps best estimated translation found by the latest call to .
The same estimated translation is provided by that method also and can be accessed through this property
for convenience.
See also and .
Error of the best pose estimation.
The property keeps error of the best pose estimation, which is calculated as average
error between real angles of the specified quadrilateral and angles of the quadrilateral which
is a projection of the best pose estimation. The error is measured degrees in (angle).
Alternate estimated pose recently found.
The property keeps alternate estimated pose found by the latest call to .
See also and .
Alternated estimated translation recently found.
The property keeps alternate estimated translation found by the latest call to .
See also and .
Error of the alternate pose estimation.
The property keeps error of the alternate pose estimation, which is calculated as average
error between real angles of the specified quadrilateral and angles of the quadrilateral which
is a projection of the alternate pose estimation. The error is measured in degrees (angle).
Coordinates of the model points which pose should be estimated.
Effective focal length of the camera used to capture the model.
Initializes a new instance of the class.
Array of vectors containing coordinates of four real model's point.
Effective focal length of the camera used to capture the model.
The model must have 4 points.
Estimate pose of a model from it's projected 2D coordinates.
4 2D points of the model's projection.
Gets best estimation of object's rotation.
Gets best estimation of object's translation.
4 points must be be given for pose estimation.
Because of the Coplanar POSIT algorithm's nature, it provides two pose estimations,
which are valid from the algorithm's math point of view. For each pose an error is calculated,
which specifies how good estimation fits to the specified real 2D coordinated. The method
provides the best estimation through its output parameters and
. This may be enough for many of the pose estimation application.
For those, who require checking the alternate pose estimation, it can be obtained using
and properties.
The calculated error is provided for both estimations through and
properties.
Shape optimizer, which removes obtuse angles (close to flat) from a shape.
This shape optimizing algorithm checks all adjacent edges of a shape
and substitutes any 2 edges with a single edge if angle between them is greater than
. The algorithm makes sure there are not obtuse angles in
a shape, which are very close to flat line.
The shape optimizer does not optimize shapes to less than 3 points, so optimized
shape always will have at least 3 points.
For example, the below circle shape comprised of 65 points, can be optimized to 10 points
by setting to 160.
Maximum angle between adjacent edges to keep in a shape, [140, 180].
The property sets maximum angle between adjacent edges, which is kept
during optimization. All edges, which have a greater angle between them, are substituted
by a single edge.
Default value is set to 160.
Initializes a new instance of the class.
Initializes a new instance of the class.
Maximum acceptable angle between two edges of a shape (see ).
Optimize specified shape.
Shape to be optimized.
Returns final optimized shape, which may have reduced amount of points.
Collection of some gemetry tool methods.
Calculate angle between to vectors measured in [0, 180] degrees range.
Starting point of both vectors.
Ending point of the first vector.
Ending point of the second vector.
Returns angle between specified vectors measured in degrees.
Calculate minimum angle between two lines measured in [0, 90] degrees range.
A point on the first line.
Another point on the first line.
A point on the second line.
Another point on the second line.
Returns minimum angle between two lines.
It is preferred to use if it is required to calculate angle
multiple times for one of the lines.
and are the same,
-OR- and are the same.
Graham scan algorithm for finding convex hull.
The class implements
Graham scan algorithm for finding convex hull
of a given set of points.
Sample usage:
// generate some random points
Random rand = new Random( );
List<IntPoint> points = new List<IntPoint>( );
for ( int i = 0; i < 10; i++ )
{
points.Add( new IntPoint(
rand.Next( 200 ) - 100,
rand.Next( 200 ) - 100 ) );
}
// find the convex hull
IConvexHullAlgorithm hullFinder = new GrahamConvexHull( );
List<IntPoint> hull = hullFinder.FindHull( points );
Find convex hull for the given set of points.
Set of points to search convex hull for.
Returns set of points, which form a convex hull for the given .
The first point in the list is the point with lowest X coordinate (and with lowest Y if there are
several points with the same X value). Points are provided in counter clockwise order
(Cartesian
coordinate system).
Interface defining methods for algorithms, which search for convex hull of the specified points' set.
The interface defines a method, which should be implemented by different classes
performing convex hull search for specified set of points.
All algorithms, implementing this interface, should follow two rules for the found convex hull:
- the first point in the returned list is the point with lowest X coordinate (and with lowest Y if
there are several points with the same X value);
- points in the returned list are given in counter clockwise order
(Cartesian
coordinate system).
Find convex hull for the given set of points.
Set of points to search convex hull for.
Returns set of points, which form a convex hull for the given .
Interface for shape optimizing algorithms.
The interface defines set of methods, which should be implemented
by shape optimizing algorithms. These algorithms take input shape, which is defined
by a set of points (corners of convex hull, etc.), and remove some insignificant points from it,
which has little influence on the final shape's look.
The shape optimizing algorithms can be useful in conjunction with such algorithms
like convex hull searching, which usually may provide many hull points, where some
of them are insignificant and could be removed.
For additional details about shape optimizing algorithms, documentation of
particular algorithm should be studied.
Optimize specified shape.
Shape to be optimized.
Returns final optimized shape, which may have reduced amount of points.
The class encapsulates 2D line and provides some tool methods related to lines.
The class provides some methods which are related to lines:
angle between lines, distance to point, finding intersection point, etc.
Generally, the equation of the line is y = * x +
. However, when is an Infinity,
would normally be meaningless, and it would be
impossible to distinguish the line x = 5 from the line x = -5. Therefore,
if is or
, the line's equation is instead
x = .
Sample usage:
// create a line
Line line = Line.FromPoints( new Point( 0, 0 ), new Point( 3, 4 ) );
// check if it is vertical or horizontal
if ( line.IsVertical || line.IsHorizontal )
{
// ...
}
// get intersection point with another line
Point intersection = line.GetIntersectionWith(
Line.FromPoints( new Point( 3, 0 ), new Point( 0, 4 ) ) );
Checks if the line vertical or not.
Checks if the line horizontal or not.
Gets the slope of the line.
If not , gets the Line's Y-intercept.
If gets the line's X-intercept.
Creates a that goes through the two specified points.
One point on the line.
Another point on the line.
Returns a representing the line between
and .
Thrown if the two points are the same.
Creates a with the specified slope and intercept.
The slope of the line
The Y-intercept of the line, unless the slope is an
infinity, in which case the line's equation is "x = intercept" instead.
Returns a representing the specified line.
The construction here follows the same rules as for the rest of this class.
Most lines are expressed as y = slope * x + intercept. Vertical lines, however, are
x = intercept. This is indicated by being true or by
returning or
.
Constructs a from a radius and an angle (in degrees).
The minimum distance from the line to the origin.
The angle of the vector from the origin to the line.
Returns a representing the specified line.
is the minimum distance from the origin
to the line, and is the counterclockwise rotation from
the positive X axis to the vector through the origin and normal to the line.
This means that if is in [0,180), the point on the line
closest to the origin is on the positive X or Y axes, or in quadrants I or II. Likewise,
if is in [180,360), the point on the line closest to the
origin is on the negative X or Y axes, or in quadrants III or IV.
Thrown if radius is negative.
Constructs a from a point and an angle (in degrees).
The minimum distance from the line to the origin.
The angle of the normal vector from the origin to the line.
is the counterclockwise rotation from
the positive X axis to the vector through the origin and normal to the line.
This means that if is in [0,180), the point on the line
closest to the origin is on the positive X or Y axes, or in quadrants I or II. Likewise,
if is in [180,360), the point on the line closest to the
origin is on the negative X or Y axes, or in quadrants III or IV.
Returns a representing the specified line.
Calculate minimum angle between this line and the specified line measured in [0, 90] degrees range.
The line to find angle between.
Returns minimum angle between lines.
Finds intersection point with the specified line.
Line to find intersection with.
Returns intersection point with the specified line, or
if the lines are parallel and distinct.
Thrown if the specified line is the same line as this line.
Finds, provided it exists, the intersection point with the specified .
to find intersection with.
Returns intersection point with the specified , or ,
if this line does not intersect with the segment.
If the line and segment do not intersect, the method returns .
If the line and segment share multiple points, the method throws an .
Thrown if is a portion
of this line.
Calculate Euclidean distance between a point and a line.
The point to calculate distance to.
Returns the Euclidean distance between this line and the specified point. Unlike
, this returns the distance from the infinite line. (0,0) is 0 units
from the line defined by (0,5) and (0,8), but is 5 units from the segment with those endpoints.
Equality operator - checks if two lines have equal parameters.
First line to check.
Second line to check.
Returns if parameters of specified
lines are equal.
Inequality operator - checks if two lines have different parameters.
First line to check.
Second line to check.
Returns if parameters of specified
lines are not equal.
Check if this instance of equals to the specified one.
Another line to check equalty to.
Return if objects are equal.
Get hash code for this instance.
Returns the hash code for this instance.
Get string representation of the class.
Returns string, which contains values of the like in readable form.
The class encapsulates 2D line segment and provides some tool methods related to lines.
The class provides some methods which are related to line segments:
distance to point, finding intersection point, etc.
A line segment may be converted to a .
Sample usage:
// create a segment
LineSegment segment = new LineSegment( new Point( 0, 0 ), new Point( 3, 4 ) );
// get segment's length
float length = segment.Length;
// get intersection point with a line
Point? intersection = segment.GetIntersectionWith(
new Line( new Point( -3, 8 ), new Point( 0, 4 ) ) );
Start point of the line segment.
End point of the line segment.
Get segment's length - Euclidean distance between its and points.
Initializes a new instance of the class.
Segment's start point.
Segment's end point.
Thrown if the two points are the same.
Converts this to a by discarding
its endpoints and extending it infinitely in both directions.
The segment to convert to a .
Returns a that contains this .
Calculate Euclidean distance between a point and a finite line segment.
The point to calculate the distance to.
Returns the Euclidean distance between this line segment and the specified point. Unlike
, this returns the distance from the finite segment. (0,0) is 5 units
from the segment (0,5)-(0,8), but is 0 units from the line through those points.
Finds, provided it exists, the intersection point with the specified .
to find intersection with.
Returns intersection point with the specified , or , if
the two segments do not intersect.
If the two segments do not intersect, the method returns . If the two
segments share multiple points, this throws an .
Thrown if the segments overlap - if they have
multiple points in common.
Finds, provided it exists, the intersection point with the specified .
to find intersection with.
Returns intersection point with the specified , or , if
the line does not intersect with this segment.
If the line and the segment do not intersect, the method returns . If the line
and the segment share multiple points, the method throws an .
Thrown if this segment is a portion of
line.
Equality operator - checks if two line segments have equal parameters.
First line segment to check.
Second line segment to check.
Returns if parameters of specified
line segments are equal.
Inequality operator - checks if two lines have different parameters.
First line segment to check.
Second line segment to check.
Returns if parameters of specified
line segments are not equal.
Check if this instance of equals to the specified one.
Another line segment to check equalty to.
Return if objects are equal.
Get hash code for this instance.
Returns the hash code for this instance.
Get string representation of the class.
Returns string, which contains values of the like in readable form.
Shape optimizer, which removes points within close range to shapes' body.
This shape optimizing algorithm checks all points of the shape and
removes those of them, which are in a certain distance to a line connecting previous and
the next points. In other words, it goes through all adjacent edges of a shape and checks
what is the distance between the corner formed by these two edges and a possible edge, which
could be used as substitution of these edges. If the distance is equal or smaller than
the specified value, then the point is removed,
so the two edges are substituted by a single one. When optimization process is done,
the new shape has reduced amount of points and none of the removed points are further away
from the new shape than the specified limit.
The shape optimizer does not optimize shapes to less than 3 points, so optimized
shape always will have at least 3 points.
For example, the below circle shape comprised of 65 points, can be optimized to 8 points
by setting to 10.
Maximum allowed distance between removed points and optimized shape, [0, ∞).
The property sets maximum allowed distance between points removed from original
shape and optimized shape - none of the removed points are further away
from the new shape than the specified limit.
Default value is set to 5.
Initializes a new instance of the class.
Initializes a new instance of the class.
Maximum allowed distance between removed points
and optimized shape (see ).
Optimize specified shape.
Shape to be optimized.
Returns final optimized shape, which may have reduced amount of points.
Set of tools for processing collection of points in 2D space.
The static class contains set of routines, which provide different
operations with collection of points in 2D space. For example, finding the
furthest point from a specified point or line.
Sample usage:
// create points' list
List<IntPoint> points = new List<IntPoint>( );
points.Add( new IntPoint( 10, 10 ) );
points.Add( new IntPoint( 20, 15 ) );
points.Add( new IntPoint( 15, 30 ) );
points.Add( new IntPoint( 40, 12 ) );
points.Add( new IntPoint( 30, 20 ) );
// get furthest point from the specified point
IntPoint p1 = PointsCloud.GetFurthestPoint( points, new IntPoint( 15, 15 ) );
Console.WriteLine( p1.X + ", " + p1.Y );
// get furthest point from line
IntPoint p2 = PointsCloud.GetFurthestPointFromLine( points,
new IntPoint( 50, 0 ), new IntPoint( 0, 50 ) );
Console.WriteLine( p2.X + ", " + p2.Y );
Shift cloud by adding specified value to all points in the collection.
Collection of points to shift their coordinates.
Point to shift by.
Get bounding rectangle of the specified list of points.
Collection of points to get bounding rectangle for.
Point comprised of smallest X and Y coordinates.
Point comprised of biggest X and Y coordinates.
Get center of gravity for the specified list of points.
List of points to calculate center of gravity for.
Returns center of gravity (mean X-Y values) for the specified list of points.
Find furthest point from the specified point.
Collection of points to search furthest point in.
The point to search furthest point from.
Returns a point, which is the furthest away from the .
Find two furthest points from the specified line.
Collection of points to search furthest points in.
First point forming the line.
Second point forming the line.
First found furthest point.
Second found furthest point (which is on the
opposite side from the line compared to the );
The method finds two furthest points from the specified line,
where one point is on one side from the line and the second point is on
another side from the line.
Find two furthest points from the specified line.
Collection of points to search furthest points in.
First point forming the line.
Second point forming the line.
First found furthest point.
Distance between the first found point and the given line.
Second found furthest point (which is on the
opposite side from the line compared to the );
Distance between the second found point and the given line.
The method finds two furthest points from the specified line,
where one point is on one side from the line and the second point is on
another side from the line.
Find the furthest point from the specified line.
Collection of points to search furthest point in.
First point forming the line.
Second point forming the line.
Returns a point, which is the furthest away from the
specified line.
The method finds the furthest point from the specified line.
Unlike the
method, this method find only one point, which is the furthest away from the line
regardless of side from the line.
Find the furthest point from the specified line.
Collection of points to search furthest points in.
First point forming the line.
Second point forming the line.
Distance between the furthest found point and the given line.
Returns a point, which is the furthest away from the
specified line.
The method finds the furthest point from the specified line.
Unlike the
method, this method find only one point, which is the furthest away from the line
regardless of side from the line.
Relative distortion limit allowed for quadrilaterals, [0.0, 0.25].
The value of this property is used to calculate distortion limit used by
, when processing potential corners and making decision
if the provided points form a quadrilateral or a triangle. The distortion limit is
calculated as:
distrtionLimit = RelativeDistortionLimit * ( W * H ) / 2,
where W and H are width and height of the "points cloud" passed to the
.
To explain the idea behind distortion limit, let’s suppose that quadrilateral finder routine found
the next candidates for corners:
As we can see on the above picture, the shape there potentially can be a triangle, but not quadrilateral
(suppose that points list comes from a hand drawn picture or acquired from camera, so some
inaccuracy may exist). It may happen that the D point is just a distortion (noise, etc).
So the check what is the distance between a potential corner
(D in this case) and a line connecting two adjacent points (AB in this case). If the distance is smaller
then the distortion limit, then the point may be rejected, so the shape turns into triangle.
An exception is the case when both C and D points are very close to the AB line,
so both their distances are less than distortion limit. In this case both points will be accepted as corners -
the shape is just a flat quadrilateral.
Default value is set to 0.1.
Find corners of quadrilateral or triangular area, which contains the specified collection of points.
Collection of points to search quadrilateral for.
Returns a list of 3 or 4 points, which are corners of the quadrilateral or
triangular area filled by specified collection of point. The first point in the list
is the point with lowest X coordinate (and with lowest Y if there are several points
with the same X value). The corners are provided in counter clockwise order
(Cartesian
coordinate system).
The method makes an assumption that the specified collection of points
form some sort of quadrilateral/triangular area. With this assumption it tries to find corners
of the area.
The method does not search for bounding quadrilateral/triangular area,
where all specified points are inside of the found quadrilateral/triangle. Some of the
specified points potentially may be outside of the found quadrilateral/triangle, since the
method takes corners only from the specified collection of points, but does not calculate such
to form true bounding quadrilateral/triangle.
See property for additional information.
3D pose estimation algorithm.
The class implements an algorithm for 3D object's pose estimation from it's
2D coordinates obtained by perspective projection, when the object is described none coplanar points.
The idea of the implemented math and algorithm is described in "Model-Based Object Pose in 25
Lines of Code" paper written by Daniel F. DeMenthon and Larry S. Davis (the implementation of
the algorithm is almost 1 to 1 translation of the pseudo code given by the paper, so should
be easy to follow).
At this point the implementation works only with models described by 4 points, which is
the minimum number of points enough for 3D pose estimation.
The 4 model's point must not be coplanar, i.e. must not reside all within
same planer. See for coplanar case.
Read 3D Pose Estimation article for
additional information and samples.
Sample usage:
// points of real object - model
Vector3[] positObject = new Vector3[4]
{
new Vector3( 28, 28, -28 ),
new Vector3( -28, 28, -28 ),
new Vector3( 28, -28, -28 ),
new Vector3( 28, 28, 28 ),
};
// focal length of camera used to capture the object
float focalLength = 640; // depends on your camera or projection system
// initialize POSIT object
Posit posit = new Posit( positObject, focalLength );
// 2D points of te object - projection
Accord.Point[] projectedPoints = new Accord.Point[4]
{
new Accord.Point( -4, 29 ),
new Accord.Point( -180, 86 ),
new Accord.Point( -5, -102 ),
new Accord.Point( 76, 137 ),
};
// estimate pose
Matrix3x3 rotationMatrix;
Vector3 translationVector;
posit.EstimatePose( projectedPoints,
out rotationMatrix, out translationVector );
Coordinates of the model points which pose should be estimated.
Effective focal length of the camera used to capture the model.
Initializes a new instance of the class.
Array of vectors containing coordinates of four real model's point (points
must not be on the same plane).
Effective focal length of the camera used to capture the model.
The model must have 4 points.
Estimate pose of a model from it's projected 2D coordinates.
4 2D points of the model's projection.
Gets object's rotation.
Gets object's translation.
4 points must be be given for pose estimation.
Enumeration of some basic shape types.
Unknown shape type.
Circle shape.
Triangle shape.
Quadrilateral shape.
Some common sub types of some basic shapes.
Unrecognized sub type of a shape (generic shape which does not have
any specific sub type).
Quadrilateral with one pair of parallel sides.
Quadrilateral with two pairs of parallel sides.
Parallelogram with perpendicular adjacent sides.
Parallelogram with all sides equal.
Rectangle with all sides equal.
Triangle with all sides/angles equal.
Triangle with two sides/angles equal.
Triangle with a 90 degrees angle.
Triangle with a 90 degrees angle and other two angles are equal.
A class for checking simple geometrical shapes.
The class performs checking/detection of some simple geometrical
shapes for provided set of points (shape's edge points). During the check
the class goes through the list of all provided points and checks how accurately
they fit into assumed shape.
All the shape checks allow some deviation of
points from the shape with assumed parameters. In other words it is allowed
that specified set of points may form a little bit distorted shape, which may be
still recognized. The allowed amount of distortion is controlled by two
properties ( and ),
which allow higher distortion level for bigger shapes and smaller amount of
distortion for smaller shapes. Checking specified set of points, the class
calculates mean distance between specified set of points and edge of the assumed
shape. If the mean distance is equal to or less than maximum allowed distance,
then a shape is recognized. The maximum allowed distance is calculated as:
maxDistance = max( minAcceptableDistortion, relativeDistortionLimit * ( width + height ) / 2 )
, where width and height is the size of bounding rectangle for the
specified points.
See also and properties,
which set acceptable errors for polygon sub type checking done by
method.
See the next article for details about the implemented algorithms:
Detecting some simple shapes in images.
Sample usage:
private List<IntPoint> idealCicle = new List<IntPoint>( );
private List<IntPoint> distorredCircle = new List<IntPoint>( );
System.Random rand = new System.Random( );
// generate sample circles
float radius = 100;
for ( int i = 0; i < 360; i += 10 )
{
float angle = (float) ( (float) i / 180 * System.Math.PI );
// add point to ideal circle
idealCicle.Add( new IntPoint(
(int) ( radius * System.Math.Cos( angle ) ),
(int) ( radius * System.Math.Sin( angle ) ) ) );
// add a bit distortion for distorred cirlce
float distorredRadius = radius + rand.Next( 7 ) - 3;
distorredCircle.Add( new IntPoint(
(int) ( distorredRadius * System.Math.Cos( angle ) ),
(int) ( distorredRadius * System.Math.Sin( angle ) ) ) );
}
// check shape
SimpleShapeChecker shapeChecker = new SimpleShapeChecker( );
if ( shapeChecker.IsCircle( idealCicle ) )
{
// ...
}
if ( shapeChecker.CheckShapeType( distorredCircle ) == ShapeType.Circle )
{
// ...
}
Minimum value of allowed shapes' distortion.
The property sets minimum value for allowed shapes'
distortion (in pixels). See documentation to
class for more details about this property.
Default value is set to 0.5.
Maximum value of allowed shapes' distortion, [0, 1].
The property sets maximum value for allowed shapes'
distortion. The value is measured in [0, 1] range, which corresponds
to [0%, 100%] range, which means that maximum allowed shapes'
distortion is calculated relatively to shape's size. This results to
higher allowed distortion level for bigger shapes and smaller allowed
distortion for smaller shapers. See documentation to
class for more details about this property.
Default value is set to 0.03 (3%).
Maximum allowed angle error in degrees, [0, 20].
The value sets maximum allowed difference between two angles to
treat them as equal. It is used by method to
check for parallel lines and angles of triangles and quadrilaterals.
For example, if angle between two lines equals 5 degrees and this properties value
is set to 7, then two compared lines are treated as parallel.
Default value is set to 7.
Maximum allowed difference in sides' length (relative to shapes' size), [0, 1].
The values sets maximum allowed difference between two sides' length
to treat them as equal. The error value is set relative to shapes size and measured
in [0, 1] range, which corresponds to [0%, 100%] range. Absolute length error in pixels
is calculated as:
LengthError * ( width + height ) / 2
, where width and height is the size of bounding rectangle for the
specified shape.
Default value is set to 0.1 (10%).
Check type of the shape formed by specified points.
Shape's points to check.
Returns type of the detected shape.
Check if the specified set of points form a circle shape.
Shape's points to check.
Returns if the specified set of points form a
circle shape or otherwise.
Circle shape must contain at least 8 points to be recognized.
The method returns always, of number of points in the specified
shape is less than 8.
Check if the specified set of points form a circle shape.
Shape's points to check.
Receives circle's center on successful return.
Receives circle's radius on successful return.
Returns if the specified set of points form a
circle shape or otherwise.
Circle shape must contain at least 8 points to be recognized.
The method returns always, of number of points in the specified
shape is less than 8.
Check if the specified set of points form a quadrilateral shape.
Shape's points to check.
Returns if the specified set of points form a
quadrilateral shape or otherwise.
Check if the specified set of points form a quadrilateral shape.
Shape's points to check.
List of quadrilateral corners on successful return.
Returns if the specified set of points form a
quadrilateral shape or otherwise.
Check if the specified set of points form a triangle shape.
Shape's points to check.
Returns if the specified set of points form a
triangle shape or otherwise.
Check if the specified set of points form a triangle shape.
Shape's points to check.
List of triangle corners on successful return.
Returns if the specified set of points form a
triangle shape or otherwise.
Check if the specified set of points form a convex polygon shape.
Shape's points to check.
List of polygon corners on successful return.
Returns if the specified set of points form a
convex polygon shape or otherwise.
The method is able to detect only triangles and quadrilaterals
for now. Check number of detected corners to resolve type of the detected polygon.
Check sub type of a convex polygon.
Corners of the convex polygon to check.
Return detected sub type of the specified shape.
The method check corners of a convex polygon detecting
its subtype. Polygon's corners are usually retrieved using
method, but can be any list of 3-4 points (only sub types of triangles and
quadrilateral are checked).
See and properties,
which set acceptable errors for polygon sub type checking.
Check if a shape specified by the set of points fits a convex polygon
specified by the set of corners.
Shape's points to check.
Corners of convex polygon to check fitting into.
Returns if the specified shape fits
the specified convex polygon or otherwise.
The method checks if the set of specified points form the same shape
as the set of provided corners.
2D circle class.
Gets the area of the circle (πR²).
Gets the circumference of the circle (2πR).
Gets the diameter of the circle (2R).
Gets or sets the radius for this circle.
Gets or sets the origin (center) of this circle.
Creates a new unit at the origin.
Creates a new with the given radius
centered at the given x and y coordinates.
The x-coordinate of the circle's center.
The y-coordinate of the circle's center.
The circle radius.
Creates a new with the given radius
centered at the given x and y coordinates.
The x-coordinate of the circle's center.
The y-coordinate of the circle's center.
The circle radius.
Creates a new with the given radius
centered at the given center point coordinates.
The point at the circle's center.
The circle radius.
Creates a new from three non-linear points.
The first point.
The second point.
The third point.
Computes the distance from circle to point.
The point to have its distance from the circle computed.
The distance from to this circle.
Discrete Curve Evolution.
The Discrete Curve Evolution (DCE) algorithm can be used to simplify
contour curves. It can preserve the outline of a shape by preserving
its most visually critical points.
The implementation available in the framework has been contributed by
Diego Catalano, from the Catalano Framework for Java. The original work
has been developed by Dr. Longin Jan Latecki, and has been redistributed
under the LGPL with explicit permission from the original author, as long
as the following references are acknowledged in derived applications:
L.J. Latecki and R. Lakaemper; Convexity rule for shape decomposition based
on discrete contour evolution. Computer Vision and Image Understanding 73 (3),
441-454, 1999.
References:
-
L.J. Latecki and R. Lakaemper; Convexity rule for shape decomposition based
on discrete contour evolution. Computer Vision and Image Understanding 73 (3),
441-454, 1999.
Gets or sets the number of vertices.
Initializes a new instance of the class.
Initializes a new instance of the class.
Number of vertices.
Optimize specified shape.
Shape to be optimized.
Returns final optimized shape, which may have reduced amount of points.
Convex Hull Defects Extractor.
Gets or sets the minimum depth which characterizes a convexity defect.
The minimum depth.
Initializes a new instance of the class.
The minimum depth which characterizes a convexity defect.
Finds the convexity defects in a contour given a convex hull.
The contour.
The convex hull of the contour.
A list of s containing each of the
defects found considering the convex hull of the contour.
Convexity defect.
Initializes a new instance of the class.
The most distant point from the hull.
The starting index of the defect in the contour.
The ending index of the defect in the contour.
The depth of the defect (highest distance from the hull to
any of the contour points).
Gets or sets the starting index of the defect in the contour.
Gets or sets the ending index of the defect in the contour.
Gets or sets the most distant point from the hull characterizing the defect.
The point.
Gets or sets the depth of the defect (highest distance
from the hull to any of the points in the contour).
K-curvatures algorithm for local maximum contour detection.
Gets or sets the number K of previous and posterior
points to consider when find local extremum points.
Gets or sets the theta angle range (in
degrees) used to define extremum points.
Gets or sets the suppression radius to
use during non-minimum suppression.
Initializes a new instance of the class.
The number K of previous and posterior
points to consider when find local extremum points.
The theta angle range (in
degrees) used to define extremum points..
Finds local extremum points in the contour.
A list of
integer points defining the contour.
A structure representing 3x3 matrix.
The structure incapsulates elements of a 3x3 matrix and
provides some operations with it.
Row 0 column 0 element of the matrix.
Row 0 column 1 element of the matrix.
Row 0 column 2 element of the matrix.
Row 1 column 0 element of the matrix.
Row 1 column 1 element of the matrix.
Row 1 column 2 element of the matrix.
Row 2 column 0 element of the matrix.
Row 2 column 1 element of the matrix.
Row 2 column 2 element of the matrix.
Provides an identity matrix with all diagonal elements set to 1.
Calculates determinant of the matrix.
Returns array representation of the matrix.
Returns array which contains all elements of the matrix in the row-major order.
Creates rotation matrix around Y axis.
Rotation angle around Y axis in radians.
Returns rotation matrix to rotate an object around Y axis.
Creates rotation matrix around X axis.
Rotation angle around X axis in radians.
Returns rotation matrix to rotate an object around X axis.
Creates rotation matrix around Z axis.
Rotation angle around Z axis in radians.
Returns rotation matrix to rotate an object around Z axis.
Creates rotation matrix to rotate an object around X, Y and Z axes.
Rotation angle around Y axis in radians.
Rotation angle around X axis in radians.
Rotation angle around Z axis in radians.
Returns rotation matrix to rotate an object around all 3 axes.
The routine assumes roll-pitch-yaw rotation order, when creating rotation
matrix, i.e. an object is first rotated around Z axis, then around X axis and finally around
Y axis.
Extract rotation angles from the rotation matrix.
Extracted rotation angle around Y axis in radians.
Extracted rotation angle around X axis in radians.
Extracted rotation angle around Z axis in radians.
The routine assumes roll-pitch-yaw rotation order when extracting rotation angle.
Using extracted angles with the should provide same rotation matrix.
The method assumes the provided matrix represent valid rotation matrix.
Sample usage:
// assume we have a rotation matrix created like this
float yaw = 10.0f / 180 * Math.PI;
float pitch = 30.0f / 180 * Math.PI;
float roll = 45.0f / 180 * Math.PI;
Matrix3x3 rotationMatrix = Matrix3x3.CreateFromYawPitchRoll( yaw, pitch, roll );
// ...
// now somewhere in the code you may want to get rotation
// angles back from a matrix assuming same rotation order
float extractedYaw;
float extractedPitch;
float extractedRoll;
rotation.ExtractYawPitchRoll( out extractedYaw, out extractedPitch, out extractedRoll );
Creates a matrix from 3 rows specified as vectors.
First row of the matrix to create.
Second row of the matrix to create.
Third row of the matrix to create.
Returns a matrix from specified rows.
Creates a matrix from 3 columns specified as vectors.
First column of the matrix to create.
Second column of the matrix to create.
Third column of the matrix to create.
Returns a matrix from specified columns.
Creates a diagonal matrix using the specified vector as diagonal elements.
Vector to use for diagonal elements of the matrix.
Returns a diagonal matrix.
Get row of the matrix.
Row index to get, [0, 2].
Returns specified row of the matrix as a vector.
Invalid row index was specified.
Get column of the matrix.
Column index to get, [0, 2].
Returns specified column of the matrix as a vector.
Invalid column index was specified.
Multiplies two specified matrices.
Matrix to multiply.
Matrix to multiply by.
Return new matrix, which the result of multiplication of the two specified matrices.
Multiplies two specified matrices.
Matrix to multiply.
Matrix to multiply by.
Return new matrix, which the result of multiplication of the two specified matrices.
Adds corresponding components of two matrices.
The matrix to add to.
The matrix to add to the first matrix.
Returns a matrix which components are equal to sum of corresponding
components of the two specified matrices.
Adds corresponding components of two matrices.
The matrix to add to.
The matrix to add to the first matrix.
Returns a matrix which components are equal to sum of corresponding
components of the two specified matrices.
Subtracts corresponding components of two matrices.
The matrix to subtract from.
The matrix to subtract from the first matrix.
Returns a matrix which components are equal to difference of corresponding
components of the two specified matrices.
Subtracts corresponding components of two matrices.
The matrix to subtract from.
The matrix to subtract from the first matrix.
Returns a matrix which components are equal to difference of corresponding
components of the two specified matrices.
Multiplies specified matrix by the specified vector.
Matrix to multiply by vector.
Vector to multiply matrix by.
Returns new vector which is the result of multiplication of the specified matrix
by the specified vector.
Multiplies specified matrix by the specified vector.
Matrix to multiply by vector.
Vector to multiply matrix by.
Returns new vector which is the result of multiplication of the specified matrix
by the specified vector.
Multiplies matrix by the specified factor.
Matrix to multiply.
Factor to multiple the specified matrix by.
Returns new matrix with all components equal to corresponding components of the
specified matrix multiples by the specified factor.
Multiplies matrix by the specified factor.
Matrix to multiply.
Factor to multiple the specified matrix by.
Returns new matrix with all components equal to corresponding components of the
specified matrix multiples by the specified factor.
Adds specified value to all components of the specified matrix.
Matrix to add value to.
Value to add to all components of the specified matrix.
Returns new matrix with all components equal to corresponding components of the
specified matrix increased by the specified value.
Adds specified value to all components of the specified matrix.
Matrix to add value to.
Value to add to all components of the specified matrix.
Returns new matrix with all components equal to corresponding components of the
specified matrix increased by the specified value.
Tests whether two specified matrices are equal.
The left-hand matrix.
The right-hand matrix.
Returns if the two matrices are equal or otherwise.
Tests whether two specified matrices are not equal.
The left-hand matrix.
The right-hand matrix.
Returns if the two matrices are not equal or otherwise.
Tests whether the matrix equals to the specified one.
The matrix to test equality with.
Returns if the two matrices are equal or otherwise.
Tests whether the matrix equals to the specified object.
The object to test equality with.
Returns if the matrix equals to the specified object or otherwise.
Returns the hashcode for this instance.
A 32-bit signed integer hash code.
Transpose the matrix, AT.
Return a matrix which equals to transposition of this matrix.
Multiply the matrix by its transposition, A*AT.
Returns a matrix which is the result of multiplying this matrix by its transposition.
Multiply transposition of this matrix by itself, AT*A.
Returns a matrix which is the result of multiplying this matrix's transposition by itself.
Calculate adjugate of the matrix, adj(A).
Returns adjugate of the matrix.
Calculate inverse of the matrix, A-1.
Returns inverse of the matrix.
Cannot calculate inverse of the matrix since it is singular.
Calculate pseudo inverse of the matrix, A+.
Returns pseudo inverse of the matrix.
The pseudo inverse of the matrix is calculate through its
as V*E+*UT.
Calculate Singular Value Decomposition (SVD) of the matrix, such as A=U*E*VT.
Output parameter which gets 3x3 U matrix.
Output parameter which gets diagonal elements of the E matrix.
Output parameter which gets 3x3 V matrix.
Having components U, E and V the source matrix can be reproduced using below code:
Matrix3x3 source = u * Matrix3x3.Diagonal( e ) * v.Transpose( );
A structure representing 4x4 matrix.
The structure incapsulates elements of a 4x4 matrix and
provides some operations with it.
Row 0 column 0 element of the matrix.
Row 0 column 1 element of the matrix.
Row 0 column 2 element of the matrix.
Row 0 column 3 element of the matrix.
Row 1 column 0 element of the matrix.
Row 1 column 1 element of the matrix.
Row 1 column 2 element of the matrix.
Row 1 column 3 element of the matrix.
Row 2 column 0 element of the matrix.
Row 2 column 1 element of the matrix.
Row 2 column 2 element of the matrix.
Row 2 column 3 element of the matrix.
Row 3 column 0 element of the matrix.
Row 3 column 1 element of the matrix.
Row 3 column 2 element of the matrix.
Row 3 column 3 element of the matrix.
Provides an identity matrix with all diagonal elements set to 1.
Returns array representation of the matrix.
Returns array which contains all elements of the matrix in the row-major order.
Creates rotation matrix around Y axis.
Rotation angle around Y axis in radians.
Returns rotation matrix to rotate an object around Y axis.
Creates rotation matrix around X axis.
Rotation angle around X axis in radians.
Returns rotation matrix to rotate an object around X axis.
Creates rotation matrix around Z axis.
Rotation angle around Z axis in radians.
Returns rotation matrix to rotate an object around Z axis.
Creates rotation matrix to rotate an object around X, Y and Z axes.
Rotation angle around Y axis in radians.
Rotation angle around X axis in radians.
Rotation angle around Z axis in radians.
Returns rotation matrix to rotate an object around all 3 axes.
The routine assumes roll-pitch-yaw rotation order, when creating rotation
matrix, i.e. an object is first rotated around Z axis, then around X axis and finally around
Y axis.
Extract rotation angles from the rotation matrix.
Extracted rotation angle around Y axis in radians.
Extracted rotation angle around X axis in radians.
Extracted rotation angle around Z axis in radians.
The routine assumes roll-pitch-yaw rotation order when extracting rotation angle.
Using extracted angles with the should provide same rotation matrix.
The method assumes the provided matrix represent valid rotation matrix.
Sample usage:
// assume we have a rotation matrix created like this
float yaw = 10.0f / 180 * Math.PI;
float pitch = 30.0f / 180 * Math.PI;
float roll = 45.0f / 180 * Math.PI;
Matrix4x4 rotationMatrix = Matrix3x3.CreateFromYawPitchRoll( yaw, pitch, roll );
// ...
// now somewhere in the code you may want to get rotation
// angles back from a matrix assuming same rotation order
float extractedYaw;
float extractedPitch;
float extractedRoll;
rotation.ExtractYawPitchRoll( out extractedYaw, out extractedPitch, out extractedRoll );
Creates 4x4 tranformation matrix from 3x3 rotation matrix.
Source 3x3 rotation matrix.
Returns 4x4 rotation matrix.
The source 3x3 rotation matrix is copied into the top left corner of the result 4x4 matrix,
i.e. it represents 0th, 1st and 2nd row/column. The element is set to 1 and the rest
elements of 3rd row and 3rd column are set to zeros.
Creates translation matrix for the specified movement amount.
Vector which set direction and amount of movement.
Returns translation matrix.
The specified vector is copied to the 3rd column of the result matrix.
All diagonal elements are set to 1. The rest of matrix is initialized with zeros.
Creates a view matrix for the specified camera position and target point.
Position of camera.
Target point towards which camera is pointing.
Returns a view matrix.
Camera's "up" vector is supposed to be (0, 1, 0).
Creates a perspective projection matrix.
Width of the view volume at the near view plane.
Height of the view volume at the near view plane.
Distance to the near view plane.
Distance to the far view plane.
Return a perspective projection matrix.
Both near and far view planes' distances must be greater than zero.
Near plane must be closer than the far plane.
Creates a matrix from 4 rows specified as vectors.
First row of the matrix to create.
Second row of the matrix to create.
Third row of the matrix to create.
Fourth row of the matrix to create.
Returns a matrix from specified rows.
Creates a matrix from 4 columns specified as vectors.
First column of the matrix to create.
Second column of the matrix to create.
Third column of the matrix to create.
Fourth column of the matrix to create.
Returns a matrix from specified columns.
Creates a diagonal matrix using the specified vector as diagonal elements.
Vector to use for diagonal elements of the matrix.
Returns a diagonal matrix.
Get row of the matrix.
Row index to get, [0, 3].
Returns specified row of the matrix as a vector.
Invalid row index was specified.
Get column of the matrix.
Column index to get, [0, 3].
Returns specified column of the matrix as a vector.
Invalid column index was specified.
Multiplies two specified matrices.
Matrix to multiply.
Matrix to multiply by.
Return new matrix, which the result of multiplication of the two specified matrices.
Multiplies two specified matrices.
Matrix to multiply.
Matrix to multiply by.
Return new matrix, which the result of multiplication of the two specified matrices.
Adds corresponding components of two matrices.
The matrix to add to.
The matrix to add to the first matrix.
Returns a matrix which components are equal to sum of corresponding
components of the two specified matrices.
Adds corresponding components of two matrices.
The matrix to add to.
The matrix to add to the first matrix.
Returns a matrix which components are equal to sum of corresponding
components of the two specified matrices.
Subtracts corresponding components of two matrices.
The matrix to subtract from.
The matrix to subtract from the first matrix.
Returns a matrix which components are equal to difference of corresponding
components of the two specified matrices.
Subtracts corresponding components of two matrices.
The matrix to subtract from.
The matrix to subtract from the first matrix.
Returns a matrix which components are equal to difference of corresponding
components of the two specified matrices.
Multiplies specified matrix by the specified vector.
Matrix to multiply by vector.
Vector to multiply matrix by.
Returns new vector which is the result of multiplication of the specified matrix
by the specified vector.
Multiplies specified matrix by the specified vector.
Matrix to multiply by vector.
Vector to multiply matrix by.
Returns new vector which is the result of multiplication of the specified matrix
by the specified vector.
Tests whether two specified matrices are equal.
The left-hand matrix.
The right-hand matrix.
Returns if the two matrices are equal or otherwise.
Tests whether two specified matrices are not equal.
The left-hand matrix.
The right-hand matrix.
Returns if the two matrices are not equal or otherwise.
Tests whether the matrix equals to the specified one.
The matrix to test equality with.
Returns if the two matrices are equal or otherwise.
Tests whether the matrix equals to the specified object.
The object to test equality with.
Returns if the matrix equals to the specified object or otherwise.
Returns the hashcode for this instance.
A 32-bit signed integer hash code.
Please use Accord.Math.Distances.Cosine instead.
Please use Accord.Math.Distances.Cosine instead.
Please use Accord.Math.Distances.Cosine instead.
Please use Accord.Math.Distances.Cosine instead.
Please use Accord.Math.Distances.Euclidean instead.
Please use Accord.Math.Distances.Euclidean instead.
Please use Accord.Math.Distances.Euclidean instead.
Please use Accord.Math.Distances.Euclidean instead.
Please use Accord.Math.Distances.Hamming instead.
Please use Accord.Math.Distances.Hamming instead.
Please use Accord.Math.Distances.IDistance instead.
Please use Accord.Math.Distances.IDistance instead.
Please use Accord.Math.Distances.ISimilarity instead.
Please use Accord.Math.Distances.ISimilarity instead.
Please use Accord.Math.Distances.Jaccard instead.
Please use Accord.Math.Jaccard.Cosine instead.
Please use Accord.Math.Distances.Manhattan instead.
Please use Accord.Math.Distances.Manhattan instead.
Please use Accord.Math.Distances.PearsonCorrelation instead.
Please use Accord.Math.Distances.PearsonCorrelation instead.
Perlin noise function.
The class implements 1-D and 2-D Perlin noise functions, which represent
sum of several smooth noise functions with different frequency and amplitude. The description
of Perlin noise function and its calculation may be found on
Hugo Elias's page.
The number of noise functions, which comprise the resulting Perlin noise function, is
set by property. Amplitude and frequency values for each octave
start from values, which are set by and
properties.
Sample usage (clouds effect):
// create Perlin noise function
PerlinNoise noise = new PerlinNoise( 8, 0.5, 1.0 / 32 );
// generate clouds effect
float[,] texture = new float[height, width];
for ( int y = 0; y < height; y++ )
{
for ( int x = 0; x < width; x++ )
{
texture[y, x] =
Math.Max( 0.0f, Math.Min( 1.0f,
(float) noise.Function2D( x, y ) * 0.5f + 0.5f
) );
}
}
Initial frequency.
The property sets initial frequency of the first octave. Frequencies for
next octaves are calculated using the next equation:
frequencyi = * 2i,
where i = [0, ).
Default value is set to 1.
Initial amplitude.
The property sets initial amplitude of the first octave. Amplitudes for
next octaves are calculated using the next equation:
amplitudei = * i,
where i = [0, ).
Default value is set to 1.
Persistence value.
The property sets so called persistence value, which controls the way
how amplitude is calculated for each octave comprising
the Perlin noise function.
Default value is set to 0.65.
Number of octaves, [1, 32]. Default is 4.
The property sets the number of noise functions, which sum up the resulting
Perlin noise function.
Default value is set to 4.
Initializes a new instance of the class.
Initializes a new instance of the class.
Number of octaves (see property).
Persistence value (see property).
Initializes a new instance of the class.
Number of octaves (see property).
Persistence value (see property).
Initial frequency (see property).
Initial amplitude (see property).
1-D Perlin noise function.
x value.
Returns function's value at point .
2-D Perlin noise function.
x value.
y value.
Returns function's value at point (, ).
Ordinary noise function
Smoothed noise.
Cosine interpolation.
Exponential random numbers generator.
The random number generator generates exponential
random numbers with specified rate value (lambda).
The generator uses generator as a base
to generate random numbers.
Sample usage:
// create instance of random generator
IRandomNumberGenerator generator = new ExponentialGenerator( 5 );
// generate random number
float randomNumber = generator.Next( );
Rate value (inverse mean).
The rate value should be positive and non zero.
Mean value of the generator.
Variance value of the generator.
Initializes a new instance of the class.
Rate value.
Rate value should be greater than zero.
Initializes a new instance of the class.
Rate value (inverse mean).
Seed value to initialize random numbers generator.
Rate value should be greater than zero.
Generate next random number
Returns next random number.
Set seed of the random numbers generator.
Seed value.
Resets random numbers generator initializing it with
specified seed value.
Gaussian random numbers generator.
The random number generator generates gaussian
random numbers with specified mean and standard deviation values.
The generator uses generator as base
to generate random numbers.
Sample usage:
// create instance of random generator
IRandomNumberGenerator generator = new GaussianGenerator( 5.0, 1.5 );
// generate random number
float randomNumber = generator.Next( );
Mean value of the generator.
Variance value of the generator.
Standard deviation value.
Initializes a new instance of the class.
Mean value.
Standard deviation value.
Initializes a new instance of the class.
Mean value.
Standard deviation value.
Seed value to initialize random numbers generator.
Generate next random number.
Returns next random number.
Set seed of the random numbers generator.
Seed value.
Resets random numbers generator initializing it with
specified seed value.
Interface for random numbers generators.
The interface defines set of methods and properties, which should
be implemented by different algorithms for random numbers generatation.
Mean value of generator.
Variance value of generator.
Generate next random number.
Returns next random number.
Set seed of the random numbers generator.
Seed value.
Standard random numbers generator.
The random number generator generates gaussian
random numbers with zero mean and standard deviation of one. The generator
implements polar form of the Box-Muller transformation.
The generator uses generator as a base
to generate random numbers.
Sample usage:
// create instance of random generator
IRandomNumberGenerator generator = new StandardGenerator( );
// generate random number
float randomNumber = generator.Next( );
Mean value of the generator.
Variance value of the generator.
Initializes a new instance of the class.
Initializes a new instance of the class.
Seed value to initialize random numbers generator.
Generate next random number.
Returns next random number.
Set seed of the random numbers generator.
Seed value.
Resets random numbers generator initializing it with
specified seed value.
Uniform random numbers generator.
The random numbers generator generates uniformly
distributed numbers in the specified range - values
are greater or equal to minimum range's value and less than maximum range's
value.
The generator uses generator
to generate random numbers.
Sample usage:
// create instance of random generator
IRandomNumberGenerator generator = new UniformGenerator( new Range( 50, 100 ) );
// generate random number
float randomNumber = generator.Next( );
Mean value of the generator.
Variance value of the generator.
Random numbers range.
Range of random numbers to generate. Generated numbers are
greater or equal to minimum range's value and less than maximum range's
value.
Initializes a new instance of the class.
Random numbers range.
Initializes random numbers generator with zero seed.
Initializes a new instance of the class.
Random numbers range.
Seed value to initialize random numbers generator.
Generate next random number.
Returns next random number.
Set seed of the random numbers generator.
Seed value.
Resets random numbers generator initializing it with
specified seed value.
Uniform random numbers generator in the range of [0, 1).
The random number generator generates uniformly
distributed numbers in the range of [0, 1) - greater or equal to 0.0
and less than 1.0.
At this point the generator is based on the
internal .NET generator, but may be rewritten to
use faster generation algorithm.
Sample usage:
// create instance of random generator
IRandomNumberGenerator generator = new UniformOneGenerator( );
// generate random number
float randomNumber = generator.Next( );
Mean value of the generator.
Variance value of the generator.
Initializes a new instance of the class.
Initializes random numbers generator with zero seed.
Initializes a new instance of the class.
Seed value to initialize random numbers generator.
Generate next random number.
Returns next random number.
Set seed of the random numbers generator.
Seed value.
Resets random numbers generator initializing it with
specified seed value.
Interface for random number generators.
The interface defines set of methods and properties, which should
be implemented by different algorithms for random numbers generation.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random observation from the current distribution.
A random observations drawn from this distribution.
Exponential random number generator using the Ziggurat method.
References:
-
John Burkard, Ziggurat Random Number Generator (RNG). Available on:
http://people.sc.fsu.edu/~jburkardt/c_src/ziggurat/ziggurat.c (LGPL)
-
Philip Leong, Guanglie Zhang, Dong-U Lee, Wayne Luk, John Villasenor,
A comment on the implementation of the ziggurat method,
Journal of Statistical Software, Volume 12, Number 7, February 2005.
-
George Marsaglia, Wai Wan Tsang, The Ziggurat Method for Generating Random Variables,
Journal of Statistical Software, Volume 5, Number 8, October 2000, seven pages.
Initializes a new instance of the class.
The random seed to use. Default is to use the next value from
the the framework-wide random generator.
Initializes a new instance of the class.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
A random vector of observations drawn from this distribution.
Dummy random number generator that always generates the same number.
Gets or sets the constant value returned by this generator.
Initializes a new instance of the class.
The constant value to be generated.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
A random vector of observations drawn from this distribution.
Uniform random number generator using the Ziggurat method.
References:
-
John Burkard, Ziggurat Random Number Generator (RNG). Available on:
http://people.sc.fsu.edu/~jburkardt/c_src/ziggurat/ziggurat.c (LGPL)
-
Philip Leong, Guanglie Zhang, Dong-U Lee, Wayne Luk, John Villasenor,
A comment on the implementation of the ziggurat method,
Journal of Statistical Software, Volume 12, Number 7, February 2005.
-
George Marsaglia, Wai Wan Tsang, The Ziggurat Method for Generating Random Variables,
Journal of Statistical Software, Volume 5, Number 8, October 2000, seven pages.
Gets or sets the lower bound for the values generated by this instance.
Gets or sets the length of the interval for values generated by this
instance. The upper bound will be given by + Length.
Initializes a new instance of the class.
The upper bound for generated values.
The lower bound for generated values.
Initializes a new instance of the class.
The random seed to use. Default is to use the next value from
the the framework-wide random generator.
The upper bound for generated values.
The lower bound for generated values.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
A random vector of observations drawn from this distribution.
Uniform random number generator using the Ziggurat method.
References:
-
John Burkard, Ziggurat Random Number Generator (RNG). Available on:
http://people.sc.fsu.edu/~jburkardt/c_src/ziggurat/ziggurat.c (LGPL)
-
Philip Leong, Guanglie Zhang, Dong-U Lee, Wayne Luk, John Villasenor,
A comment on the implementation of the ziggurat method,
Journal of Statistical Software, Volume 12, Number 7, February 2005.
-
George Marsaglia, Wai Wan Tsang, The Ziggurat Method for Generating Random Variables,
Journal of Statistical Software, Volume 5, Number 8, October 2000, seven pages.
Initializes a new instance of the class.
Initializes a new instance of the class.
The random seed to use. Default is to use the next value from
the the framework-wide random generator.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
A random vector of observations drawn from this distribution.
Generates a new non-negative integer random number.
Normal random number generator using the Ziggurat method.
References:
-
John Burkard, Ziggurat Random Number Generator (RNG). Available on:
http://people.sc.fsu.edu/~jburkardt/c_src/ziggurat/ziggurat.c (LGPL)
-
Philip Leong, Guanglie Zhang, Dong-U Lee, Wayne Luk, John Villasenor,
A comment on the implementation of the ziggurat method,
Journal of Statistical Software, Volume 12, Number 7, February 2005.
-
George Marsaglia, Wai Wan Tsang, The Ziggurat Method for Generating Random Variables,
Journal of Statistical Software, Volume 5, Number 8, October 2000, seven pages.
Initializes a new instance of the class.
The random seed to use. Default is to use the next value from
the the framework-wide random generator.
Initializes a new instance of the class.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
The number of samples to generate.
The location where to store the samples.
A random vector of observations drawn from this distribution.
Generates a random vector of observations from the current distribution.
A random vector of observations drawn from this distribution.
Framework-wide random number generator. If you would like to always generate
the same results when using the framework, set the property
of this class to a fixed value.
By setting to a given value, it is possible to adjust how
random numbers are generated within the framework. Preferably, this property
should be adjusted before other computations.
If the is set to a value that is less than or equal to zero, all
generators will start with the same fixed seed, even among multiple threads.
If set to any other value, the generators in other threads will start with fixed, but
different, seeds.
Gets a value indicating whether the random number generator has been used
during the execution of any past code. This can be useful to determine whether
a method or learning algorithm is fully deterministic or not. Note that it is
also possible for a method to be non-deterministic even if it uses the random
number generator if it use multiple threads.
Gets the timestamp for when the global random generator
was last changed (i.e. after setting ).
Gets the timestamp for when the thread random generator was last
changed (i.e. after creating the first random generator in this
thread context or by setting ).
Gets or sets the seed for the current thread. Changing
this seed will not impact other threads or generators
that have already been created from this thread.
Gets a reference to the random number generator used internally by
the Accord.NET classes and methods. Objects retrieved from this property
should not be shared across threads. Instead, call this property from
each thread you would like to use a random generator for.
Sets a random seed for the framework's main internal number
generator. Preferably, this method should be called before other
computations. If set to a value less than or equal to zero, all generators will
start with the same fixed seed, even among multiple threads. If set to any
other value, the generators in other threads will start with fixed, but different,
seeds.
Adjusting the global generator seed causes the calling thread to sleep for 100ms
so new threads spawned in a short time span after the call can be properly initialized
with the new random seeds. In order to better control the random behavior of different
algorithms, please consider specifying random generators directly using appropriate
interfaces for these algorithms in case they are available.
If you do not need to change the seed number for threads other than the current,
you can adjust the random seed for the current thread using
instead. Setting should not introduce delays.
3D Vector structure with X, Y and Z coordinates.
The structure incapsulates X, Y and Z coordinates of a 3D vector and
provides some operations with it.
X coordinate of the vector.
Y coordinate of the vector.
Z coordinate of the vector.
Returns maximum value of the vector.
Returns maximum value of all 3 vector's coordinates.
Returns minimum value of the vector.
Returns minimum value of all 3 vector's coordinates.
Returns index of the coordinate with maximum value.
Returns index of the coordinate, which has the maximum value - 0 for X,
1 for Y or 2 for Z.
If there are multiple coordinates which have the same maximum value, the
property returns smallest index.
Returns index of the coordinate with minimum value.
Returns index of the coordinate, which has the minimum value - 0 for X,
1 for Y or 2 for Z.
If there are multiple coordinates which have the same minimum value, the
property returns smallest index.
Returns vector's norm.
Returns Euclidean norm of the vector, which is a
square root of the sum: X2+Y2+Z2.
Returns square of the vector's norm.
Return X2+Y2+Z2, which is
a square of vector's norm or a dot product of this vector
with itself.
Initializes a new instance of the structure.
X coordinate of the vector.
Y coordinate of the vector.
Z coordinate of the vector.
Initializes a new instance of the structure.
Value, which is set to all 3 coordinates of the vector.
Returns a string representation of this object.
A string representation of this object.
Returns array representation of the vector.
Array with 3 values containing X/Y/Z coordinates.
Adds corresponding coordinates of two vectors.
The vector to add to.
The vector to add to the first vector.
Returns a vector which coordinates are equal to sum of corresponding
coordinates of the two specified vectors.
Adds corresponding coordinates of two vectors.
The vector to add to.
The vector to add to the first vector.
Returns a vector which coordinates are equal to sum of corresponding
coordinates of the two specified vectors.
Adds a value to all coordinates of the specified vector.
Vector to add the specified value to.
Value to add to all coordinates of the vector.
Returns new vector with all coordinates increased by the specified value.
Adds a value to all coordinates of the specified vector.
Vector to add the specified value to.
Value to add to all coordinates of the vector.
Returns new vector with all coordinates increased by the specified value.
Subtracts corresponding coordinates of two vectors.
The vector to subtract from.
The vector to subtract from the first vector.
Returns a vector which coordinates are equal to difference of corresponding
coordinates of the two specified vectors.
Subtracts corresponding coordinates of two vectors.
The vector to subtract from.
The vector to subtract from the first vector.
Returns a vector which coordinates are equal to difference of corresponding
coordinates of the two specified vectors.
Subtracts a value from all coordinates of the specified vector.
Vector to subtract the specified value from.
Value to subtract from all coordinates of the vector.
Returns new vector with all coordinates decreased by the specified value.
Subtracts a value from all coordinates of the specified vector.
Vector to subtract the specified value from.
Value to subtract from all coordinates of the vector.
Returns new vector with all coordinates decreased by the specified value.
Multiplies corresponding coordinates of two vectors.
The first vector to multiply.
The second vector to multiply.
Returns a vector which coordinates are equal to multiplication of corresponding
coordinates of the two specified vectors.
Multiplies corresponding coordinates of two vectors.
The first vector to multiply.
The second vector to multiply.
Returns a vector which coordinates are equal to multiplication of corresponding
coordinates of the two specified vectors.
Multiplies coordinates of the specified vector by the specified factor.
Vector to multiply coordinates of.
Factor to multiple coordinates of the specified vector by.
Returns new vector with all coordinates multiplied by the specified factor.
Multiplies coordinates of the specified vector by the specified factor.
Vector to multiply coordinates of.
Factor to multiple coordinates of the specified vector by.
Returns new vector with all coordinates multiplied by the specified factor.
Divides corresponding coordinates of two vectors.
The first vector to divide.
The second vector to devide.
Returns a vector which coordinates are equal to coordinates of the first vector divided by
corresponding coordinates of the second vector.
Divides corresponding coordinates of two vectors.
The first vector to divide.
The second vector to devide.
Returns a vector which coordinates are equal to coordinates of the first vector divided by
corresponding coordinates of the second vector.
Divides coordinates of the specified vector by the specified factor.
Vector to divide coordinates of.
Factor to divide coordinates of the specified vector by.
Returns new vector with all coordinates divided by the specified factor.
Divides coordinates of the specified vector by the specified factor.
Vector to divide coordinates of.
Factor to divide coordinates of the specified vector by.
Returns new vector with all coordinates divided by the specified factor.
Tests whether two specified vectors are equal.
The left-hand vector.
The right-hand vector.
Returns if the two vectors are equal or otherwise.
Tests whether two specified vectors are not equal.
The left-hand vector.
The right-hand vector.
Returns if the two vectors are not equal or otherwise.
Tests whether the vector equals to the specified one.
The vector to test equality with.
Returns if the two vectors are equal or otherwise.
Tests whether the vector equals to the specified object.
The object to test equality with.
Returns if the vector equals to the specified object or otherwise.
Returns the hashcode for this instance.
A 32-bit signed integer hash code.
Normalizes the vector by dividing it’s all coordinates with the vector's norm.
Returns the value of vectors’ norm before normalization.
Inverse the vector.
Returns a vector with all coordinates equal to 1.0 divided by the value of corresponding coordinate
in this vector (or equal to 0.0 if this vector has corresponding coordinate also set to 0.0).
Calculate absolute values of the vector.
Returns a vector with all coordinates equal to absolute values of this vector's coordinates.
Calculates cross product of two vectors.
First vector to use for cross product calculation.
Second vector to use for cross product calculation.
Returns cross product of the two specified vectors.
Calculates dot product of two vectors.
First vector to use for dot product calculation.
Second vector to use for dot product calculation.
Returns dot product of the two specified vectors.
Converts the vector to a 4D vector.
Returns 4D vector which is an extension of the 3D vector.
The method returns a 4D vector which has X, Y and Z coordinates equal to the
coordinates of this 3D vector and W coordinate set to 1.0.
4D Vector structure with X, Y, Z and W coordinates.
The structure incapsulates X, Y, Z and W coordinates of a 4D vector and
provides some operations with it.
X coordinate of the vector.
Y coordinate of the vector.
Z coordinate of the vector.
W coordinate of the vector.
Returns maximum value of the vector.
Returns maximum value of all 4 vector's coordinates.
Returns minimum value of the vector.
Returns minimum value of all 4 vector's coordinates.
Returns index of the coordinate with maximum value.
Returns index of the coordinate, which has the maximum value - 0 for X,
1 for Y, 2 for Z or 3 for W.
If there are multiple coordinates which have the same maximum value, the
property returns smallest index.
Returns index of the coordinate with minimum value.
Returns index of the coordinate, which has the minimum value - 0 for X,
1 for Y, 2 for Z or 3 for W.
If there are multiple coordinates which have the same minimum value, the
property returns smallest index.
Returns vector's norm.
Returns Euclidean norm of the vector, which is a
square root of the sum: X2+Y2+Z2+W2.
Returns square of the vector's norm.
Return X2+Y2+Z2+W2, which is
a square of vector's norm or a dot product of this vector
with itself.
Initializes a new instance of the structure.
X coordinate of the vector.
Y coordinate of the vector.
Z coordinate of the vector.
W coordinate of the vector.
Initializes a new instance of the structure.
Value, which is set to all 4 coordinates of the vector.
Returns a string representation of this object.
A string representation of this object.
Returns array representation of the vector.
Array with 4 values containing X/Y/Z/W coordinates.
Adds corresponding coordinates of two vectors.
The vector to add to.
The vector to add to the first vector.
Returns a vector which coordinates are equal to sum of corresponding
coordinates of the two specified vectors.
Adds corresponding coordinates of two vectors.
The vector to add to.
The vector to add to the first vector.
Returns a vector which coordinates are equal to sum of corresponding
coordinates of the two specified vectors.
Adds a value to all coordinates of the specified vector.
Vector to add the specified value to.
Value to add to all coordinates of the vector.
Returns new vector with all coordinates increased by the specified value.
Adds a value to all coordinates of the specified vector.
Vector to add the specified value to.
Value to add to all coordinates of the vector.
Returns new vector with all coordinates increased by the specified value.
Subtracts corresponding coordinates of two vectors.
The vector to subtract from.
The vector to subtract from the first vector.
Returns a vector which coordinates are equal to difference of corresponding
coordinates of the two specified vectors.
Subtracts corresponding coordinates of two vectors.
The vector to subtract from.
The vector to subtract from the first vector.
Returns a vector which coordinates are equal to difference of corresponding
coordinates of the two specified vectors.
Subtracts a value from all coordinates of the specified vector.
Vector to subtract the specified value from.
Value to subtract from all coordinates of the vector.
Returns new vector with all coordinates decreased by the specified value.
Subtracts a value from all coordinates of the specified vector.
Vector to subtract the specified value from.
Value to subtract from all coordinates of the vector.
Returns new vector with all coordinates decreased by the specified value.
Multiplies corresponding coordinates of two vectors.
The first vector to multiply.
The second vector to multiply.
Returns a vector which coordinates are equal to multiplication of corresponding
coordinates of the two specified vectors.
Multiplies corresponding coordinates of two vectors.
The first vector to multiply.
The second vector to multiply.
Returns a vector which coordinates are equal to multiplication of corresponding
coordinates of the two specified vectors.
Multiplies coordinates of the specified vector by the specified factor.
Vector to multiply coordinates of.
Factor to multiple coordinates of the specified vector by.
Returns new vector with all coordinates multiplied by the specified factor.
Multiplies coordinates of the specified vector by the specified factor.
Vector to multiply coordinates of.
Factor to multiple coordinates of the specified vector by.
Returns new vector with all coordinates multiplied by the specified factor.
Divides corresponding coordinates of two vectors.
The first vector to divide.
The second vector to devide.
Returns a vector which coordinates are equal to coordinates of the first vector divided by
corresponding coordinates of the second vector.
Divides corresponding coordinates of two vectors.
The first vector to divide.
The second vector to devide.
Returns a vector which coordinates are equal to coordinates of the first vector divided by
corresponding coordinates of the second vector.
Divides coordinates of the specified vector by the specified factor.
Vector to divide coordinates of.
Factor to divide coordinates of the specified vector by.
Returns new vector with all coordinates divided by the specified factor.
Divides coordinates of the specified vector by the specified factor.
Vector to divide coordinates of.
Factor to divide coordinates of the specified vector by.
Returns new vector with all coordinates divided by the specified factor.
Tests whether two specified vectors are equal.
The left-hand vector.
The right-hand vector.
Returns if the two vectors are equal or otherwise.
Tests whether two specified vectors are not equal.
The left-hand vector.
The right-hand vector.
Returns if the two vectors are not equal or otherwise.
Tests whether the vector equals to the specified one.
The vector to test equality with.
Returns if the two vectors are equal or otherwise.
Tests whether the vector equals to the specified object.
The object to test equality with.
Returns if the vector equals to the specified object or otherwise.
Returns the hashcode for this instance.
A 32-bit signed integer hash code.
Normalizes the vector by dividing it’s all coordinates with the vector's norm.
Returns the value of vectors’ norm before normalization.
Inverse the vector.
Returns a vector with all coordinates equal to 1.0 divided by the value of corresponding coordinate
in this vector (or equal to 0.0 if this vector has corresponding coordinate also set to 0.0).
Calculate absolute values of the vector.
Returns a vector with all coordinates equal to absolute values of this vector's coordinates.
Calculates dot product of two vectors.
First vector to use for dot product calculation.
Second vector to use for dot product calculation.
Returns dot product of the two specified vectors.
Converts the vector to a 3D vector.
Returns 3D vector which has X/Y/Z coordinates equal to X/Y/Z coordinates
of this vector divided by .
Determines the Generalized eigenvalues and eigenvectors of two real square matrices.
A generalized eigenvalue problem is the problem of finding a vector v that
obeys A * v = λ * B * v where A and B are matrices. If v
obeys this equation, with some λ, then we call v the generalized eigenvector
of A and B, and λ is called the generalized eigenvalue of A
and B which corresponds to the generalized eigenvector v. The possible
values of λ, must obey the identity det(A - λ*B) = 0.
Part of this code has been adapted from the original EISPACK routines in Fortran.
References:
-
http://en.wikipedia.org/wiki/Generalized_eigenvalue_problem#Generalized_eigenvalue_problem
-
http://www.netlib.org/eispack/
// Suppose we have the following
// matrices A and B shown below:
double[][] A =
{
new double[] { 1, 2, 3},
new double[] { 8, 1, 4},
new double[] { 3, 2, 3}
};
double[][] B =
{
new double[] { 5, 1, 1},
new double[] { 1, 5, 1},
new double[] { 1, 1, 5}
};
// Now, suppose we would like to find values for λ
// that are solutions for the equation det(A - λB) = 0
// For this, we can use a Generalized Eigendecomposition
var gevd = new JaggedGeneralizedEigenvalueDecomposition(A, B);
// Now, if A and B are Hermitian and B is positive
// -definite, then the eigenvalues λ will be real:
double[] lambda = gevd.RealEigenvalues;
// Lets check if they are indeed a solution:
for (int i = 0; i < lambda.Length; i++)
{
// Compute the determinant equation show above
double det = Matrix.Determinant(A.Subtract(lambda[i].Multiply(B))); // almost zero
}
Constructs a new generalized eigenvalue decomposition.
The first matrix of the (A,B) matrix pencil.
The second matrix of the (A,B) matrix pencil.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Returns the effective numerical matrix rank.
Number of non-negligible eigen values.
Returns the real parts of the alpha values.
Returns the imaginary parts of the alpha values.
Returns the beta values.
Returns true if matrix B is singular.
This method checks if any of the generated betas is zero. It
does not says that the problem is singular, but only that one
of the matrices of the pencil (A,B) is singular.
Returns true if the eigenvalue problem is degenerate (ill-posed).
Returns the real parts of the eigenvalues.
The eigenvalues are computed using the ratio alpha[i]/beta[i],
which can lead to valid, but infinite eigenvalues.
Returns the imaginary parts of the eigenvalues.
The eigenvalues are computed using the ratio alpha[i]/beta[i],
which can lead to valid, but infinite eigenvalues.
Returns the eigenvector matrix.
Returns the block diagonal eigenvalue matrix.
Adaptation of the original Fortran QZHES routine from EISPACK.
This subroutine is the first step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart.
This subroutine accepts a pair of real general matrices and
reduces one of them to upper Hessenberg form and the other
to upper triangular form using orthogonal transformations.
it is usually followed by qzit, qzval and, possibly, qzvec.
For the full documentation, please check the original function.
Adaptation of the original Fortran QZIT routine from EISPACK.
This subroutine is the second step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart,
as modified in technical note nasa tn d-7305(1973) by ward.
This subroutine accepts a pair of real matrices, one of them
in upper Hessenberg form and the other in upper triangular form.
it reduces the Hessenberg matrix to quasi-triangular form using
orthogonal transformations while maintaining the triangular form
of the other matrix. it is usually preceded by qzhes and
followed by qzval and, possibly, qzvec.
For the full documentation, please check the original function.
Adaptation of the original Fortran QZVAL routine from EISPACK.
This subroutine is the third step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart.
This subroutine accepts a pair of real matrices, one of them
in quasi-triangular form and the other in upper triangular form.
it reduces the quasi-triangular matrix further, so that any
remaining 2-by-2 blocks correspond to pairs of complex
Eigenvalues, and returns quantities whose ratios give the
generalized eigenvalues. it is usually preceded by qzhes
and qzit and may be followed by qzvec.
For the full documentation, please check the original function.
Adaptation of the original Fortran QZVEC routine from EISPACK.
This subroutine is the optional fourth step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart.
This subroutine accepts a pair of real matrices, one of them in
quasi-triangular form (in which each 2-by-2 block corresponds to
a pair of complex eigenvalues) and the other in upper triangular
form. It computes the eigenvectors of the triangular problem and
transforms the results back to the original coordinate system.
it is usually preceded by qzhes, qzit, and qzval.
For the full documentation, please check the original function.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Singular Value Decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the singular value decomposition
is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U * S * V'.
The singular values, sigma[k] = S[k,k], are ordered so that
sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will
never fail. The matrix condition number and the effective numerical
rank can be computed from this decomposition.
WARNING! Please be aware that if A has less rows than columns, it is better
to compute the decomposition on the transpose of A and then swap the left
and right eigenvectors. If the routine is computed on A directly, the diagonal
of singular values may contain one or more zeros. The identity A = U * S * V'
may still hold, however. To overcome this problem, pass true to the
autoTranspose
argument of the class constructor.
This routine computes the economy decomposition of A.
Returns the condition number max(S) / min(S).
Returns the singularity threshold.
Returns the Two norm.
Returns the effective numerical matrix rank.
Number of non-negligible singular values.
Gets whether the decomposed matrix is singular.
Gets the one-dimensional array of singular values.
Returns the block diagonal matrix of singular values.
Returns the V matrix of Singular Vectors.
Returns the U matrix of Singular Vectors.
Returns the ordering in which the singular values have been sorted.
Returns the absolute value of the matrix determinant.
Returns the log of the absolute value for the matrix determinant.
Returns the pseudo-determinant for the matrix.
Returns the log of the pseudo-determinant for the matrix.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Solves a linear equation system of the form xA = b.
The b from the equation xA = b.
The x from equation Ax = b.
Solves a linear equation system of the form Ax = b.
The b from the equation Ax = b.
The x from equation Ax = b.
Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Singular Value Decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the singular value decomposition
is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U * S * V'.
The singular values, sigma[k] = S[k,k], are ordered so that
sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will
never fail. The matrix condition number and the effective numerical
rank can be computed from this decomposition.
WARNING! Please be aware that if A has less rows than columns, it is better
to compute the decomposition on the transpose of A and then swap the left
and right eigenvectors. If the routine is computed on A directly, the diagonal
of singular values may contain one or more zeros. The identity A = U * S * V'
may still hold, however. To overcome this problem, pass true to the
autoTranspose
argument of the class constructor.
This routine computes the economy decomposition of A.
Returns the condition number max(S) / min(S).
Returns the singularity threshold.
Returns the Two norm.
Returns the effective numerical matrix rank.
Number of non-negligible singular values.
Gets whether the decomposed matrix is singular.
Gets the one-dimensional array of singular values.
Returns the block diagonal matrix of singular values.
Returns the V matrix of Singular Vectors.
Returns the U matrix of Singular Vectors.
Returns the ordering in which the singular values have been sorted.
Returns the absolute value of the matrix determinant.
Returns the log of the absolute value for the matrix determinant.
Returns the pseudo-determinant for the matrix.
Returns the log of the pseudo-determinant for the matrix.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Solves a linear equation system of the form xA = b.
The b from the equation xA = b.
The x from equation Ax = b.
Solves a linear equation system of the form Ax = b.
The b from the equation Ax = b.
The x from equation Ax = b.
Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Singular Value Decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the singular value decomposition
is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U * S * V'.
The singular values, sigma[k] = S[k,k], are ordered so that
sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will
never fail. The matrix condition number and the effective numerical
rank can be computed from this decomposition.
WARNING! Please be aware that if A has less rows than columns, it is better
to compute the decomposition on the transpose of A and then swap the left
and right eigenvectors. If the routine is computed on A directly, the diagonal
of singular values may contain one or more zeros. The identity A = U * S * V'
may still hold, however. To overcome this problem, pass true to the
autoTranspose
argument of the class constructor.
This routine computes the economy decomposition of A.
Returns the condition number max(S) / min(S).
Returns the singularity threshold.
Returns the Two norm.
Returns the effective numerical matrix rank.
Number of non-negligible singular values.
Gets whether the decomposed matrix is singular.
Gets the one-dimensional array of singular values.
Returns the block diagonal matrix of singular values.
Returns the V matrix of Singular Vectors.
Returns the U matrix of Singular Vectors.
Returns the ordering in which the singular values have been sorted.
Returns the absolute value of the matrix determinant.
Returns the log of the absolute value for the matrix determinant.
Returns the pseudo-determinant for the matrix.
Returns the log of the pseudo-determinant for the matrix.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Solves a linear equation system of the form xA = b.
The b from the equation xA = b.
The x from equation Ax = b.
Solves a linear equation system of the form Ax = b.
The b from the equation Ax = b.
The x from equation Ax = b.
Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Singular Value Decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the singular value decomposition
is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U * S * V'.
The singular values, sigma[k] = S[k,k], are ordered so that
sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will
never fail. The matrix condition number and the effective numerical
rank can be computed from this decomposition.
WARNING! Please be aware that if A has less rows than columns, it is better
to compute the decomposition on the transpose of A and then swap the left
and right eigenvectors. If the routine is computed on A directly, the diagonal
of singular values may contain one or more zeros. The identity A = U * S * V'
may still hold, however. To overcome this problem, pass true to the
autoTranspose
argument of the class constructor.
This routine computes the economy decomposition of A.
Returns the condition number max(S) / min(S).
Returns the singularity threshold.
Returns the Two norm.
Returns the effective numerical matrix rank.
Number of non-negligible singular values.
Gets whether the decomposed matrix is singular.
Gets the one-dimensional array of singular values.
Returns the block diagonal matrix of singular values.
Returns the V matrix of Singular Vectors.
Returns the U matrix of Singular Vectors.
Returns the ordering in which the singular values have been sorted.
Returns the absolute value of the matrix determinant.
Returns the log of the absolute value for the matrix determinant.
Returns the pseudo-determinant for the matrix.
Returns the log of the pseudo-determinant for the matrix.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form xA = b.
The b from the equation xA = b.
The x from equation Ax = b.
Solves a linear equation system of the form Ax = b.
The b from the equation Ax = b.
The x from equation Ax = b.
Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Singular Value Decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the singular value decomposition
is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U * S * V'.
The singular values, sigma[k] = S[k,k], are ordered so that
sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will
never fail. The matrix condition number and the effective numerical
rank can be computed from this decomposition.
WARNING! Please be aware that if A has less rows than columns, it is better
to compute the decomposition on the transpose of A and then swap the left
and right eigenvectors. If the routine is computed on A directly, the diagonal
of singular values may contain one or more zeros. The identity A = U * S * V'
may still hold, however. To overcome this problem, pass true to the
autoTranspose
argument of the class constructor.
This routine computes the economy decomposition of A.
Returns the condition number max(S) / min(S).
Returns the singularity threshold.
Returns the Two norm.
Returns the effective numerical matrix rank.
Number of non-negligible singular values.
Gets whether the decomposed matrix is singular.
Gets the one-dimensional array of singular values.
Returns the block diagonal matrix of singular values.
Returns the V matrix of Singular Vectors.
Returns the U matrix of Singular Vectors.
Returns the ordering in which the singular values have been sorted.
Returns the absolute value of the matrix determinant.
Returns the log of the absolute value for the matrix determinant.
Returns the pseudo-determinant for the matrix.
Returns the log of the pseudo-determinant for the matrix.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form xA = b.
The b from the equation xA = b.
The x from equation Ax = b.
Solves a linear equation system of the form Ax = b.
The b from the equation Ax = b.
The x from equation Ax = b.
Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Singular Value Decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the singular value decomposition
is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U * S * V'.
The singular values, sigma[k] = S[k,k], are ordered so that
sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will
never fail. The matrix condition number and the effective numerical
rank can be computed from this decomposition.
WARNING! Please be aware that if A has less rows than columns, it is better
to compute the decomposition on the transpose of A and then swap the left
and right eigenvectors. If the routine is computed on A directly, the diagonal
of singular values may contain one or more zeros. The identity A = U * S * V'
may still hold, however. To overcome this problem, pass true to the
autoTranspose
argument of the class constructor.
This routine computes the economy decomposition of A.
Returns the condition number max(S) / min(S).
Returns the singularity threshold.
Returns the Two norm.
Returns the effective numerical matrix rank.
Number of non-negligible singular values.
Gets whether the decomposed matrix is singular.
Gets the one-dimensional array of singular values.
Returns the block diagonal matrix of singular values.
Returns the V matrix of Singular Vectors.
Returns the U matrix of Singular Vectors.
Returns the ordering in which the singular values have been sorted.
Returns the absolute value of the matrix determinant.
Returns the log of the absolute value for the matrix determinant.
Returns the pseudo-determinant for the matrix.
Returns the log of the pseudo-determinant for the matrix.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Constructs a new singular value decomposition.
The matrix to be decomposed.
Pass if the left singular vector matrix U
should be computed. Pass otherwise. Default
is .
Pass if the right singular vector matrix V
should be computed. Pass otherwise. Default
is .
Pass to automatically transpose the value matrix in
case JAMA's assumptions about the dimensionality of the matrix are violated.
Pass otherwise. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form AX = B.
Parameter B from the equation AX = B.
The solution X from equation AX = B.
Solves a linear equation system of the form xA = b.
The b from the equation xA = b.
The x from equation Ax = b.
Solves a linear equation system of the form Ax = b.
The b from the equation Ax = b.
The x from equation Ax = b.
Computes the (pseudo-)inverse of the matrix given to the Singular value decomposition.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Contains numerical decompositions such as QR,
SVD, LU,
Cholesky, and
NMF with specialized definitions for most .NET data types: float, double, and decimals.
The namespace class diagram is shown below.
Determines the eigenvalues and eigenvectors of a real square matrix.
In the mathematical discipline of linear algebra, eigendecomposition
or sometimes spectral decomposition is the factorization of a matrix
into a canonical form, whereby the matrix is represented in terms of
its eigenvalues and eigenvectors.
If A is symmetric, then A = V * D * V' and A = V * V'
where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal.
If A is not symmetric, the eigenvalue matrix D is block diagonal
with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].
The columns of V represent the eigenvectors in the sense that A * V = V * D.
The matrix V may be badly conditioned, or even singular, so the validity of the equation
A = V * D * inverse(V) depends upon the condition of V.
Returns the effective numerical matrix rank.
Number of non-negligible eigen values.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Defines if the matrix should be assumed as being symmetric
regardless if it is or not. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Returns the real parts of the eigenvalues.
Returns the imaginary parts of the eigenvalues.
Returns the eigenvector matrix.
Returns the block diagonal eigenvalue matrix.
Reverses the decomposition, reconstructing the original matrix X.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Determines the eigenvalues and eigenvectors of a real square matrix.
In the mathematical discipline of linear algebra, eigendecomposition
or sometimes spectral decomposition is the factorization of a matrix
into a canonical form, whereby the matrix is represented in terms of
its eigenvalues and eigenvectors.
If A is symmetric, then A = V * D * V' and A = V * V'
where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal.
If A is not symmetric, the eigenvalue matrix D is block diagonal
with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].
The columns of V represent the eigenvectors in the sense that A * V = V * D.
The matrix V may be badly conditioned, or even singular, so the validity of the equation
A = V * D * inverse(V) depends upon the condition of V.
Returns the effective numerical matrix rank.
Number of non-negligible eigen values.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Defines if the matrix should be assumed as being symmetric
regardless if it is or not. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Returns the real parts of the eigenvalues.
Returns the imaginary parts of the eigenvalues.
Returns the eigenvector matrix.
Returns the block diagonal eigenvalue matrix.
Reverses the decomposition, reconstructing the original matrix X.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
QR decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the QR decomposition
is an m-by-n orthogonal matrix Q and an n-by-n upper triangular
matrix R so that A = Q * R.
The QR decomposition always exists, even if the matrix does not have
full rank, so the constructor will never fail. The primary use of the
QR decomposition is in the least squares solution of nonsquare systems
of simultaneous linear equations.
This will fail if returns .
Constructs a QR decomposition.
The matrix A to be decomposed.
True if the decomposition should be performed on
the transpose of A rather than A itself, false otherwise. Default is false.
True if the decomposition should be done in place,
overriding the given matrix . Default is false.
True to perform the economy decomposition, where only
.the information needed to solve linear systems is computed. If set to false,
the full QR decomposition will be computed.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Least squares solution of X * A = B
Right-hand-side matrix with as many columns as A and any number of rows.
A matrix that minimized the two norm of X * Q * R - B.
Matrix column dimensions must be the same.
Matrix is rank deficient.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Shows if the matrix A is of full rank.
The value is if R, and hence A, has full rank.
Returns the upper triangular factor R.
Returns the orthogonal factor Q.
Returns the diagonal of R.
Least squares solution of A * X = I
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
QR decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the QR decomposition
is an m-by-n orthogonal matrix Q and an n-by-n upper triangular
matrix R so that A = Q * R.
The QR decomposition always exists, even if the matrix does not have
full rank, so the constructor will never fail. The primary use of the
QR decomposition is in the least squares solution of nonsquare systems
of simultaneous linear equations.
This will fail if returns .
Constructs a QR decomposition.
The matrix A to be decomposed.
True if the decomposition should be performed on
the transpose of A rather than A itself, false otherwise. Default is false.
True if the decomposition should be done in place,
overriding the given matrix . Default is false.
True to perform the economy decomposition, where only
.the information needed to solve linear systems is computed. If set to false,
the full QR decomposition will be computed.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Least squares solution of X * A = B
Right-hand-side matrix with as many columns as A and any number of rows.
A matrix that minimized the two norm of X * Q * R - B.
Matrix column dimensions must be the same.
Matrix is rank deficient.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Shows if the matrix A is of full rank.
The value is if R, and hence A, has full rank.
Returns the upper triangular factor R.
Returns the orthogonal factor Q.
Returns the diagonal of R.
Least squares solution of A * X = I
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
QR decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the QR decomposition
is an m-by-n orthogonal matrix Q and an n-by-n upper triangular
matrix R so that A = Q * R.
The QR decomposition always exists, even if the matrix does not have
full rank, so the constructor will never fail. The primary use of the
QR decomposition is in the least squares solution of nonsquare systems
of simultaneous linear equations.
This will fail if returns .
Constructs a QR decomposition.
The matrix A to be decomposed.
True if the decomposition should be performed on
the transpose of A rather than A itself, false otherwise. Default is false.
True if the decomposition should be done in place,
overriding the given matrix . Default is false.
True to perform the economy decomposition, where only
.the information needed to solve linear systems is computed. If set to false,
the full QR decomposition will be computed.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Least squares solution of X * A = B
Right-hand-side matrix with as many columns as A and any number of rows.
A matrix that minimized the two norm of X * Q * R - B.
Matrix column dimensions must be the same.
Matrix is rank deficient.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Shows if the matrix A is of full rank.
The value is if R, and hence A, has full rank.
Returns the upper triangular factor R.
Returns the orthogonal factor Q.
Returns the diagonal of R.
Least squares solution of A * X = I
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
QR decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the QR decomposition
is an m-by-n orthogonal matrix Q and an n-by-n upper triangular
matrix R so that A = Q * R.
The QR decomposition always exists, even if the matrix does not have
full rank, so the constructor will never fail. The primary use of the
QR decomposition is in the least squares solution of nonsquare systems
of simultaneous linear equations.
This will fail if returns .
Constructs a QR decomposition.
The matrix A to be decomposed.
True if the decomposition should be performed on
the transpose of A rather than A itself, false otherwise. Default is false.
True if the decomposition should be done in place,
overriding the given matrix . Default is false.
True to perform the economy decomposition, where only
.the information needed to solve linear systems is computed. If set to false,
the full QR decomposition will be computed.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Least squares solution of X * A = B
Right-hand-side matrix with as many columns as A and any number of rows.
A matrix that minimized the two norm of X * Q * R - B.
Matrix column dimensions must be the same.
Matrix is rank deficient.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Shows if the matrix A is of full rank.
The value is if R, and hence A, has full rank.
Returns the upper triangular factor R.
Returns the (economy-size) orthogonal factor Q.
Returns the diagonal of R.
Least squares solution of A * X = I
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
QR decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the QR decomposition
is an m-by-n orthogonal matrix Q and an n-by-n upper triangular
matrix R so that A = Q * R.
The QR decomposition always exists, even if the matrix does not have
full rank, so the constructor will never fail. The primary use of the
QR decomposition is in the least squares solution of nonsquare systems
of simultaneous linear equations.
This will fail if returns .
Constructs a QR decomposition.
The matrix A to be decomposed.
True if the decomposition should be performed on
the transpose of A rather than A itself, false otherwise. Default is false.
True if the decomposition should be done in place,
overriding the given matrix . Default is false.
True to perform the economy decomposition, where only
.the information needed to solve linear systems is computed. If set to false,
the full QR decomposition will be computed.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Least squares solution of X * A = B
Right-hand-side matrix with as many columns as A and any number of rows.
A matrix that minimized the two norm of X * Q * R - B.
Matrix column dimensions must be the same.
Matrix is rank deficient.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Shows if the matrix A is of full rank.
The value is if R, and hence A, has full rank.
Returns the upper triangular factor R.
Returns the (economy-size) orthogonal factor Q.
Returns the diagonal of R.
Least squares solution of A * X = I
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
QR decomposition for a rectangular matrix.
For an m-by-n matrix A with m >= n, the QR decomposition
is an m-by-n orthogonal matrix Q and an n-by-n upper triangular
matrix R so that A = Q * R.
The QR decomposition always exists, even if the matrix does not have
full rank, so the constructor will never fail. The primary use of the
QR decomposition is in the least squares solution of nonsquare systems
of simultaneous linear equations.
This will fail if returns .
Constructs a QR decomposition.
The matrix A to be decomposed.
True if the decomposition should be performed on
the transpose of A rather than A itself, false otherwise. Default is false.
True if the decomposition should be done in place,
overriding the given matrix . Default is false.
True to perform the economy decomposition, where only
.the information needed to solve linear systems is computed. If set to false,
the full QR decomposition will be computed.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Least squares solution of X * A = B
Right-hand-side matrix with as many columns as A and any number of rows.
A matrix that minimized the two norm of X * Q * R - B.
Matrix column dimensions must be the same.
Matrix is rank deficient.
Least squares solution of A * X = B
Right-hand-side matrix with as many rows as A and any number of columns.
A matrix that minimized the two norm of Q * R * X - B.
Matrix row dimensions must be the same.
Matrix is rank deficient.
Shows if the matrix A is of full rank.
The value is if R, and hence A, has full rank.
Returns the upper triangular factor R.
Returns the (economy-size) orthogonal factor Q.
Returns the diagonal of R.
Least squares solution of A * X = I
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Cholesky Decomposition of a symmetric, positive definite matrix.
For a symmetric, positive definite matrix A, the Cholesky decomposition is a
lower triangular matrix L so that A = L * L'.
If the matrix is not positive definite, the constructor returns a partial
decomposition and sets two internal variables that can be queried using the
and properties.
Any square matrix A with non-zero pivots can be written as the product of a
lower triangular matrix L and an upper triangular matrix U; this is called
the LU decomposition. However, if A is symmetric and positive definite, we
can choose the factors such that U is the transpose of L, and this is called
the Cholesky decomposition. Both the LU and the Cholesky decomposition are
used to solve systems of linear equations.
When it is applicable, the Cholesky decomposition is twice as efficient
as the LU decomposition.
Constructs a new Cholesky Decomposition.
The symmetric matrix, given in upper triangular form, to be decomposed.
True to perform a square-root free LDLt decomposition, false otherwise.
True to perform the decomposition in place, storing the factorization in the
lower triangular part of the given matrix.
How to interpret the matrix given to be decomposed. Using this parameter, a lower or
upper-triangular matrix can be interpreted as a symmetric matrix by assuming both lower
and upper parts contain the same elements. Use this parameter in conjunction with inPlace
to save memory by storing the original matrix and its decomposition at the same memory
location (lower part will contain the decomposition's L matrix, upper part will contains
the original matrix).
Gets whether the decomposed matrix was positive definite.
Gets a value indicating whether the LDLt factorization
has been computed successfully or if it is undefined.
true if the factorization is not defined; otherwise, false.
Gets the left (lower) triangular factor
L so that A = L * D * L'.
Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
Gets the determinant of the decomposed matrix.
If the matrix is positive-definite, gets the
log-determinant of the decomposed matrix.
Gets a value indicating whether the decomposed
matrix is non-singular (i.e. invertible).
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * X = I.
Computes the diagonal of the inverse of the decomposed matrix.
Computes the diagonal of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
The array to hold the result of the
computation. Should be of same length as the the diagonal
of the original matrix.
Computes the trace of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new Cholesky decomposition directly from
an already computed left triangular matrix L.
The left triangular matrix from a Cholesky decomposition.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Cholesky Decomposition of a symmetric, positive definite matrix.
For a symmetric, positive definite matrix A, the Cholesky decomposition is a
lower triangular matrix L so that A = L * L'.
If the matrix is not positive definite, the constructor returns a partial
decomposition and sets two internal variables that can be queried using the
and properties.
Any square matrix A with non-zero pivots can be written as the product of a
lower triangular matrix L and an upper triangular matrix U; this is called
the LU decomposition. However, if A is symmetric and positive definite, we
can choose the factors such that U is the transpose of L, and this is called
the Cholesky decomposition. Both the LU and the Cholesky decomposition are
used to solve systems of linear equations.
When it is applicable, the Cholesky decomposition is twice as efficient
as the LU decomposition.
Constructs a new Cholesky Decomposition.
The symmetric matrix, given in upper triangular form, to be decomposed.
True to perform a square-root free LDLt decomposition, false otherwise.
True to perform the decomposition in place, storing the factorization in the
lower triangular part of the given matrix.
How to interpret the matrix given to be decomposed. Using this parameter, a lower or
upper-triangular matrix can be interpreted as a symmetric matrix by assuming both lower
and upper parts contain the same elements. Use this parameter in conjunction with inPlace
to save memory by storing the original matrix and its decomposition at the same memory
location (lower part will contain the decomposition's L matrix, upper part will contains
the original matrix).
Gets whether the decomposed matrix was positive definite.
Gets a value indicating whether the LDLt factorization
has been computed successfully or if it is undefined.
true if the factorization is not defined; otherwise, false.
Gets the left (lower) triangular factor
L so that A = L * D * L'.
Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
Gets the determinant of the decomposed matrix.
If the matrix is positive-definite, gets the
log-determinant of the decomposed matrix.
Gets a value indicating whether the decomposed
matrix is non-singular (i.e. invertible).
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * X = I.
Computes the diagonal of the inverse of the decomposed matrix.
Computes the diagonal of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
The array to hold the result of the
computation. Should be of same length as the the diagonal
of the original matrix.
Computes the trace of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new Cholesky decomposition directly from
an already computed left triangular matrix L.
The left triangular matrix from a Cholesky decomposition.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Cholesky Decomposition of a symmetric, positive definite matrix.
For a symmetric, positive definite matrix A, the Cholesky decomposition is a
lower triangular matrix L so that A = L * L'.
If the matrix is not positive definite, the constructor returns a partial
decomposition and sets two internal variables that can be queried using the
and properties.
Any square matrix A with non-zero pivots can be written as the product of a
lower triangular matrix L and an upper triangular matrix U; this is called
the LU decomposition. However, if A is symmetric and positive definite, we
can choose the factors such that U is the transpose of L, and this is called
the Cholesky decomposition. Both the LU and the Cholesky decomposition are
used to solve systems of linear equations.
When it is applicable, the Cholesky decomposition is twice as efficient
as the LU decomposition.
Constructs a new Cholesky Decomposition.
The symmetric matrix, given in upper triangular form, to be decomposed.
True to perform a square-root free LDLt decomposition, false otherwise.
True to perform the decomposition in place, storing the factorization in the
lower triangular part of the given matrix.
How to interpret the matrix given to be decomposed. Using this parameter, a lower or
upper-triangular matrix can be interpreted as a symmetric matrix by assuming both lower
and upper parts contain the same elements. Use this parameter in conjunction with inPlace
to save memory by storing the original matrix and its decomposition at the same memory
location (lower part will contain the decomposition's L matrix, upper part will contains
the original matrix).
Gets whether the decomposed matrix was positive definite.
Gets a value indicating whether the LDLt factorization
has been computed successfully or if it is undefined.
true if the factorization is not defined; otherwise, false.
Gets the left (lower) triangular factor
L so that A = L * D * L'.
Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
Gets the determinant of the decomposed matrix.
If the matrix is positive-definite, gets the
log-determinant of the decomposed matrix.
Gets a value indicating whether the decomposed
matrix is non-singular (i.e. invertible).
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * X = I.
Computes the diagonal of the inverse of the decomposed matrix.
Computes the diagonal of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
The array to hold the result of the
computation. Should be of same length as the the diagonal
of the original matrix.
Computes the trace of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new Cholesky decomposition directly from
an already computed left triangular matrix L.
The left triangular matrix from a Cholesky decomposition.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Determines the eigenvalues and eigenvectors of a real square matrix.
In the mathematical discipline of linear algebra, eigendecomposition
or sometimes spectral decomposition is the factorization of a matrix
into a canonical form, whereby the matrix is represented in terms of
its eigenvalues and eigenvectors.
If A is symmetric, then A = V * D * V' and A = V * V'
where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal.
If A is not symmetric, the eigenvalue matrix D is block diagonal
with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].
The columns of V represent the eigenvectors in the sense that A * V = V * D.
The matrix V may be badly conditioned, or even singular, so the validity of the equation
A = V * D * inverse(V) depends upon the condition of V.
Returns the effective numerical matrix rank.
Number of non-negligible eigen values.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Defines if the matrix should be assumed as being symmetric
regardless if it is or not. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Returns the real parts of the eigenvalues.
Returns the imaginary parts of the eigenvalues.
Returns the eigenvector matrix.
Returns the block diagonal eigenvalue matrix.
Reverses the decomposition, reconstructing the original matrix X.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Determines the eigenvalues and eigenvectors of a real square matrix.
In the mathematical discipline of linear algebra, eigendecomposition
or sometimes spectral decomposition is the factorization of a matrix
into a canonical form, whereby the matrix is represented in terms of
its eigenvalues and eigenvectors.
If A is symmetric, then A = V * D * V' and A = V * V'
where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal.
If A is not symmetric, the eigenvalue matrix D is block diagonal
with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].
The columns of V represent the eigenvectors in the sense that A * V = V * D.
The matrix V may be badly conditioned, or even singular, so the validity of the equation
A = V * D * inverse(V) depends upon the condition of V.
Returns the effective numerical matrix rank.
Number of non-negligible eigen values.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Construct an eigenvalue decomposition.
The matrix to be decomposed.
Defines if the matrix should be assumed as being symmetric
regardless if it is or not. Default is .
Pass to perform the decomposition in place. The matrix
will be destroyed in the process, resulting in less
memory comsumption.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Returns the real parts of the eigenvalues.
Returns the imaginary parts of the eigenvalues.
Returns the eigenvector matrix.
Returns the block diagonal eigenvalue matrix.
Reverses the decomposition, reconstructing the original matrix X.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Gram-Schmidt Orthogonalization.
Initializes a new instance of the class.
The matrix A to be decomposed.
Initializes a new instance of the class.
The matrix A to be decomposed.
True to use modified Gram-Schmidt; false
otherwise. Default is true (and is the recommended setup).
Returns the orthogonal factor matrix Q.
Returns the upper triangular factor matrix R.
LU decomposition of a jagged rectangular matrix.
For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
unit lower triangular matrix L, an n-by-n upper triangular matrix U,
and a permutation vector piv of length m so that A(piv) = L*U.
If m < n, then L is m-by-m and U is m-by-n.
The LU decomposition with pivoting always exists, even if the matrix is
singular, so the constructor will never fail. The primary use of the
LU decomposition is in the solution of square systems of simultaneous
linear equations. This will fail if returns
.
If you need to compute a LU decomposition for matrices with data types other than
double, see , . If you
need to compute a LU decomposition for a multidimensional matrix, see ,
, and .
-
http://en.wikipedia.org/wiki/Generalized_eigenvalue_problem#Generalized_eigenvalue_problem
-
http://www.netlib.org/eispack/
// Suppose we have the following
// matrices A and B shown below:
double[,] A =
{
{ 1, 2, 3},
{ 8, 1, 4},
{ 3, 2, 3}
};
double[,] B =
{
{ 5, 1, 1},
{ 1, 5, 1},
{ 1, 1, 5}
};
// Now, suppose we would like to find values for λ
// that are solutions for the equation det(A - λB) = 0
// For this, we can use a Generalized Eigendecomposition
var gevd = new GeneralizedEigenvalueDecomposition(A, B);
// Now, if A and B are Hermitian and B is positive
// -definite, then the eigenvalues λ will be real:
double[] lambda = gevd.RealEigenvalues;
// Lets check if they are indeed a solution:
for (int i = 0; i < lambda.Length; i++)
{
// Compute the determinant equation show above
double det = Matrix.Determinant(A.Subtract(lambda[i].Multiply(B))); // almost zero
}
Constructs a new generalized eigenvalue decomposition.
The first matrix of the (A,B) matrix pencil.
The second matrix of the (A,B) matrix pencil.
Pass to sort the eigenvalues and eigenvectors at the end
of the decomposition.
Returns the real parts of the alpha values.
Returns the imaginary parts of the alpha values.
Returns the beta values.
Returns true if matrix B is singular.
This method checks if any of the generated betas is zero. It
does not says that the problem is singular, but only that one
of the matrices of the pencil (A,B) is singular.
Returns true if the eigenvalue problem is degenerate (ill-posed).
Returns the real parts of the eigenvalues.
The eigenvalues are computed using the ratio alpha[i]/beta[i],
which can lead to valid, but infinite eigenvalues.
Returns the imaginary parts of the eigenvalues.
The eigenvalues are computed using the ratio alpha[i]/beta[i],
which can lead to valid, but infinite eigenvalues.
Returns the eigenvector matrix.
Returns the block diagonal eigenvalue matrix.
Adaptation of the original Fortran QZHES routine from EISPACK.
This subroutine is the first step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart.
This subroutine accepts a pair of real general matrices and
reduces one of them to upper Hessenberg form and the other
to upper triangular form using orthogonal transformations.
it is usually followed by qzit, qzval and, possibly, qzvec.
For the full documentation, please check the original function.
Adaptation of the original Fortran QZIT routine from EISPACK.
This subroutine is the second step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart,
as modified in technical note nasa tn d-7305(1973) by ward.
This subroutine accepts a pair of real matrices, one of them
in upper Hessenberg form and the other in upper triangular form.
it reduces the Hessenberg matrix to quasi-triangular form using
orthogonal transformations while maintaining the triangular form
of the other matrix. it is usually preceded by qzhes and
followed by qzval and, possibly, qzvec.
For the full documentation, please check the original function.
Adaptation of the original Fortran QZVAL routine from EISPACK.
This subroutine is the third step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart.
This subroutine accepts a pair of real matrices, one of them
in quasi-triangular form and the other in upper triangular form.
it reduces the quasi-triangular matrix further, so that any
remaining 2-by-2 blocks correspond to pairs of complex
Eigenvalues, and returns quantities whose ratios give the
generalized eigenvalues. it is usually preceded by qzhes
and qzit and may be followed by qzvec.
For the full documentation, please check the original function.
Adaptation of the original Fortran QZVEC routine from EISPACK.
This subroutine is the optional fourth step of the qz algorithm
for solving generalized matrix eigenvalue problems,
Siam J. Numer. anal. 10, 241-256(1973) by Moler and Stewart.
This subroutine accepts a pair of real matrices, one of them in
quasi-triangular form (in which each 2-by-2 block corresponds to
a pair of complex eigenvalues) and the other in upper triangular
form. It computes the eigenvectors of the triangular problem and
transforms the results back to the original coordinate system.
it is usually preceded by qzhes, qzit, and qzval.
For the full documentation, please check the original function.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Cholesky Decomposition of a symmetric, positive definite matrix.
For a symmetric, positive definite matrix A, the Cholesky decomposition is a
lower triangular matrix L so that A = L * L'.
If the matrix is not positive definite, the constructor returns a partial
decomposition and sets two internal variables that can be queried using the
and properties.
Any square matrix A with non-zero pivots can be written as the product of a
lower triangular matrix L and an upper triangular matrix U; this is called
the LU decomposition. However, if A is symmetric and positive definite, we
can choose the factors such that U is the transpose of L, and this is called
the Cholesky decomposition. Both the LU and the Cholesky decomposition are
used to solve systems of linear equations.
When it is applicable, the Cholesky decomposition is twice as efficient
as the LU decomposition.
Constructs a new Cholesky Decomposition.
The symmetric matrix, given in upper triangular form, to be decomposed.
True to perform a square-root free LDLt decomposition, false otherwise.
True to perform the decomposition in place, storing the factorization in the
lower triangular part of the given matrix.
How to interpret the matrix given to be decomposed. Using this parameter, a lower or
upper-triangular matrix can be interpreted as a symmetric matrix by assuming both lower
and upper parts contain the same elements. Use this parameter in conjunction with inPlace
to save memory by storing the original matrix and its decomposition at the same memory
location (lower part will contain the decomposition's L matrix, upper part will contains
the original matrix).
Gets whether the decomposed matrix was positive definite.
Gets a value indicating whether the LDLt factorization
has been computed successfully or if it is undefined.
true if the factorization is not defined; otherwise, false.
Gets the left (lower) triangular factor
L so that A = L * D * L'.
Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
Gets the determinant of the decomposed matrix.
If the matrix is positive-definite, gets the
log-determinant of the decomposed matrix.
Gets a value indicating whether the decomposed
matrix is non-singular (i.e. invertible).
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Solves a set of equation systems of type A * X = I.
Computes the diagonal of the inverse of the decomposed matrix.
Computes the diagonal of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
The array to hold the result of the
computation. Should be of same length as the the diagonal
of the original matrix.
Computes the trace of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new Cholesky decomposition directly from
an already computed left triangular matrix L.
The left triangular matrix from a Cholesky decomposition.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Cholesky Decomposition of a symmetric, positive definite matrix.
For a symmetric, positive definite matrix A, the Cholesky decomposition is a
lower triangular matrix L so that A = L * L'.
If the matrix is not positive definite, the constructor returns a partial
decomposition and sets two internal variables that can be queried using the
and properties.
Any square matrix A with non-zero pivots can be written as the product of a
lower triangular matrix L and an upper triangular matrix U; this is called
the LU decomposition. However, if A is symmetric and positive definite, we
can choose the factors such that U is the transpose of L, and this is called
the Cholesky decomposition. Both the LU and the Cholesky decomposition are
used to solve systems of linear equations.
When it is applicable, the Cholesky decomposition is twice as efficient
as the LU decomposition.
Constructs a new Cholesky Decomposition.
The symmetric matrix, given in upper triangular form, to be decomposed.
True to perform a square-root free LDLt decomposition, false otherwise.
True to perform the decomposition in place, storing the factorization in the
lower triangular part of the given matrix.
How to interpret the matrix given to be decomposed. Using this parameter, a lower or
upper-triangular matrix can be interpreted as a symmetric matrix by assuming both lower
and upper parts contain the same elements. Use this parameter in conjunction with inPlace
to save memory by storing the original matrix and its decomposition at the same memory
location (lower part will contain the decomposition's L matrix, upper part will contains
the original matrix).
Gets whether the decomposed matrix was positive definite.
Gets a value indicating whether the LDLt factorization
has been computed successfully or if it is undefined.
true if the factorization is not defined; otherwise, false.
Gets the left (lower) triangular factor
L so that A = L * D * L'.
Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
Gets the determinant of the decomposed matrix.
If the matrix is positive-definite, gets the
log-determinant of the decomposed matrix.
Gets a value indicating whether the decomposed
matrix is non-singular (i.e. invertible).
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Solves a set of equation systems of type A * X = I.
Computes the diagonal of the inverse of the decomposed matrix.
Computes the diagonal of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
The array to hold the result of the
computation. Should be of same length as the the diagonal
of the original matrix.
Computes the trace of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new Cholesky decomposition directly from
an already computed left triangular matrix L.
The left triangular matrix from a Cholesky decomposition.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Cholesky Decomposition of a symmetric, positive definite matrix.
For a symmetric, positive definite matrix A, the Cholesky decomposition is a
lower triangular matrix L so that A = L * L'.
If the matrix is not positive definite, the constructor returns a partial
decomposition and sets two internal variables that can be queried using the
and properties.
Any square matrix A with non-zero pivots can be written as the product of a
lower triangular matrix L and an upper triangular matrix U; this is called
the LU decomposition. However, if A is symmetric and positive definite, we
can choose the factors such that U is the transpose of L, and this is called
the Cholesky decomposition. Both the LU and the Cholesky decomposition are
used to solve systems of linear equations.
When it is applicable, the Cholesky decomposition is twice as efficient
as the LU decomposition.
Constructs a new Cholesky Decomposition.
The symmetric matrix, given in upper triangular form, to be decomposed.
True to perform a square-root free LDLt decomposition, false otherwise.
True to perform the decomposition in place, storing the factorization in the
lower triangular part of the given matrix.
How to interpret the matrix given to be decomposed. Using this parameter, a lower or
upper-triangular matrix can be interpreted as a symmetric matrix by assuming both lower
and upper parts contain the same elements. Use this parameter in conjunction with inPlace
to save memory by storing the original matrix and its decomposition at the same memory
location (lower part will contain the decomposition's L matrix, upper part will contains
the original matrix).
Gets whether the decomposed matrix was positive definite.
Gets a value indicating whether the LDLt factorization
has been computed successfully or if it is undefined.
true if the factorization is not defined; otherwise, false.
Gets the left (lower) triangular factor
L so that A = L * D * L'.
Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
Gets the determinant of the decomposed matrix.
If the matrix is positive-definite, gets the
log-determinant of the decomposed matrix.
Gets a value indicating whether the decomposed
matrix is non-singular (i.e. invertible).
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * X = B.
Right hand side matrix with as many rows as A and any number of columns.
Matrix X so that L * L' * X = B.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
Solves a set of equation systems of type A * x = b.
Right hand side column vector with as many rows as A.
Vector x so that L * L' * x = b.
Matrix dimensions do not match.
Matrix is not symmetric.
Matrix is not positive-definite.
True to compute the solving in place, false otherwise.
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
Diagonal fo the right hand side matrix with as many rows as A.
Matrix X so that L * U * X = B.
Solves a set of equation systems of type A * X = I.
Computes the diagonal of the inverse of the decomposed matrix.
Computes the diagonal of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
The array to hold the result of the
computation. Should be of same length as the the diagonal
of the original matrix.
Computes the trace of the inverse of the decomposed matrix.
True to conserve memory by reusing the
same space used to hold the decomposition, thus destroying
it in the process. Pass false otherwise.
Reverses the decomposition, reconstructing the original matrix X.
Computes (Xt * X)^1 (the inverse of the covariance matrix). This
matrix can be used to determine standard errors for the coefficients when
solving a linear set of equations through any of the
methods.
Creates a new Cholesky decomposition directly from
an already computed left triangular matrix L.
The left triangular matrix from a Cholesky decomposition.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
LU decomposition of a jagged rectangular matrix.
For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
unit lower triangular matrix L, an n-by-n upper triangular matrix U,
and a permutation vector piv of length m so that A(piv) = L*U.
If m < n, then L is m-by-m and U is m-by-n.
The LU decomposition with pivoting always exists, even if the matrix is
singular, so the constructor will never fail. The primary use of the
LU decomposition is in the solution of square systems of simultaneous
linear equations. This will fail if returns
.
If you need to compute a LU decomposition for matrices with data types other than
double, see , . If you
need to compute a LU decomposition for a multidimensional matrix, see ,
, and .
-
http://en.wikipedia.org/wiki/Non-negative_matrix_factorization
-
Lee, D., Seung, H., 1999. Learning the Parts of Objects by Non-Negative
Matrix Factorization. Nature 401, 788–791.
-
Michael W. Berry, et al. (June 2006). Algorithms and Applications for
Approximate Nonnegative Matrix Factorization.
Gets the nonnegative factor matrix W.
Gets the nonnegative factor matrix H.
Initializes a new instance of the NMF algorithm
The input data matrix (must be positive).
The reduced dimension.
Initializes a new instance of the NMF algorithm
The input data matrix (must be positive).
The reduced dimension.
The number of iterations to perform.
Performs NMF using the multiplicative method
The maximum number of iterations
At the end of the computation H contains the projected data
and W contains the weights. The multiplicative method is the
simplest factorization method.
Static class Distance. Defines a set of methods defining distance measures.
Static class Distance. Defines a set of extension methods defining distance measures.
Gets the Yule distance between two points.
The first point x.
The second point y.
The Yule distance between x and y.
For examples, please see documentation page.
Gets the Yule distance between two points.
The first point x.
The second point y.
The Yule distance between x and y.
For examples, please see documentation page.
Gets the Jaccard distance between two points.
The first point x.
The second point y.
The Jaccard distance between x and y.
For examples, please see documentation page.
Gets the Hellinger distance between two points.
The first point x.
The second point y.
The Hellinger distance between x and y.
For examples, please see documentation page.
Gets the Euclidean distance between two points.
The first point x.
The second point y.
The Euclidean distance between x and y.
For examples, please see documentation page.
Gets the Euclidean distance between two points.
The first point x.
The second point y.
The Euclidean distance between x and y.
For examples, please see documentation page.
Gets the Euclidean distance between two points.
The Euclidean distance between x and y.
For examples, please see documentation page.
Gets the Euclidean distance between two points.
The first point x.
The second point y.
The Euclidean distance between x and y.
For examples, please see documentation page.
Gets the Euclidean distance between two points.
The first point x.
The second point y.
The Euclidean distance between x and y.
For examples, please see documentation page.
Gets the SquareMahalanobis distance between two points.
The first point x.
The second point y.
The SquareMahalanobis distance between x and y.
For examples, please see documentation page.
Gets the SquareMahalanobis distance between two points.
The first point x.
The second point y.
The SquareMahalanobis distance between x and y.
For examples, please see documentation page.
Gets the SquareMahalanobis distance between two points.
The first point x.
The second point y.
The SquareMahalanobis distance between x and y.
For examples, please see documentation page.
Gets the SquareMahalanobis distance between two points.
The first point x.
The second point y.
The SquareMahalanobis distance between x and y.
For examples, please see documentation page.
Gets the RusselRao distance between two points.
The first point x.
The second point y.
The RusselRao distance between x and y.
For examples, please see documentation page.
Gets the RusselRao distance between two points.
The first point x.
The second point y.
The RusselRao distance between x and y.
For examples, please see documentation page.
Gets the Chebyshev distance between two points.
The first point x.
The second point y.
The Chebyshev distance between x and y.
For examples, please see documentation page.
Gets the Dice distance between two points.
The first point x.
The second point y.
The Dice distance between x and y.
For examples, please see documentation page.
Gets the Dice distance between two points.
The first point x.
The second point y.
The Dice distance between x and y.
For examples, please see documentation page.
Gets the SokalMichener distance between two points.
The first point x.
The second point y.
The SokalMichener distance between x and y.
For examples, please see documentation page.
Gets the SokalMichener distance between two points.
The first point x.
The second point y.
The SokalMichener distance between x and y.
For examples, please see documentation page.
Gets the WeightedEuclidean distance between two points.
The first point x.
The second point y.
The WeightedEuclidean distance between x and y.
For examples, please see documentation page.
Gets the WeightedEuclidean distance between two points.
The first point x.
The second point y.
The WeightedEuclidean distance between x and y.
For examples, please see documentation page.
Gets the WeightedEuclidean distance between two points.
The first point x.
The second point y.
The WeightedEuclidean distance between x and y.
For examples, please see documentation page.
Gets the Angular distance between two points.
The first point x.
The second point y.
The Angular distance between x and y.
For examples, please see documentation page.
Gets the SquareEuclidean distance between two points.
The first point x.
The second point y.
The SquareEuclidean distance between x and y.
For examples, please see documentation page.
Gets the SquareEuclidean distance between two points.
The first point x.
The second point y.
The SquareEuclidean distance between x and y.
For examples, please see documentation page.
Gets the SquareEuclidean distance between two points.
The first point x.
The second point y.
The SquareEuclidean distance between x and y.
For examples, please see documentation page.
Gets the SquareEuclidean distance between two points.
The SquareEuclidean distance between x and y.
For examples, please see documentation page.
Gets the Hamming distance between two points.
The first point x.
The second point y.
The Hamming distance between x and y.
For examples, please see documentation page.
Gets the Hamming distance between two points.
The first point x.
The second point y.
The Hamming distance between x and y.
For examples, please see documentation page.
Gets the Hamming distance between two points.
The first point x.
The second point y.
The Hamming distance between x and y.
For examples, please see documentation page.
Gets the Hamming distance between two points.
The first point x.
The second point y.
The Hamming distance between x and y.
For examples, please see documentation page.
Gets the ArgMax distance between two points.
The first point x.
The second point y.
The ArgMax distance between x and y.
For examples, please see documentation page.
Gets the Modular distance between two points.
The first point x.
The second point y.
The Modular distance between x and y.
For examples, please see documentation page.
Gets the Modular distance between two points.
The first point x.
The second point y.
The Modular distance between x and y.
For examples, please see documentation page.
Gets the Modular distance between two points.
The first point x.
The second point y.
The Modular distance between x and y.
For examples, please see documentation page.
Gets the Modular distance between two points.
The first point x.
The second point y.
The Modular distance between x and y.
For examples, please see documentation page.
Gets the Cosine distance between two points.
The first point x.
The second point y.
The Cosine distance between x and y.
For examples, please see documentation page.
Gets the Mahalanobis distance between two points.
The first point x.
The second point y.
The Mahalanobis distance between x and y.
For examples, please see documentation page.
Gets the Mahalanobis distance between two points.
The first point x.
The second point y.
The Mahalanobis distance between x and y.
For examples, please see documentation page.
Gets the Mahalanobis distance between two points.
The first point x.
The second point y.
The Mahalanobis distance between x and y.
For examples, please see documentation page.
Gets the Mahalanobis distance between two points.
The first point x.
The second point y.
The Mahalanobis distance between x and y.
For examples, please see documentation page.
Gets the BrayCurtis distance between two points.
The first point x.
The second point y.
The BrayCurtis distance between x and y.
For examples, please see documentation page.
Gets the Minkowski distance between two points.
The first point x.
The second point y.
The Minkowski distance between x and y.
For examples, please see documentation page.
Gets the Minkowski distance between two points.
The first point x.
The second point y.
The Minkowski distance between x and y.
For examples, please see documentation page.
Gets the Minkowski distance between two points.
The first point x.
The second point y.
The Minkowski distance between x and y.
For examples, please see documentation page.
Gets the Minkowski distance between two points.
The first point x.
The second point y.
The Minkowski distance between x and y.
For examples, please see documentation page.
Gets the Levenshtein distance between two points.
The first point x.
The second point y.
The Levenshtein distance between x and y.
For examples, please see documentation page.
Gets the SokalSneath distance between two points.
The first point x.
The second point y.
The SokalSneath distance between x and y.
For examples, please see documentation page.
Gets the SokalSneath distance between two points.
The first point x.
The second point y.
The SokalSneath distance between x and y.
For examples, please see documentation page.
Gets the Matching distance between two points.
The first point x.
The second point y.
The Matching distance between x and y.
For examples, please see documentation page.
Gets the Matching distance between two points.
The first point x.
The second point y.
The Matching distance between x and y.
For examples, please see documentation page.
Gets the Canberra distance between two points.
The first point x.
The second point y.
The Canberra distance between x and y.
For examples, please see documentation page.
Gets the RogersTanimoto distance between two points.
The first point x.
The second point y.
The RogersTanimoto distance between x and y.
For examples, please see documentation page.
Gets the RogersTanimoto distance between two points.
The first point x.
The second point y.
The RogersTanimoto distance between x and y.
For examples, please see documentation page.
Gets the Manhattan distance between two points.
The first point x.
The second point y.
The Manhattan distance between x and y.
For examples, please see documentation page.
Gets the Manhattan distance between two points.
The first point x.
The second point y.
The Manhattan distance between x and y.
For examples, please see documentation page.
Gets the Kulczynski distance between two points.
The first point x.
The second point y.
The Kulczynski distance between x and y.
For examples, please see documentation page.
Gets the Kulczynski distance between two points.
The first point x.
The second point y.
The Kulczynski distance between x and y.
For examples, please see documentation page.
Gets the WeightedSquareEuclidean distance between two points.
The first point x.
The second point y.
The WeightedSquareEuclidean distance between x and y.
For examples, please see documentation page.
Gets the WeightedSquareEuclidean distance between two points.
The first point x.
The second point y.
The WeightedSquareEuclidean distance between x and y.
For examples, please see documentation page.
Gets the WeightedSquareEuclidean distance between two points.
The first point x.
The second point y.
The WeightedSquareEuclidean distance between x and y.
For examples, please see documentation page.
Checks whether a function is a real metric distance, i.e. respects
the triangle inequality. Please note that a function can still pass
this test and not respect the triangle inequality.
Checks whether a function is a real metric distance, i.e. respects
the triangle inequality. Please note that a function can still pass
this test and not respect the triangle inequality.
Checks whether a function is a real metric distance, i.e. respects
the triangle inequality. Please note that a function can still pass
this test and not respect the triangle inequality.
Gets the a object implementing a
particular method of the static class.
This method is intended to be used in scenarios where you have been using any
of the static methods in the class, but now you would like
to obtain a reference to an object that implements the same distance you have been
using before, but in a object-oriented, polymorphic manner. Please see the example
below for more details.
Note: This method relies on reflection and might not work
on all scenarios, environments, and/or platforms.
The type of the elements being compared in the distance function.
The method of .
An object of the class that implements the given distance.
-
https://en.wikipedia.org/wiki/Jaccard_index
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Gets a similarity measure between two points.
The first point to be compared.
The second point to be compared.
A similarity measure between x and y.
ArgMax distance (L0) distance.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Matching dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Rogers-Tanimoto dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Russel-Rao dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Sokal-Michener dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Sokal-Sneath dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Kulczynski dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Yule dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Dice dissimilarity.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Hamming distance.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Jaccard (Index) distance.
The Jaccard index, also known as the Jaccard similarity coefficient (originally
coined coefficient de communauté by Paul Jaccard), is a statistic used for comparing
the similarity and diversity of sample sets. The Jaccard coefficient measures
similarity between finite sample sets, and is defined as the size of the intersection
divided by the size of the union of the sample sets.
References:
-
https://en.wikipedia.org/wiki/Jaccard_index
The type of the elements in the arrays to be compared.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Gets a similarity measure between two points.
The first point to be compared.
The second point to be compared.
A similarity measure between x and y.
Herlinger distance.
In probability and statistics, the Hellinger distance (also called
Bhattacharyya distance as this was originally introduced by Anil Kumar
Bhattacharya) is used to quantify the similarity between two probability
distributions. It is a type of f-divergence. The Hellinger distance is
defined in terms of the Hellinger integral, which was introduced by Ernst
Hellinger in 1909.
References:
-
https://en.wikipedia.org/wiki/Hellinger_distance
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Canberra distance.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Chebyshev distance.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Levenshtein distance.
In information theory and computer science, the Levenshtein distance is a
string metric for measuring the difference between two sequences. Informally,
the Levenshtein distance between two words is the minimum number of single-character
edits (i.e. insertions, deletions or substitutions) required to change one
word into the other. It is named after Vladimir Levenshtein, who considered
this distance in 1965.
Levenshtein distance may also be referred to as edit distance, although that
may also denote a larger family of distance metrics. It is closely related to
pairwise string alignments.
References:
-
https://en.wikipedia.org/wiki/Levenshtein_distance
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Mahalanobis distance.
-
http://crsouza.com/2009/09/modulo-and-modular-distance-in-c
Gets the maximum value that the distance can
have before it wraps around in the circle.
Initializes a new instance of the class.
The maximum value that the distance can
have before it wraps around in the circle (i.e. 360).
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
The Minkowski distance is a metric in a normed vector space which can be
considered as a generalization of both the Euclidean
distance and the Manhattan distance.
The framework distinguishes between metrics and distances by using different
types for them. This makes it possible to let the compiler figure out logic
problems such as the specification of a non-metric for a method that requires
a proper metric (i.e. that respects the triangle inequality).
The objective of this technique is to make it harder to make some mistakes.
However, it is possible to bypass this mechanism by using the named constructors
such as to create distances implementing the
interface that are not really metrics. Use at your own risk.
Gets the order p of this Minkowski distance.
Initializes a new instance of the class.
The Minkowski order p.
The Minkowski distance is not a metric for p < 1.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Creates a non-metric Minkowski distance, bypassing
argument checking. Use at your own risk.
The Minkowski order p.
A Minkowski object implementing a Minkowski distance
that is not necessarily a metric. Use at your own risk.
Gets the distance as a special
case of the distance.
Gets the distance as a special
case of the distance.
Hamming distance.
The type of the elements to be compared.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Levenshtein distance.
In information theory and computer science, the Levenshtein distance is a
string metric for measuring the difference between two sequences. Informally,
the Levenshtein distance between two words is the minimum number of single-character
edits (i.e. insertions, deletions or substitutions) required to change one
word into the other. It is named after Vladimir Levenshtein, who considered
this distance in 1965.
Levenshtein distance may also be referred to as edit distance, although that
may also denote a larger family of distance metrics. It is closely related to
pairwise string alignments.
References:
-
https://en.wikipedia.org/wiki/Levenshtein_distance
The type of elements in the string. Default is char.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Manhattan (also known as Taxicab or L1) distance.
Taxicab geometry, considered by Hermann Minkowski in 19th century Germany,
is a form of geometry in which the usual distance function of metric or
Euclidean geometry is replaced by a new metric in which the distance between
two points is the sum of the absolute differences of their Cartesian
coordinates. The taxicab metric is also known as rectilinear distance, L1
distance or L1 norm (see Lp space), city block distance, Manhattan distance,
or Manhattan length, with corresponding variations in the name of the geometry.
The latter names allude to the grid layout of most streets on the island of
Manhattan, which causes the shortest path a car could take between two intersections
in the borough to have length equal to the intersections' distance in taxicab
geometry.
References:
-
https://en.wikipedia.org/wiki/Taxicab_geometry
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Bray-Curtis distance.
Computes the distance d(x,y) between points
and .
The first point x.
The second point y.
A double-precision value representing the distance d(x,y)
between and according
to the distance function implemented by this class.
Squared Mahalanobis distance.
Introduction
Declaring and using matrices in the Accord.NET Framework does
not requires much. In fact, it does not require anything else
that is not already present at the .NET Framework. If you have
already existing and working code using other libraries, you
don't have to convert your matrices to any special format used
by Accord.NET. This is because Accord.NET is built to interoperate
with other libraries and existing solutions, relying solely on
default .NET structures to work.
To begin, please add the following using directive on
top of your .cs (or equivalent) source code file:
using Accord.Math;
This is all you need to start using the Accord.NET matrix library.
Creating matrices
Let's start by declaring a matrix, or otherwise specifying matrices
from other sources. The most straightforward way to declare a matrix
in Accord.NET is simply using:
double[,] matrix =
{
{ 1, 2 },
{ 3, 4 },
{ 5, 6 },
};
Yep, that is right. You don't need to create any fancy custom Matrix
classes or vectors to make Accord.NET work, which is a plus if you
have already existent code using other libraries. You are also free
to use both the multidimensional matrix syntax above or the jagged
matrix syntax below:
double[][] matrix =
{
new double[] { 1, 2 },
new double[] { 3, 4 },
new double[] { 5, 6 },
};
Special purpose matrices can also be created through specialized methods.
Those include
// Creates a vector of indices
int[] idx = Matrix.Indices(0, 10); // { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
// Creates a step vector within a given interval
double[] interval = Matrix.Interval(from: -2, to: 4); // { -2, -1, 0, 1, 2, 3, 4 };
// Special matrices
double[,] I = Matrix.Identity(3); // creates a 3x3 identity matrix
double[,] magic = Matrix.Magic(5); // creates a magic square matrix of size 5
double[] v = Matrix.Vector(5, 1.0); // generates { 1, 1, 1, 1, 1 }
double[,] diagonal = Matrix.Diagonal(v); // matrix with v on its diagonal
Another way to declare matrices is by parsing the contents of a string:
string str = @"1 2
3 4";
double[,] matrix = Matrix.Parse(str);
You can even read directly from matrices formatted in C# syntax:
string str = @"double[,] matrix =
{
{ 1, 2 },
{ 3, 4 },
{ 5, 6 },
}";
double[,] multid = Matrix.Parse(str, CSharpMatrixFormatProvider.InvariantCulture);
double[,] jagged = Matrix.ParseJagged(str, CSharpMatrixFormatProvider.InvariantCulture);
And even from Octave-compatible syntax!
string str = "[1 2; 3 4]";
double[,] matrix = Matrix.Parse(str, OctaveMatrixFormatProvider.InvariantCulture);
There are also other methods, such as specialization for arrays and other formats.
For more details, please take a look on ,
, ,
and .
Matrix operations
Albeit being simple matrices, the framework leverages
.NET extension methods to support all basic matrix operations. For instance,
consider the elementwise operations (also known as dot operations in Octave):
double[] vector = { 0, 2, 4 };
double[] a = vector.ElementwiseMultiply(2); // vector .* 2, generates { 0, 4, 8 }
double[] b = vector.ElementwiseDivide(2); // vector ./ 2, generates { 0, 1, 2 }
double[] c = vector.ElementwisePower(2); // vector .^ 2, generates { 0, 4, 16 }
Operations between vectors, matrices, and both are also completely supported:
// Declare two vectors
double[] u = { 1, 6, 3 };
double[] v = { 9, 4, 2 };
// Products between vectors
double inner = u.InnerProduct(v); // 39.0
double[,] outer = u.OuterProduct(v); // see below
double[] kronecker = u.KroneckerProduct(v); // { 9, 4, 2, 54, 24, 12, 27, 12, 6 }
double[][] cartesian = u.CartesianProduct(v); // all possible pair-wise combinations
/* outer =
{
{ 9, 4, 2 },
{ 54, 24, 12 },
{ 27, 12, 6 },
}; */
// Addition
double[] addv = u.Add(v); // { 10, 10, 5 }
double[] add5 = u.Add(5); // { 6, 11, 8 }
// Elementwise operations
double[] abs = u.Abs(); // { 1, 6, 3 }
double[] log = u.Log(); // { 0, 1.79, 1.09 }
// Apply *any* function to all elements in a vector
double[] cos = u.Apply(Math.Cos); // { 0.54, 0.96, -0.989 }
u.ApplyInPlace(Math.Cos); // can also do optionally in-place
// Declare a matrix
double[,] M =
{
{ 0, 5, 2 },
{ 2, 1, 5 }
};
// Extract a subvector from v:
double[] vcut = v.Submatrix(0, 1); // { 9, 4 }
// Some operations between vectors and matrices
double[] Mv = m.Multiply(v); // { 24, 32 }
double[] vM = vcut.Multiply(m); // { 8, 49, 38 }
// Some operations between matrices
double[,] Md = m.MultiplyByDiagonal(v); // { { 0, 20, 4 }, { 18, 4, 10 } }
double[,] MMt = m.MultiplyByTranspose(m); // { { 29, 15 }, { 15, 30 } }
Please note this is by no means an extensive list; please take a look on
all members available on this class or (preferably) use IntelliSense to
navigate through all possible options when trying to perform an operation.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two vectors contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two vectors contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two vectors contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two vectors contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
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Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines whether two matrices contain the same values.
Determines whether two matrices contain the same values.
Determines whether two vectors contain the same values.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Determines a matrix is symmetric.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Gets the inner product (scalar product) between two vectors (a'*b).
A vector.
A vector.
The inner product of the multiplication of the vectors.
In mathematics, the dot product is an algebraic operation that takes two
equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and adding up
those products. The name is derived from the dot that is often used to designate
this operation; the alternative name scalar product emphasizes the scalar
(rather than vector) nature of the result.
The principal use of this product is the inner product in a Euclidean vector space:
when two vectors are expressed on an orthonormal basis, the dot product of their
coordinate vectors gives their inner product.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product A*b of a matrix A and a column vector b.
The left matrix A.
The right vector b.
The product A*b of the given matrix A and vector b.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product a*B of a row vector a and a matrix B.
The left vector a.
The right matrix B.
The product a*B of the given vector a and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of two matrices A and B.
The left matrix A.
The right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product A*b' of matrix A and transpose of b.
The left matrix A.
The right vector b.
The product A*B' of the given matrix A and vector b.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product a*B' of row vector a and transpose of B.
The left vector a.
The transposed right matrix B.
The product a*B' of the given vector a and matrix B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A*B' of matrix A and transpose of B.
The left matrix A.
The transposed right matrix B.
The product A*B' of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product a'*B of column vector a and B.
The column vector a.
The right matrix B.
The product a'*B of the given vector a and matrix B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A'*B of transposed of matrix A and B.
The transposed left matrix A.
The right matrix B.
The product A'*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The product A*B of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The product A*B of the given matrices A and B.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the inner product (dot product) between two vectors (a*bT).
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The Kronecker product of the two vectors.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The Kronecker product of the two matrices.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product a*B*c of a row vector a,
a square matrix B and a column vector c.
The left vector a.
The square matrix B.
The column vector c.
The product a*B*c of the given vector a,
matrix B and vector c.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Multiplies a row vector v and a matrix A,
giving the product v'*A.
The row vector v.
The matrix A.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Multiplies a matrix A and a column vector v,
giving the product A*v
The matrix A.
The column vector v.
The matrix R to store the product.
Computes the product R = A*B of two matrices A
and B, storing the result in matrix R.
The left matrix A.
The right matrix B.
The matrix R to store the product.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A*B' of matrix A and
transpose of B, storing the result in matrix R.
The left matrix A.
The transposed right matrix B.
The matrix R to store the product R = A*B'
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*B of matrix A transposed and matrix B.
The transposed left matrix A.
The right matrix B.
The matrix R to store the product R = A'*B
of the given matrices A and B.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*b of matrix A transposed and column vector b.
The transposed left matrix A.
The right column vector b.
The vector r to store the product r = A'*b
of the given matrix A and vector b.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A'*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*B of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Computes the product A*inv(B) of matrix A and diagonal matrix B.
The left matrix A.
The diagonal vector of inverse right matrix B.
The matrix R to store the product R = A*B
of the given matrices A and B.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Gets the outer product (matrix product) between two vectors (a*bT).
In linear algebra, the outer product typically refers to the tensor
product of two vectors. The result of applying the outer product to
a pair of vectors is a matrix. The name contrasts with the inner product,
which takes as input a pair of vectors and produces a scalar.
Vector product.
The cross product, vector product or Gibbs vector product is a binary operation
on two vectors in three-dimensional space. It has a vector result, a vector which
is always perpendicular to both of the vectors being multiplied and the plane
containing them. It has many applications in mathematics, engineering and physics.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two matrices.
The left matrix a.
The right matrix b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two matrices.
Computes the Kronecker product between two vectors.
The left vector a.
The right vector b.
The matrix R to store the
Kronecker product between matrices A and B.
The Kronecker product of the two vectors.
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The value to which matrix elements will be set.
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The value to which matrix elements will be set.
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Start column index
End column index
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Start column index
End column index
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Start column index
End column index
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of column indices.
Start row index
End row index
Returns a sub matrix extracted from the current matrix.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of column indices.
Start row index
End row index
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Start column index
End column index
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Starting row index
End row index
Array of column indices
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Starting row index
End row index
Array of column indices
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Starting row index
End row index
Starting column index
End column index
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Starting row index
End row index
Starting column index
End column index
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Array of column indices
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Array of column indices
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Array of column indices
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of row indices
Array of column indices
Sets a region of a matrix to the given values.
The matrix where elements will be set.
The matrix of values to which matrix elements will be set.
Array of indices.
Sets a subvector to the given value.
The vector to return the subvector from.
The matrix of values to which matrix elements will be set.
Starting index.
End index.
Sets a subvector to the given value.
The vector to return the subvector from.
The matrix of values to which matrix elements will be set.
The index of the element to be set.
Sets a subvector to the given value.
The vector to return the subvector from.
The matrix of values to which matrix elements will be set.
Array of indices.
Returns the solution matrix if the matrix is square or the least squares solution otherwise.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Double[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side matrix b:
Double[,] rightSide = { {1}, {2}, {3} };
// Solve the linear system Ax = b by finding x:
Double[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { {-1/18}, {2/18}, {5/18} }.
Returns the solution matrix if the matrix is square or the least squares solution otherwise.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Double[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side vector b:
Double[] rightSide = { 1, 2, 3 };
// Solve the linear system Ax = b by finding x:
Double[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { -1/18, 2/18, 5/18 }.
Computes the inverse of a matrix.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Double[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side matrix b:
Double[,] rightSide = { {1}, {2}, {3} };
// Solve the linear system Ax = b by finding x:
Double[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { {-1/18}, {2/18}, {5/18} }.
Returns the solution matrix if the matrix is square or the least squares solution otherwise.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Double[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side vector b:
Double[] rightSide = { 1, 2, 3 };
// Solve the linear system Ax = b by finding x:
Double[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { -1/18, 2/18, 5/18 }.
Returns the solution matrix for a linear system involving a diagonal matrix ion the right-hand side.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
Creates a matrix decomposition that be used to compute the solution matrix if the
matrix is square or the least squares solution otherwise.
Creates a matrix decomposition that be used to compute the solution matrix if the
matrix is square or the least squares solution otherwise.
Computes the inverse of a matrix.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Single[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side matrix b:
Single[,] rightSide = { {1}, {2}, {3} };
// Solve the linear system Ax = b by finding x:
Single[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { {-1/18}, {2/18}, {5/18} }.
Returns the solution matrix if the matrix is square or the least squares solution otherwise.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Single[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side vector b:
Single[] rightSide = { 1, 2, 3 };
// Solve the linear system Ax = b by finding x:
Single[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { -1/18, 2/18, 5/18 }.
Computes the inverse of a matrix.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Single[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side matrix b:
Single[,] rightSide = { {1}, {2}, {3} };
// Solve the linear system Ax = b by finding x:
Single[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { {-1/18}, {2/18}, {5/18} }.
Returns the solution matrix if the matrix is square or the least squares solution otherwise.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Single[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side vector b:
Single[] rightSide = { 1, 2, 3 };
// Solve the linear system Ax = b by finding x:
Single[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { -1/18, 2/18, 5/18 }.
Returns the solution matrix for a linear system involving a diagonal matrix ion the right-hand side.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
Creates a matrix decomposition that be used to compute the solution matrix if the
matrix is square or the least squares solution otherwise.
Creates a matrix decomposition that be used to compute the solution matrix if the
matrix is square or the least squares solution otherwise.
Computes the inverse of a matrix.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Decimal[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side matrix b:
Decimal[,] rightSide = { {1}, {2}, {3} };
// Solve the linear system Ax = b by finding x:
Decimal[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { {-1/18}, {2/18}, {5/18} }.
Returns the solution matrix if the matrix is square or the least squares solution otherwise.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Decimal[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side vector b:
Decimal[] rightSide = { 1, 2, 3 };
// Solve the linear system Ax = b by finding x:
Decimal[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { -1/18, 2/18, 5/18 }.
Computes the inverse of a matrix.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Decimal[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side matrix b:
Decimal[,] rightSide = { {1}, {2}, {3} };
// Solve the linear system Ax = b by finding x:
Decimal[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { {-1/18}, {2/18}, {5/18} }.
Returns the solution matrix if the matrix is square or the least squares solution otherwise.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.
Decimal[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};
// Define a right side vector b:
Decimal[] rightSide = { 1, 2, 3 };
// Solve the linear system Ax = b by finding x:
Decimal[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
// The answer should be { -1/18, 2/18, 5/18 }.
Returns the solution matrix for a linear system involving a diagonal matrix ion the right-hand side.
The matrix for the linear problem.
The right side b.
True to produce a solution even if the
is singular; false otherwise. Default is false.
Please note that this does not check if the matrix is non-singular
before attempting to solve. If a least squares solution is desired
in case the matrix is singular, pass true to the
parameter when calling this function.
Creates a matrix decomposition that be used to compute the solution matrix if the
matrix is square or the least squares solution otherwise.
Creates a matrix decomposition that be used to compute the solution matrix if the
matrix is square or the least squares solution otherwise.
Computes the inverse of a matrix.
// The Mesh method can be used to generate all
// possible (x,y) pairs between two ranges.
// We can create a grid as
double[][] grid = Matrix.Mesh
(
rowMin: 0, rowMax: 1, rowSteps: 10,
colMin: 0, colMax: 1, colSteps: 5
);
// Now we can plot the points on-screen
ScatterplotBox.Show("Grid (fixed steps)", grid).Hold();
The resulting image is shown below.
Creates a bi-dimensional mesh matrix.
// The Mesh method can be used to generate all
// possible (x,y) pairs between two ranges.
// We can create a grid as
double[][] grid = Matrix.Mesh
(
rowMin: 0, rowMax: 1, rowSteps: 10,
colMin: 0, colMax: 1, colSteps: 5
);
// Now we can plot the points on-screen
ScatterplotBox.Show("Grid (fixed steps)", grid).Hold();
The resulting image is shown below.
Obsolete. Please specify the number of steps instead of the step size for the rows and columns.
Creates a bi-dimensional mesh matrix.
The values to be replicated vertically.
The values to be replicated horizontally.
// The Mesh method generates all possible (x,y) pairs
// between two vector of points. For example, let's
// suppose we have the values:
//
double[] a = { 0, 1 };
double[] b = { 0, 1 };
// We can create a grid as
double[][] grid = a.Mesh(b);
// the result will be:
double[][] expected =
{
new double[] { 0, 0 },
new double[] { 0, 1 },
new double[] { 1, 0 },
new double[] { 1, 1 },
};
Generates a 2-D mesh grid from two vectors a and b,
generating two matrices len(a) x len(b) with all
all possible combinations of values between the two vectors. This
method is analogous to MATLAB/Octave's meshgrid function.
A tuple containing two matrices: the first containing values
for the x-coordinates and the second for the y-coordinates.
// The MeshGrid method generates two matrices that can be
// used to generate all possible (x,y) pairs between two
// vector of points. For example, let's suppose we have
// the values:
//
double[] a = { 1, 2, 3 };
double[] b = { 4, 5, 6 };
// We can create a grid
var grid = a.MeshGrid(b);
// get the x-axis values // | 1 1 1 |
double[,] x = grid.Item1; // x = | 2 2 2 |
// | 3 3 3 |
// get the y-axis values // | 4 5 6 |
double[,] y = grid.Item2; // y = | 4 5 6 |
// | 4 5 6 |
// we can either use those matrices separately (such as for plotting
// purposes) or we can also generate a grid of all the (x,y) pairs as
//
double[,][] xy = x.ApplyWithIndex((v, i, j) => new[] { x[i, j], y[i, j] });
// The result will be
//
// | (1, 4) (1, 5) (1, 6) |
// xy = | (2, 4) (2, 5) (2, 6) |
// | (3, 4) (3, 5) (3, 6) |
Combines two vectors horizontally.
Combines a vector and a element horizontally.
Combines a vector and a element horizontally.
Combines a matrix and a vector horizontally.
Combines two matrices horizontally.
Combines two matrices horizontally.
Combines a matrix and a vector horizontally.
Combines a matrix and a vector horizontally.
Combine vectors horizontally.
Combines vectors vertically.
Combines vectors vertically.
Combines vectors vertically.
Combines vectors vertically.
Combines vectors vertically.
Combines matrices vertically.
Combines matrices vertically.
Combines matrices vertically.
Expands a data vector given in summary form.
A base vector.
An array containing by how much each line should be replicated.
Expands a data matrix given in summary form.
A base matrix.
An array containing by how much each line should be replicated.
Splits a given vector into a smaller vectors of the given size.
This operation can be reverted using .
The vector to be splitted.
The size of the resulting vectors.
An array of vectors containing the subdivisions of the given vector.
Merges a series of vectors into a single vector. This
operation can be reverted using .
The vectors to be merged.
The size of the inner vectors.
A single array containing the given vectors.
Merges a series of vectors into a single vector. This
operation can be reverted using .
The vectors to be merged.
A single array containing the given vectors.
Pads a matrix by filling all of its sides with zeros.
The matrix whose contents will be padded.
How many rows and columns to add at each side of the matrix.
The original matrix with an extra row of zeros at the selected places.
Pads a matrix by filling all of its sides with zeros.
The matrix whose contents will be padded.
How many columns to add at the sides of the matrix.
How many rows to add at the bottom and top of the matrix.
The original matrix with an extra row of zeros at the selected places.
Pads a matrix by filling all of its sides with zeros.
The matrix whose contents will be padded.
How many rows to add at the bottom.
How many rows to add at the top.
How many columns to add at the sides.
The original matrix with an extra row of zeros at the selected places.
Pads a matrix by filling all of its sides with zeros.
The matrix whose contents will be padded.
How many rows to add at the bottom.
How many rows to add at the top.
How many columns to add at the left side.
How many columns to add at the right side.
The original matrix with an extra row of zeros at the selected places.
Transforms a vector into a matrix of given dimensions.
Transforms a vector into a matrix of given dimensions.
Returns a representation of a given matrix.
The matrix.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
If set to true, the matrix will be written using multiple
lines. If set to false, the matrix will be written in a
single line.
The to be used
when creating the resulting string. Default is to use
.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
The to be used
when creating the resulting string. Default is to use
.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
The format to use when creating the resulting string.
The to be used
when creating the resulting string. Default is to use
.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
The format to use when creating the resulting string.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
The to be used
when creating the resulting string. Default is to use
.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
The format to use when creating the resulting string.
The to be used
when creating the resulting string. Default is to use
.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a given matrix.
The matrix.
The format to use when creating the resulting string.
A that represents this instance.
Please see ,
, ,
, or
for more details.
Returns a representation of a a given array.
The array.
A that represents this instance.
Please see ,
or
for examples and more details.
Returns a representation of a a given array.
The array.
A that represents this instance.
Please see ,
or
for examples and more details.
Returns a representation of a a given array.
The array.
A that represents this instance.
Please see ,
or
for examples and more details.
Returns a representation of a a given array.
The array.
The to be used
when creating the resulting string. Default is to use
.
A that represents this instance.
Please see ,
or
for examples and more details.
Returns a representation of a a given array.
The matrix.
The format to use when creating the resulting string.
The to be used
when creating the resulting string. Default is to use
.
A that represents this instance.
Please see ,
or
for examples and more details.
Returns a representation of a a given array.
The array.
The format to use when creating the resulting string.
A that represents this instance.
Please see ,
or
for examples and more details.
Converts the string representation of a matrix to its
double-precision floating-point number matrix equivalent.
The string representation of the matrix.
A double-precision floating-point number matrix parsed
from the given string using the given format provider.
Converts the string representation of a matrix to its
double-precision floating-point number matrix equivalent.
The string representation of the matrix.
The format provider to use in the conversion. Default is to use
.
A double-precision floating-point number matrix parsed
from the given string using the given format provider.
Converts the string representation of a matrix to its
double-precision floating-point number matrix equivalent.
The string representation of the matrix.
The format provider to use in the conversion. Default is to use
.
A double-precision floating-point number matrix parsed
from the given string using the given format provider.
Converts the string representation of a matrix to its
double-precision floating-point number matrix equivalent.
A return value indicates whether the conversion succeeded or failed.
The string representation of the matrix.
The format provider to use in the conversion. Default is to use
.
A double-precision floating-point number matrix parsed
from the given string using the given format provider.
When this method returns, contains the double-precision floating-point
number matrix equivalent to the parameter, if the conversion succeeded,
or null if the conversion failed. The conversion fails if the parameter
is null, is not a matrix in a valid format, or contains elements which represent
a number less than MinValue or greater than MaxValue. This parameter is passed
uninitialized.
Converts the string representation of a matrix to its
double-precision floating-point number matrix equivalent.
A return value indicates whether the conversion succeeded or failed.
The string representation of the matrix.
The format provider to use in the conversion. Default is to use
.
A double-precision floating-point number matrix parsed
from the given string using the given format provider.
When this method returns, contains the double-precision floating-point
number matrix equivalent to the parameter, if the conversion succeeded,
or null if the conversion failed. The conversion fails if the parameter
is null, is not a matrix in a valid format, or contains elements which represent
a number less than MinValue or greater than MaxValue. This parameter is passed
uninitialized.
Elementwise absolute value.
Elementwise absolute value.
Elementwise absolute value.
Elementwise absolute value.
Elementwise absolute value.
Elementwise Square root.
Elementwise Square root.
Elementwise Log operation.
Elementwise Exp operation.
Elementwise Exp operation.
Elementwise Log operation.
Elementwise Log operation.
Elementwise power operation.
Elementwise power operation.
Elementwise divide operation.
Elementwise divide operation.
Elementwise divide operation.
Elementwise division.
Elementwise division.
Elementwise multiply operation.
Elementwise multiply operation.
Elementwise multiply operation.
Elementwise multiply operation.
Elementwise multiplication.
Elementwise multiplication.
Elementwise multiplication.
Converts a jagged-array into a multidimensional array.
Converts a jagged-array into a multidimensional array.
Converts an array into a multidimensional array.
Obsolete.
Converts an array into a multidimensional array.
Converts a multidimensional array into a jagged array.
Obsolete.
Converts the values of a vector using the given converter expression.
The type of the input.
The type of the output.
The vector to be converted.
Converts the values of a vector using the given converter expression.
The type of the input.
The type of the output.
The vector to be converted.
The converter function.
Converts the values of a matrix using the given converter expression.
The type of the input.
The type of the output.
The matrix to be converted.
The converter function.
Converts the values of a matrix using the given converter expression.
The type of the input.
The type of the output.
The vector to be converted.
The converter function.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
The type of the output.
The vector or array to be converted.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
The vector or array to be converted.
The type of the output.
Gets the value at the specified position in the multidimensional System.Array.
The indexes are specified as an array of 32-bit integers.
A jagged or multidimensional array.
If set to true, internal arrays in jagged arrays will be followed.
A one-dimensional array of 32-bit integers that represent the
indexes specifying the position of the System.Array element to get.
Gets the value at the specified position in the multidimensional System.Array.
The indexes are specified as an array of 32-bit integers.
A jagged or multidimensional array.
If set to true, internal arrays in jagged arrays will be followed.
A one-dimensional array of 32-bit integers that represent the
indexes specifying the position of the System.Array element to get.
The value retrieved from the array.
Sets a value to the element at the specified position in the multidimensional
or jagged System.Array. The indexes are specified as an array of 32-bit integers.
A jagged or multidimensional array.
The new value for the specified element.
If set to true, internal arrays in jagged arrays will be followed.
A one-dimensional array of 32-bit integers that represent
the indexes specifying the position of the element to set.
Creates a vector containing every index that can be used to
address a given , in order.
The array whose indices will be returned.
Pass true to retrieve all dimensions of the array,
even if it contains nested arrays (as in jagged matrices).
Bases computations on the maximum length possible for
each dimension (in case the jagged matrices has different lengths).
An enumerable object that can be used to iterate over all
positions of the given System.Array.
double[,] a =
{
{ 5.3, 2.3 },
{ 4.2, 9.2 }
};
foreach (int[] idx in a.GetIndices())
{
// Get the current element
double e = (double)a.GetValue(idx);
}
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts a DataTable to a double[,] array.
Converts an array of values into a ,
attempting to guess column types by inspecting the data.
The values to be converted.
A containing the given values.
// Specify some data in a table format
//
object[,] data =
{
{ "Id", "IsSmoker", "Age" },
{ 0, 1, 10 },
{ 1, 1, 15 },
{ 2, 0, 40 },
{ 3, 1, 20 },
{ 4, 0, 70 },
{ 5, 0, 55 },
};
// Create a new table with the data
DataTable dataTable = data.ToTable();
Converts an array of values into a ,
attempting to guess column types by inspecting the data.
The values to be converted.
The column names to use in the data table.
A containing the given values.
// Specify some data in a table format
//
object[,] data =
{
{ "Id", "IsSmoker", "Age" },
{ 0, 1, 10 },
{ 1, 1, 15 },
{ 2, 0, 40 },
{ 3, 1, 20 },
{ 4, 0, 70 },
{ 5, 0, 55 },
};
// Create a new table with the data
DataTable dataTable = data.ToTable();
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataTable to a double[][] array.
Converts a DataColumn to a double[] array.
Converts a DataColumn to a double[] array.
Converts a DataColumn to a double[] array.
Converts a DataColumn to a double[] array.
Converts a DataColumn to a double[] array.
Converts a DataColumn to a double[] array.
Converts a DataColumn to a generic array.
Converts a DataColumn to a generic array.
Converts a DataTable to a generic array.
Converts a DataTable to a generic array.
Converts a DataColumn to a int[] array.
Converts a DataTable to a int[][] array.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Obsolete. Please use the method instead.
Normalizes a vector to have unit length.
A vector.
A norm to use. Default is .
True to perform the operation in-place,
overwriting the original array; false to return a new array.
A multiple of vector a where ||a|| = 1.
Normalizes a vector to have unit length.
A vector.
A norm to use. Default is .
True to perform the operation in-place,
overwriting the original array; false to return a new array.
A multiple of vector a where ||a|| = 1.
Normalizes a vector to have unit length.
A vector.
True to perform the operation in-place,
overwriting the original array; false to return a new array.
A multiple of vector a where ||a|| = 1.
Normalizes a vector to have unit length.
A vector.
True to perform the operation in-place,
overwriting the original array; false to return a new array.
A multiple of vector a where ||a|| = 1.
Multiplies a matrix by itself n times.
Computes the Cartesian product of many sets.
References:
- http://blogs.msdn.com/b/ericlippert/archive/2010/06/28/computing-a-Cartesian-product-with-linq.aspx
Computes the Cartesian product of many sets.
Computes the Cartesian product of two sets.
Returns a sub matrix extracted from the current matrix.
The matrix to return the submatrix from.
Array of row indices. Pass null to select all indices.
Array of column indices. Pass null to select all indices.
Gets a column vector from a matrix.
Gets a column vector from a matrix.
Gets a column vector from a matrix.
Gets a column vector from a matrix.
Gets a row vector from a matrix.
Gets a row vector from a matrix.
Gets a row vector from a matrix.
Gets a row vector from a matrix.
Gets a column vector from a matrix.
Gets a column vector from a matrix.
Stores a column vector into the given column position of the matrix.
Stores a column vector into the given column position of the matrix.
Stores a column vector into the given column position of the matrix.
Stores a row vector into the given row position of the matrix.
Stores a row vector into the given row position of the matrix.
Stores a row vector into the given row position of the matrix.
Returns a new matrix without one of its columns.
Returns a new matrix without one of its columns.
Returns a new matrix with a new column vector inserted at the end of the original matrix.
Returns a new matrix with a new column vector inserted at the end of the original matrix.
Returns a new matrix with a given column vector inserted at the end of the original matrix.
Returns a new matrix with a given column vector inserted at the end of the original matrix.
Returns a new matrix with a given column vector inserted at the end of the original matrix.
Returns a new matrix with a given column vector inserted at the end of the original matrix.
Returns a new matrix with a given column vector inserted at the end of the original matrix.
Returns a new matrix with a given row vector inserted at the end of the original matrix.
Returns a new matrix with a given row vector inserted at the end of the original matrix.
Returns a new matrix with a new row vector inserted at the end of the original matrix.
Returns a new matrix with a new row vector inserted at the end of the original matrix.
Returns a new matrix with a given column vector inserted at a given index.
Returns a new matrix with a given column vector inserted at a given index.
Returns a new matrix with a given column vector inserted at a given index.
Returns a new matrix with a given column vector inserted at a given index.
Returns a new matrix with a given column vector inserted at a given index.
Returns a new matrix with a given row vector inserted at a given index.
Returns a new matrix with a given row vector inserted at a given index.
Returns a new matrix with a given row vector inserted at a given index.
Returns a new matrix without one of its rows.
Removes an element from a vector.
Gets the number of elements matching a certain criteria.
The type of the array.
The array to search inside.
The search criteria.
Gets the indices of the first element matching a certain criteria.
The type of the array.
The array to search inside.
The search criteria.
Gets the indices of the first element matching a certain criteria, or null if the element could not be found.
The type of the array.
The array to search inside.
The search criteria.
Searches for the specified value and returns the index of the first occurrence within the array.
The type of the array.
The array to search.
The value to be searched.
The index of the searched value within the array, or -1 if not found.
Gets the indices of all elements matching a certain criteria.
The type of the array.
The array to search inside.
The search criteria.
Gets the indices of all elements matching a certain criteria.
The type of the array.
The array to search inside.
The search criteria.
Set to true to stop when the first element is
found, set to false to get all elements.
Gets the indices of all elements matching a certain criteria.
The type of the array.
The array to search inside.
The search criteria.
Gets the indices of all elements matching a certain criteria.
The type of the array.
The array to search inside.
The search criteria.
Set to true to stop when the first element is
found, set to false to get all elements.
Removes all elements in the array that are equal to the given .
The values.
The value to be removed.
Performs an in-place re-ordering of elements in
a given array using the given vector of indices.
The values to be ordered.
The new index positions.
Swaps the contents of two object references.
Swaps two elements in an array, given their indices.
The array whose elements will be swapped.
The index of the first element to be swapped.
The index of the second element to be swapped.
Retrieves a list of the distinct values for each matrix column.
The matrix.
An array containing arrays of distinct values for
each column in the .
Retrieves a list of the distinct values for each matrix column.
The matrix.
An array containing arrays of distinct values for
each column in the .
Retrieves only distinct values contained in an array.
The array.
An array containing only the distinct values in .
Retrieves only distinct values contained in an array.
The array.
Whether to allow null values in
the method's output. Default is true.
An array containing only the distinct values in .
Retrieves only distinct values contained in an array.
The array.
The property of the object used to determine distinct instances.
An array containing only the distinct values in .
Gets the number of distinct values
present in each column of a matrix.
Gets the number of distinct values
present in each column of a matrix.
Gets the number of distinct values
present in each column of a matrix.
Sorts the columns of a matrix by sorting keys.
The key value for each column.
The matrix to be sorted.
-
Wikipedia contributors. "Loss function." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 18 Mar. 2016. Web.
The type for the predicted score values.
The type for the loss value. Default is double.
Computes the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The actual values that have been predicted.
The loss value between the expected values and
the actual predicted values.
Common interface for differentiable loss functions, such as ,
, and
.
Computes the derivative of the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The actual values that have been predicted.
The expected values that should have been predicted.
The loss value between the expected values and
the actual predicted values.
Computes the derivative of the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The actual values that have been predicted.
The expected values that should have been predicted.
The loss value between the expected values and
the actual predicted values.
Common interface for loss functions, such as
, and
.
In mathematical optimization, statistics, decision theory and machine learning, a loss
function or cost function is a function that maps an event or values of one or more
variables onto a real number intuitively representing some "cost" associated with the
event. An optimization problem seeks to minimize a loss function. An objective function
is either a loss function or its negative (sometimes called a reward function, a profit
function, a utility function, a fitness function, etc.), in which case it is to be
maximized.
References:
-
Wikipedia contributors. "Loss function." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 18 Mar. 2016. Web.
The type for the expected data.
Logistic loss.
Gets the expected outputs (the ground truth).
Initializes a new instance of the class.
The expected outputs (ground truth).
Initializes a new instance of the class.
The expected outputs (ground truth).
Initializes a new instance of the class.
The expected outputs (ground truth).
Computes the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The actual values that have been predicted.
The loss value between the expected values and
the actual predicted values.
Computes the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The actual values that have been predicted.
The loss value between the expected values and
the actual predicted values.
Computes the derivative of the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The expected values that should have been predicted.
The actual values that have been predicted.
The loss value between the expected values and
the actual predicted values.
Computes the derivative of the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The expected values that should have been predicted.
The actual values that have been predicted.
The loss value between the expected values and
the actual predicted values.
Computes the derivative of the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The expected values that should have been predicted.
The actual values that have been predicted.
The loss value between the expected values and
the actual predicted values.
Computes the derivative of the loss between the expected values (ground truth)
and the given actual values that have been predicted.
The expected values that should have been predicted.
The actual values that have been predicted.
The loss value between the expected values and
the actual predicted values.
R² (r-squared) loss.
The coefficient of determination is used in the context of statistical models
whose main purpose is the prediction of future outcomes on the basis of other
related information. It is the proportion of variability in a data set that
is accounted for by the statistical model. It provides a measure of how well
future outcomes are likely to be predicted by the model.
The R² coefficient of determination is a statistical measure of how well the
regression line approximates the real data points. An R² of 1.0 indicates
that the regression line perfectly fits the data.
References:
-
Wikipedia contributors. Coefficient of determination. Wikipedia, The Free Encyclopedia.
September 6, 2017, 19:48 UTC. Available at: https://en.wikipedia.org/wiki/Coefficient_of_determination.
This example shows how to fit a multiple linear regression model and compute
adjusted and non-adjusted versions of the R² coefficient of determination at
the end:
-
Yi Cao (2011). Hungarian Algorithm for Linear Assignment Problems (V2.3). Available in http://fr.mathworks.com/matlabcentral/fileexchange/20652-hungarian-algorithm-for-linear-assignment-problems--v2-3-
-
R. A. Pilgrim (2000). Munkres' Assignment Algorithm Modified for
Rectangular Matrices. Available in http://csclab.murraystate.edu/~bob.pilgrim/445/munkres.html
-
Wikipedia contributors. "Hungarian algorithm." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 23 Jan. 2016.
-
Wikipedia, The Free Encyclopedia. Trust region. Available on:
http://en.wikipedia.org/wiki/Trust_region
-
Chih-Jen Lin and Jorge Moré, TRON. Available on: http://www.mcs.anl.gov/~more/tron/index.html
-
Chih-Jen Lin and Jorge J. Moré. 1999. Newton's Method for Large Bound-Constrained
Optimization Problems. SIAM J. on Optimization 9, 4 (April 1999), 1100-1127.
-
Machine Learning Group. LIBLINEAR -- A Library for Large Linear Classification.
National Taiwan University. Available at: http://www.csie.ntu.edu.tw/~cjlin/liblinear/
Gets or sets the tolerance under which the
solution should be found. Default is 0.1.
Gets or sets the maximum number of iterations that should
be performed until the algorithm stops. Default is 1000.
Gets or sets the Hessian estimation function.
Creates a new function optimizer.
The number of parameters in the function to be optimized.
Creates a new function optimizer.
The number of free parameters in the function to be optimized.
The function to be optimized.
The gradient of the function.
The hessian of the function.
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
General Sequential Minimal Optimization algorithm for Quadratic Programming problems.
This class implements the same optimization method found in LibSVM. It can be used
to solve quadratic programming problems where the quadratic matrix Q may be too large
to fit in memory.
The method is described in Fan et al., JMLR 6(2005), p. 1889--1918. It solves the
minimization problem:
min 0.5(\alpha^T Q \alpha) + p^T \alpha
y^T \alpha = \delta
y_i = +1 or -1
0 <= alpha_i <= C_i
Given Q, p, y, C, and an initial feasible point \alpha, where l is
the size of vectors and matrices and eps is the stopping tolerance.
Gets the number of variables (free parameters) in the optimization
problem. In a SVM learning problem, this is the number of samples in
the learning dataset.
The number of parameters for the optimization problem.
Gets the current solution found, the values of
the parameters which optimizes the function.
Gets or sets a cancellation token that can be used to
stop the learning algorithm while it is running.
Gets the output of the function at the current .
Gets the threshold (bias) value for a SVM trained using this method.
Gets or sets the precision tolerance before
the method stops. Default is 0.001.
Gets or sets a value indicating whether shrinking
heuristics should be used. Default is false.
true to use shrinking heuristics; otherwise, false.
Gets the upper bounds for the optimization problem. In
a SVM learning problem, this would be the capacity limit
for each Lagrange multiplier (alpha) in the machine. The
default is to use a vector filled with 1's.
Initializes a new instance of the class.
The number of free parameters in the optimization problem.
The quadratic matrix Q. It should be specified as a lambda
function so Q doesn't need to be always kept in memory.
Initializes a new instance of the class.
The number of free parameters in the optimization problem.
The quadratic matrix Q. It should be specified as a lambda
function so Q doesn't need to be always kept in memory.
The vector of linear terms p. Default is a zero vector.
The class labels y. Default is a unit vector.
Finds the minimum value of a function. The solution vector
will be made available at the property.
Returns true if the method converged to a .
In this case, the found value will also be available at the
property.
Not supported.
Contains classes for constrained and unconstrained optimization. Includes
Conjugate Gradient (CG),
Bounded and Unbounded Broyden–Fletcher–Goldfarb–Shanno (BFGS),
gradient-free optimization methods such as and the Goldfarb-Idnani
solver for Quadratic Programming (QP) problems.
This namespace contains different methods for solving both constrained and unconstrained
optimization problems. For unconstrained optimization, methods available include
Conjugate Gradient (CG),
Bounded and Unbounded Broyden–Fletcher–Goldfarb–Shanno (BFGS),
Resilient Backpropagation and a simplified implementation of the
Trust Region Newton Method (TRON).
For constrained optimization problems, methods available include the
Augmented Lagrangian method for general non-linear optimization, for
gradient-free non-linear optimization, and the Goldfarb-Idnani
method for solving Quadratic Programming (QP) problems.
This namespace also contains optimizers specialized for least squares problems, such as
Gauss Newton and the Levenberg-Marquart least squares solvers.
For univariate problems, standard search algorithms are also available, such as
Brent and Binary search.
The namespace class diagram is shown below.
Base class for gradient-based optimization methods.
Gets or sets a function returning the gradient
vector of the function to be optimized for a
given value of its free parameters.
The gradient function.
Initializes a new instance of the class.
Initializes a new instance of the class.
The number of free parameters in the optimization problem.
Initializes a new instance of the class.
The number of free parameters in the optimization problem.
The objective function whose optimum values should be found.
The gradient of the objective .
Finds the maximum value of a function. The solution vector
will be made available at the property.
Returns true if the method converged to a .
In this case, the found value will also be available at the
property.
Finds the minimum value of a function. The solution vector
will be made available at the property.
Returns true if the method converged to a .
In this case, the found value will also be available at the
property.
Base class for optimization methods.
Gets or sets a cancellation token that can be used to
stop the learning algorithm while it is running.
Gets or sets the function to be optimized.
The function to be optimized.
Gets the number of variables (free parameters)
in the optimization problem.
The number of parameters.
Gets the current solution found, the values of
the parameters which optimizes the function.
Gets the output of the function at the current .
Initializes a new instance of the class.
Initializes a new instance of the class.
The number of free parameters in the optimization problem.
Initializes a new instance of the class.
The number of free parameters in the optimization problem.
The objective function whose optimum values should be found.
Initializes a new instance of the class.
The objective function whose optimum values should be found.
Called when the property has changed.
Finds the maximum value of a function. The solution vector
will be made available at the property.
The initial solution vector to start the search.
Returns true if the method converged to a .
In this case, the found value will also be available at the
property.
Finds the minimum value of a function. The solution vector
will be made available at the property.
The initial solution vector to start the search.
Returns true if the method converged to a .
In this case, the found value will also be available at the
property.
Finds the maximum value of a function. The solution vector
will be made available at the property.
Returns true if the method converged to a .
In this case, the found value will also be available at the
property.
Finds the minimum value of a function. The solution vector
will be made available at the property.
Returns true if the method converged to a .
In this case, the found value will also be available at the
property.
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
Creates an exception with a given inner optimization algorithm code (for debugging purposes).
Creates an exception with a given inner optimization algorithm code (for debugging purposes).
Common interface for function optimization methods which depend on
having both an objective function and a gradient function definition
available.
Common interface for function optimization methods which depend on
having both an objective function and a gradient function definition
available.
Gets or sets a function returning the gradient
vector of the function to be optimized for a
given value of its free parameters.
The gradient function.
Least Squares function delegate.
This delegate represents a parameterized function that, given a set of
and an vector,
produces an associated output value.
The function parameters, also known as weights or coefficients.
An input vector.
The output value produced given the vector
using the given .
Gradient function delegate.
This delegate represents the gradient of a Least
Squares objective function. This function should compute the gradient vector
in respect to the function .
The function parameters, also known as weights or coefficients.
An input vector.
The resulting gradient vector (w.r.t to the parameters).
Common interface for Least Squares algorithms, i.e. algorithms
that can be used to solve Least Squares optimization problems.
Gets or sets a cancellation token that can be used to
stop the learning algorithm while it is running.
Gets or sets a parameterized model function mapping input vectors
into output values, whose optimum parameters must be found.
The function to be optimized.
Gets or sets a function that computes the gradient vector in respect
to the function parameters, given a set of input and output values.
The gradient function.
Gets the number of variables (free parameters) in the optimization problem.
The number of parameters.
Attempts to find the best values for the parameter vector
minimizing the discrepancy between the generated outputs
and the expected outputs for a given set of input data.
A set of input data.
The values associated with each
vector in the data.
Gets the solution found, the values of the parameters which
optimizes the function, in a least squares sense.
Gets standard error for each parameter in the solution.
Gets the value at the solution found. This should be
the minimum value found for the objective function.
Binary search root finding algorithm.
Gets or sets the (inclusive) lower bound for the search interval a.
Gets or sets the (exclusive) upper bound for the search interval a.
Gets the solution found in the last call
to or .
Gets the value at the solution found in the last call
to .
Gets the function to be searched.
Constructs a new Binary search algorithm.
The function to be searched.
Start of search region (inclusive).
End of search region (exclusive).
Finds a value of a function in the interval [a;b). The function can
be monotonically increasing or decreasing over the interface [a;b).
The location of the zero value in the given interval.
Finds a value of a function in the interval [a;b). The function can
be monotonically increasing or decreasing over the interface [a;b).
The location of the zero value in the given interval.
Finds a value of a function in the interval [a;b). The function can
be monotonically increasing or decreasing over the interface [a;b).
The function to have its root computed.
Start of search region (inclusive).
End of search region (exclusive).
The value to be looked for in the function.
The location of the zero value in the given interval.
Cobyla exit codes.
Optimization successfully completed.
Maximum number of iterations (function/constraints evaluations) reached during optimization.
Size of rounding error is becoming damaging, terminating prematurely.
The posed constraints cannot be fulfilled.
Constrained optimization by linear approximation.
Constrained optimization by linear approximation (COBYLA) is a numerical
optimization method for constrained problems where the derivative of the
objective function is not known, invented by Michael J. D. Powell.
COBYLA2 is an implementation of Powell’s nonlinear derivative–free constrained
optimization that uses a linear approximation approach. The algorithm is a
sequential trust–region algorithm that employs linear approximations to the
objective and constraint functions, where the approximations are formed by linear
interpolation at n + 1 points in the space of the variables and tries to maintain
a regular–shaped simplex over iterations.
This algorithm is able to solve non-smooth NLP problems with a moderate number
of variables (about 100), with inequality constraints only.
References:
-
Wikipedia, The Free Encyclopedia. Cobyla. Available on:
http://en.wikipedia.org/wiki/COBYLA
Let's say we would like to optimize a function whose gradient
we do not know or would is too difficult to compute. All we
have to do is to specify the function, pass it to Cobyla and
call its Minimize() method:
// We would like to find the minimum of min f(x) = 10 * (x+1)^2 + y^2
Func<double[], double> function = x => 10 * Math.Pow(x[0] + 1, 2) + Math.Pow(x[1], 2);
// Create a cobyla method for 2 variables
Cobyla cobyla = new Cobyla(2, function);
bool success = cobyla.Minimize();
double minimum = minimum = cobyla.Value; // Minimum should be 0.
double[] solution = cobyla.Solution; // Vector should be (-1, 0)
Cobyla can be used even when we have constraints in our optimization problem.
The following example can be found in Fletcher's book Practical Methods of
Optimization, under the equation number (9.1.15).
// We will optimize the 2-variable function f(x, y) = -x -y
var f = new NonlinearObjectiveFunction(2, x => -x[0] - x[1]);
// Under the following constraints
var constraints = new[]
{
new NonlinearConstraint(2, x => x[1] - x[0] * x[0] >= 0),
new NonlinearConstraint(2, x => 1 - x[0] * x[0] - x[1] * x[1] >= 0),
};
// Create a Cobyla algorithm for the problem
var cobyla = new Cobyla(function, constraints);
// Optimize it
bool success = cobyla.Minimize();
double minimum = cobyla.Value; // Minimum should be -2 * sqrt(0.5)
double[] solution = cobyla.Solution; // Vector should be [sqrt(0.5), sqrt(0.5)]
Gets the number of iterations performed in the last
call to .
The number of iterations performed
in the previous optimization.
Gets or sets the maximum number of iterations
to be performed during optimization. Default
is 0 (iterate until convergence).
Get the exit code returned in the last call to the
or
methods.
Creates a new instance of the Cobyla optimization algorithm.
The number of free parameters in the function to be optimized.
Creates a new instance of the Cobyla optimization algorithm.
The number of free parameters in the function to be optimized.
The function to be optimized.
Creates a new instance of the Cobyla optimization algorithm.
The function to be optimized.
Creates a new instance of the Cobyla optimization algorithm.
The function to be optimized.
The constraints of the optimization problem.
Creates a new instance of the Cobyla optimization algorithm.
The function to be optimized.
The constraints of the optimization problem.
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
Defines an interface for an optimization constraint.
Gets the type of the constraint.
Gets the value in the right hand
side of the constraint equation.
Gets the violation tolerance for the constraint.
Gets the number of variables in the constraint.
Calculates the left hand side of the constraint
equation given a vector x.
The vector.
The left hand side of the constraint equation as evaluated at x.
Calculates the gradient of the constraint
equation given a vector x
The vector.
The gradient of the constraint as evaluated at x.
Linear Constraint Collection.
Initializes a new instance of the class.
Initializes a new instance of the class.
Initializes a new instance of the class.
Creates a matrix of linear constraints in canonical form.
The number of variables in the objective function.
The vector of independent terms (the right hand side of the constraints).
The number of equalities in the matrix.
The matrix A of linear constraints.
Creates a matrix of linear constraints in canonical form.
The number of variables in the objective function.
The vector of independent terms (the right hand side of the constraints).
The amount each constraint can be violated before the answer is declared close enough.
The number of equalities in the matrix.
The matrix A of linear constraints.
Creates a from a matrix
specifying the constraint variables and a vector specifying their
expected value.
The constraint matrix.
The constraint values.
The number of equalities at the start of the
matrix . Contraints thereafter are taken to be
less than or equal to the constraint values.
Creates a from a matrix
specifying the constraint variables and a vector specifying their
expected value.
The constraint matrix.
The constraint values.
The number of equalities at the start of the
matrix . Contraints thereafter are taken to be
greater than or equal to the constraint values.
Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method.
The L-BFGS algorithm is a member of the broad family of quasi-Newton optimization
methods. L-BFGS stands for 'Limited memory BFGS'. Indeed, L-BFGS uses a limited
memory variation of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) update to approximate
the inverse Hessian matrix (denoted by Hk). Unlike the original BFGS method which
stores a dense approximation, L-BFGS stores only a few vectors that represent the
approximation implicitly. Due to its moderate memory requirement, L-BFGS method is
particularly well suited for optimization problems with a large number of variables.
L-BFGS never explicitly forms or stores Hk. Instead, it maintains a history of the past
m updates of the position x and gradient g, where generally the history
mcan be short, often less than 10. These updates are used to implicitly do operations
requiring the Hk-vector product.
The framework implementation of this method is based on the original FORTRAN source code
by Jorge Nocedal (see references below). The original FORTRAN source code of L-BFGS (for
unconstrained problems) is available at http://www.netlib.org/opt/lbfgs_um.shar and had
been made available under the public domain.
References:
-
Jorge Nocedal. Limited memory BFGS method for large scale optimization (Fortran source code). 1990.
Available in http://www.netlib.org/opt/lbfgs_um.shar
-
Jorge Nocedal. Updating Quasi-Newton Matrices with Limited Storage. Mathematics of Computation,
Vol. 35, No. 151, pp. 773--782, 1980.
-
Dong C. Liu, Jorge Nocedal. On the limited memory BFGS method for large scale optimization.
The following example shows the basic usage of the L-BFGS solver
to find the minimum of a function specifying its function and
gradient.
// Suppose we would like to find the minimum of the function
//
// f(x,y) = -exp{-(x-1)²} - exp{-(y-2)²/2}
//
// First we need write down the function either as a named
// method, an anonymous method or as a lambda function:
Func<double[], double> f = (x) =>
-Math.Exp(-Math.Pow(x[0] - 1, 2)) - Math.Exp(-0.5 * Math.Pow(x[1] - 2, 2));
// Now, we need to write its gradient, which is just the
// vector of first partial derivatives del_f / del_x, as:
//
// g(x,y) = { del f / del x, del f / del y }
//
Func<double[], double[]> g = (x) => new double[]
{
// df/dx = {-2 e^(- (x-1)^2) (x-1)}
2 * Math.Exp(-Math.Pow(x[0] - 1, 2)) * (x[0] - 1),
// df/dy = {- e^(-1/2 (y-2)^2) (y-2)}
Math.Exp(-0.5 * Math.Pow(x[1] - 2, 2)) * (x[1] - 2)
};
// Finally, we can create the L-BFGS solver, passing the functions as arguments
var lbfgs = new BroydenFletcherGoldfarbShanno(numberOfVariables: 2, function: f, gradient: g);
// And then minimize the function:
bool success = lbfgs.Minimize();
double minValue = lbfgs.Value;
double[] solution = lbfgs.Solution;
// The resultant minimum value should be -2, and the solution
// vector should be { 1.0, 2.0 }. The answer can be checked on
// Wolfram Alpha by clicking the following the link:
// http://www.wolframalpha.com/input/?i=maximize+%28exp%28-%28x-1%29%C2%B2%29+%2B+exp%28-%28y-2%29%C2%B2%2F2%29%29
Occurs when progress is made during the optimization.
Gets the number of iterations performed in the last
call to
or .
The number of iterations performed
in the previous optimization.
Gets or sets the maximum number of iterations
to be performed during optimization. Default
is 0 (iterate until convergence).
Gets the number of function evaluations performed
in the last call to
or .
The number of evaluations performed
in the previous optimization.
Gets or sets the number of corrections used in the L-BFGS
update. Recommended values are between 3 and 7. Default is 5.
Gets or sets the upper bounds of the interval
in which the solution must be found.
Gets or sets the lower bounds of the interval
in which the solution must be found.
Gets or sets the accuracy with which the solution
is to be found. Default value is 1e5. Smaller values
up until zero result in higher accuracy.
The iteration will stop when
(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch
where epsmch is the machine precision, which is automatically
generated by the code. Typical values for this parameter are:
1e12 for low accuracy; 1e7 for moderate accuracy; 1e1 for extremely
high accuracy.
Gets or sets a tolerance value when detecting convergence
of the gradient vector steps. Default is 0.
On entry pgtol >= 0 is specified by the user. The iteration
will stop when
max{|proj g_i | i = 1, ..., n} <= pgtol
where pg_i is the ith component of the projected gradient.
Get the exit code returned in the last call to the
or
methods.
Creates a new instance of the L-BFGS optimization algorithm.
The number of free parameters in the optimization problem.
Creates a new instance of the L-BFGS optimization algorithm.
The number of free parameters in the function to be optimized.
The function to be optimized.
The gradient of the function.
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
Return values of lbfgs().
Roughly speaking, a negative value indicates an error.
L-BFGS reaches convergence.
The initial variables already minimize the objective function.
Unknown error.
Logic error.
Insufficient memory.
The minimization process has been canceled.
Invalid number of variables specified.
Invalid number of variables (for SSE) specified.
The array x must be aligned to 16 (for SSE).
Invalid parameter lbfgs_parameter_t::epsilon specified.
Invalid parameter lbfgs_parameter_t::past specified.
Invalid parameter lbfgs_parameter_t::delta specified.
Invalid parameter lbfgs_parameter_t::linesearch specified.
Invalid parameter lbfgs_parameter_t::max_step specified.
Invalid parameter lbfgs_parameter_t::max_step specified.
Invalid parameter lbfgs_parameter_t::ftol specified.
Invalid parameter lbfgs_parameter_t::wolfe specified.
Invalid parameter lbfgs_parameter_t::gtol specified.
Invalid parameter lbfgs_parameter_t::xtol specified.
Invalid parameter lbfgs_parameter_t::max_linesearch specified.
Invalid parameter lbfgs_parameter_t::orthantwise_c specified.
Invalid parameter lbfgs_parameter_t::orthantwise_start specified.
Invalid parameter lbfgs_parameter_t::orthantwise_end specified.
The line-search step went out of the interval of uncertainty.
A logic error occurred; alternatively, the interval of uncertainty
became too small.
A rounding error occurred; alternatively, no line-search step
satisfies the sufficient decrease and curvature conditions.
The line-search step became smaller than lbfgs_parameter_t::min_step.
The line-search step became larger than lbfgs_parameter_t::max_step.
The line-search routine reaches the maximum number of evaluations.
The algorithm routine reaches the maximum number of iterations.
Relative width of the interval of uncertainty is at most
lbfgs_parameter_t::xtol.
A logic error (negative line-search step) occurred.
The current search direction increases the objective function value.
Callback interface to provide objective function and gradient evaluations.
The lbfgs() function call this function to obtain the values of objective
function and its gradients when needed. A client program must implement
this function to evaluate the values of the objective function and its
gradients, given current values of variables.
@param instance The user data sent for lbfgs() function by the client.
@param x The current values of variables.
@param g The gradient vector. The callback function must compute
the gradient values for the current variables.
@param n The number of variables.
@param step The current step of the line search routine.
@retval double The value of the objective function for the current
variables.
Callback interface to receive the progress of the optimization process.
The lbfgs() function call this function for each iteration. Implementing
this function, a client program can store or display the current progress
of the optimization process.
@param instance The user data sent for lbfgs() function by the client.
@param x The current values of variables.
@param g The current gradient values of variables.
@param fx The current value of the objective function.
@param xnorm The Euclidean norm of the variables.
@param gnorm The Euclidean norm of the gradients.
@param step The line-search step used for this iteration.
@param n The number of variables.
@param k The iteration count.
@param ls The number of evaluations called for this iteration.
@retval int Zero to continue the optimization process. Returning a
non-zero value will cancel the optimization process.
Find a minimizer of an interpolated cubic function.
@param cm The minimizer of the interpolated cubic.
@param u The value of one point, u.
@param fu The value of f(u).
@param du The value of f'(u).
@param v The value of another point, v.
@param fv The value of f(v).
@param du The value of f'(v).
Find a minimizer of an interpolated cubic function.
@param cm The minimizer of the interpolated cubic.
@param u The value of one point, u.
@param fu The value of f(u).
@param du The value of f'(u).
@param v The value of another point, v.
@param fv The value of f(v).
@param du The value of f'(v).
@param xmin The maximum value.
@param xmin The minimum value.
Find a minimizer of an interpolated quadratic function.
@param qm The minimizer of the interpolated quadratic.
@param u The value of one point, u.
@param fu The value of f(u).
@param du The value of f'(u).
@param v The value of another point, v.
@param fv The value of f(v).
Find a minimizer of an interpolated quadratic function.
@param qm The minimizer of the interpolated quadratic.
@param u The value of one point, u.
@param du The value of f'(u).
@param v The value of another point, v.
@param dv The value of f'(v).
Update a safeguarded trial value and interval for line search.
The parameter x represents the step with the least function value.
The parameter t represents the current step. This function assumes
that the derivative at the point of x in the direction of the step.
If the bracket is set to true, the minimizer has been bracketed in
an interval of uncertainty with endpoints between x and y.
@param x The pointer to the value of one endpoint.
@param fx The pointer to the value of f(x).
@param dx The pointer to the value of f'(x).
@param y The pointer to the value of another endpoint.
@param fy The pointer to the value of f(y).
@param dy The pointer to the value of f'(y).
@param t The pointer to the value of the trial value, t.
@param ft The pointer to the value of f(t).
@param dt The pointer to the value of f'(t).
@param tmin The minimum value for the trial value, t.
@param tmax The maximum value for the trial value, t.
@param brackt The pointer to the predicate if the trial value is
bracketed.
@retval int Status value. Zero indicates a normal termination.
@see
Jorge J. More and David J. Thuente. Line search algorithm with
guaranteed sufficient decrease. ACM Transactions on Mathematical
Software (TOMS), Vol 20, No 3, pp. 286-307, 1994.
Status codes for the
function optimizer.
The optimization stopped before convergence; maximum
number of iterations could have been reached.
Maximum number of iterations was reached.
The function output converged to a static
value within the desired precision.
The function gradient converged to a minimum
value within the desired precision.
The inner line search function failed. This could be an indication
that there might be something wrong with the gradient function.
Inner status of the
optimization algorithm. This class contains implementation details that
can change at any time.
Initializes a new instance of the class with the inner
status values from the original FORTRAN L-BFGS implementation.
The isave L-BFGS status argument.
The dsave L-BFGS status argument.
The lsave L-BFGS status argument.
The csave L-BFGS status argument.
The work L-BFGS status argument.
Gets or sets the isave status from the
original FORTRAN L-BFGS implementation.
Gets or sets the dsave status from the
original FORTRAN L-BFGS implementation.
Gets or sets the lsave status from the
original FORTRAN L-BFGS implementation.
Gets or sets the csave status from the
original FORTRAN L-BFGS implementation.
Gets or sets the work vector from the
original FORTRAN L-BFGS implementation.
Gauss-Newton algorithm for solving Least-Squares problems.
This class isn't suitable for most real-world problems. Instead, this class
is intended to be use as a baseline comparison to help debug and check other
optimization methods, such as .
While it is possible to use the class as a standalone
method for solving least squares problems, this class is intended to be used as
a strategy for NonlinearLeastSquares, as shown in the example below:
-
Steven G. Johnson, The NLopt nonlinear-optimization package,
http://ab-initio.mit.edu/nlopt
-
Wikipedia, The Free Encyclopedia. Nelder Mead method. Available on:
http://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method
-
Steven G. Johnson, The NLopt nonlinear-optimization package,
http://ab-initio.mit.edu/nlopt
-
Wikipedia, The Free Encyclopedia. Nelder Mead method. Available on:
http://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method
Creates a new optimization algorithm.
The number of free parameters in the optimization problem.
Creates a new optimization algorithm.
The number of free parameters in the optimization problem.
The objective function whose optimum values should be found.
Creates a new optimization algorithm.
The objective function whose optimum values should be found.
Get the exit code returned in the last call to the
or
methods.
Gets or sets the maximum value that the objective
function could produce before the algorithm could
be terminated as if the solution was good enough.
Gets the step sizes to be used by the optimization
algorithm. Default is to initialize each with 1e-5.
Gets or sets multiple convergence options to
determine when the optimization can terminate.
Gets the lower bounds that should be respected in this
optimization problem. Default is to initialize this vector
with .
Gets the upper bounds that should be respected in this
optimization problem. Default is to initialize this vector
with .
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
Wrapper around objective function for subspace optimization.
Status codes for the
optimization algorithm.
The algorithm has found a feasible solution.
The optimization could not make progress towards finding a feasible
solution. Try increasing the
of the constraints.
The optimization has reached the
maximum number of function evaluations.
The optimization has been cancelled by the user (such as for
example by using ).
Augmented Lagrangian method for constrained non-linear optimization.
References:
-
Steven G. Johnson, The NLopt nonlinear-optimization package, http://ab-initio.mit.edu/nlopt
-
E. G. Birgin and J. M. Martinez, "Improving ultimate convergence of an augmented Lagrangian
method," Optimization Methods and Software vol. 23, no. 2, p. 177-195 (2008).
In this framework, it is possible to state a non-linear programming problem
using either symbolic processing or vector-valued functions. The following
example demonstrates the symbolic processing case:
-
J. C. Gilbert and J. Nocedal. Global Convergence Properties of Conjugate Gradient
Methods for Optimization, (1992) SIAM J. on Optimization, 2, 1.
-
Wikipedia contributors, "Nonlinear conjugate gradient method," Wikipedia, The Free
Encyclopedia, http://en.wikipedia.org/w/index.php?title=Nonlinear_conjugate_gradient_method
(accessed December 22, 2011).
-
Wikipedia contributors, "Conjugate gradient method," Wikipedia, The Free Encyclopedia,
http://en.wikipedia.org/w/index.php?title=Conjugate_gradient_method
(accessed December 22, 2011).
Gets or sets the relative difference threshold
to be used as stopping criteria between two
iterations. Default is 0 (iterate until convergence).
Gets or sets the maximum number of iterations
to be performed during optimization. Default
is 0 (iterate until convergence).
Gets or sets the conjugate gradient update
method to be used during optimization.
Gets the number of iterations performed
in the last call to .
The number of iterations performed
in the previous optimization.
Gets the number of function evaluations performed
in the last call to .
The number of evaluations performed
in the previous optimization.
Gets the number of linear searches performed
in the last call to .
Get the exit code returned in the last call to the
or
methods.
Occurs when progress is made during the optimization.
Creates a new instance of the CG optimization algorithm.
Creates a new instance of the CG optimization algorithm.
The number of free parameters in the optimization problem.
Creates a new instance of the CG optimization algorithm.
The number of free parameters in the function to be optimized.
The function to be optimized.
The gradient of the function.
Called when the property has changed.
The number of variables.
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
Constraint type.
Equality constraint.
Inequality constraint specifying a greater than or equal to relationship.
Inequality constraint specifying a lesser than or equal to relationship.
Constraint with only linear terms.
Linear constraints are commonly used in optimisation routines.
The framework provides support for linear constraints to be specified
using a representation, an
or using a vector of constraint values.
f(x,y,z) = ax² + by² +cz² + dxy + exz + fyz + gx + hy + iz + j
Please note that the function's constructor expects the function
expression to be given on this form. Scalar values must be located
on the left of the variables, and no term should be duplicated in
the quadratic expression. Please take a look on the examples section
of this page for some examples of expected functions.
References:
-
Wikipedia, The Free Encyclopedia. Quadratic Function. Available on:
https://en.wikipedia.org/wiki/Quadratic_function
Examples of valid quadratic functions are:
var f1 = new QuadraticObjectiveFunction("x² + 1");
var f2 = new QuadraticObjectiveFunction("-x*y + y*z");
var f3 = new QuadraticObjectiveFunction("-2x² + xy - y² - 10xz + z²");
var f4 = new QuadraticObjectiveFunction("-2x² + xy - y² + 5y");
It is also possible to specify quadratic functions using lambda expressions.
In this case, it is first necessary to create some dummy symbol variables to
act as placeholders in the quadratic expressions. Their value is not important,
as they will only be used to parse the form of the expression, not its value.
// Declare symbol variables
double x = 0, y = 0, z = 0;
var g1 = new QuadraticObjectiveFunction(() => x * x + 1);
var g2 = new QuadraticObjectiveFunction(() => -x * y + y * z);
var g3 = new QuadraticObjectiveFunction(() => -2 * x * x + x * y - y * y - 10 * x * z + z * z);
var g4 = new QuadraticObjectiveFunction(() => -2 * x * x + x * y - y * y + 5 * y);
Finally, for large problems, it is usually best to declare quadratic
problems using matrices and vectors. Without loss of generality, the
quadratic matrix can always be taken to be symmetric (as the anti-
symmetric part has no contribution to the function). For efficiency
reasons, the quadratic matrix must be symmetric.
var h1 = new QuadraticObjectiveFunction("3x² - 4y² + 6xy + 3x + 2y");
double[,] Q = { { 6, 6 }, { 6, -8 } }; // Note the factor of 2
double[] d = { 3, 2 };
// Equivalently this can be written:
var h2 = new QuadraticObjectiveFunction(Q, d);
After those functions are created, you can either query their values
using
f1.Function(new [] { 5.0 }); // x*x+1 = x² + 1 = 25 + 1 = 26
Or you can pass it to a quadratic optimization method such
as Goldfarb-Idnani to explore its minimum or maximal points:
// Declare symbol variables
double x = 0, y = 0, z = 0;
// Create the function to be optimized
var f = new QuadraticObjectiveFunction(() => x * x - 2 * x * y + 3 * y * y + z * z - 4 * x - 5 * y - z);
// Create some constraints for the solution
var constraints = new List<LinearConstraint>();
constraints.Add(new LinearConstraint(f, () => 6 * x - 7 * y <= 8));
constraints.Add(new LinearConstraint(f, () => 9 * x + 1 * y <= 11));
constraints.Add(new LinearConstraint(f, () => 9 * x - y <= 11));
constraints.Add(new LinearConstraint(f, () => -z - y == 12));
// Create the Quadratic Programming solver
GoldfarbIdnani solver = new GoldfarbIdnani(f, constraints);
// Minimize the function
bool success = solver.Minimize();
double value = solver.Value;
double[] solutions = solver.Solution;
Sometimes it is easiest to compose quadratic functions as linear
combinations of other quadratic functions. The
supports this by overloading the addition and multiplication operators.
-f(x + a * d) ≤ f(x) + FunctionTolerance * a * g(x)^T d,
where x is the current point, d is the current search direction, and
a is the step length.
Backtracking method with regular Wolfe condition.
The backtracking method finds the step length such that it satisfies
both the Armijo condition (LineSearch.LBFGS_LINESEARCH_BACKTRACKING_ARMIJO)
and the curvature condition,
- g(x + a * d)^T d ≥ lbfgs_parameter_t::wolfe * g(x)^T d,
where x is the current point, d is the current search direction, and
a is the step length.
Backtracking method with strong Wolfe condition.
The backtracking method finds the step length such that it satisfies
both the Armijo condition (LineSearch.LBFGS_LINESEARCH_BACKTRACKING_ARMIJO)
and the following condition,
- |g(x + a * d)^T d| ≤ lbfgs_parameter_t::wolfe * |g(x)^T d|,
where x is the current point, d is the current search direction, and
a is the step length.
Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method.
The L-BFGS algorithm is a member of the broad family of quasi-Newton optimization
methods. L-BFGS stands for 'Limited memory BFGS'. Indeed, L-BFGS uses a limited
memory variation of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) update to approximate
the inverse Hessian matrix (denoted by Hk). Unlike the original BFGS method which
stores a dense approximation, L-BFGS stores only a few vectors that represent the
approximation implicitly. Due to its moderate memory requirement, L-BFGS method is
particularly well suited for optimization problems with a large number of variables.
L-BFGS never explicitly forms or stores Hk. Instead, it maintains a history of the past
m updates of the position x and gradient g, where generally the history
mcan be short, often less than 10. These updates are used to implicitly do operations
requiring the Hk-vector product.
The framework implementation of this method is based on the original FORTRAN source code
by Jorge Nocedal (see references below). The original FORTRAN source code of L-BFGS (for
unconstrained problems) is available at http://www.netlib.org/opt/lbfgs_um.shar and had
been made available under the public domain.
References:
-
Jorge Nocedal. Limited memory BFGS method for large scale optimization (Fortran source code). 1990.
Available in http://www.netlib.org/opt/lbfgs_um.shar
-
Jorge Nocedal. Updating Quasi-Newton Matrices with Limited Storage. Mathematics of Computation,
Vol. 35, No. 151, pp. 773--782, 1980.
-
Dong C. Liu, Jorge Nocedal. On the limited memory BFGS method for large scale optimization.
The following example shows the basic usage of the L-BFGS solver
to find the minimum of a function specifying its function and
gradient.
// Suppose we would like to find the minimum of the function
//
// f(x,y) = -exp{-(x-1)²} - exp{-(y-2)²/2}
//
// First we need write down the function either as a named
// method, an anonymous method or as a lambda function:
Func<double[], double> f = (x) =>
-Math.Exp(-Math.Pow(x[0] - 1, 2)) - Math.Exp(-0.5 * Math.Pow(x[1] - 2, 2));
// Now, we need to write its gradient, which is just the
// vector of first partial derivatives del_f / del_x, as:
//
// g(x,y) = { del f / del x, del f / del y }
//
Func<double[], double[]> g = (x) => new double[]
{
// df/dx = {-2 e^(- (x-1)^2) (x-1)}
2 * Math.Exp(-Math.Pow(x[0] - 1, 2)) * (x[0] - 1),
// df/dy = {- e^(-1/2 (y-2)^2) (y-2)}
Math.Exp(-0.5 * Math.Pow(x[1] - 2, 2)) * (x[1] - 2)
};
// Finally, we can create the L-BFGS solver, passing the functions as arguments
var lbfgs = new BroydenFletcherGoldfarbShanno(numberOfVariables: 2, function: f, gradient: g);
// And then minimize the function:
bool success = lbfgs.Minimize();
double minValue = lbfgs.Value;
double[] solution = lbfgs.Solution;
// The resultant minimum value should be -2, and the solution
// vector should be { 1.0, 2.0 }. The answer can be checked on
// Wolfram Alpha by clicking the following the link:
// http://www.wolframalpha.com/input/?i=maximize+%28exp%28-%28x-1%29%C2%B2%29+%2B+exp%28-%28y-2%29%C2%B2%2F2%29%29
The number of corrections to approximate the inverse Hessian matrix.
Default is 6. Values less than 3 are not recommended. Large values
will result in excessive computing time.
The L-BFGS routine stores the computation results of the previous m
iterations to approximate the inverse Hessian matrix of the current
iteration. This parameter controls the size of the limited memories
(corrections). The default value is 6. Values less than 3 are not
recommended. Large values will result in excessive computing time.
Epsilon for convergence test.
This parameter determines the accuracy with which the solution is to
be found. A minimization terminates when
||g|| < epsilon * max(1, ||x||),
where ||.|| denotes the Euclidean (L2) norm. The default value is 1e-5.
Distance for delta-based convergence test.
This parameter determines the distance, in iterations, to compute
the rate of decrease of the objective function. If the value of this
parameter is zero, the library does not perform the delta-based
convergence test. The default value is 0.
Delta for convergence test.
This parameter determines the minimum rate of decrease of the
objective function. The library stops iterations when the
following condition is met:
(f' - f) / f < delta
where f' is the objective value of past iterations
ago, and f is the objective value of the current iteration. Default value
is 0.
The maximum number of iterations.
The minimize function terminates an optimization process with
status
code when the iteration count exceeds this parameter. Setting this parameter
to zero continues an optimization process until a convergence or error. The
default value is 0.
The line search algorithm.
This parameter specifies a line search
algorithm to be used by the L-BFGS routine.
The maximum number of trials for the line search.
This parameter controls the number of function and gradients evaluations
per iteration for the line search routine. The default value is 20.
The minimum step of the line search routine.
The default value is 1e-20. This value need not be modified unless
the exponents are too large for the machine being used, or unless the problem
is extremely badly scaled (in which case the exponents should be increased).
The maximum step of the line search.
The default value is 1e+20. This value need not be modified unless the
exponents are too large for the machine being used, or unless the problem is
extremely badly scaled (in which case the exponents should be increased).
A parameter to control the accuracy of the line search routine. The default
value is 1e-4. This parameter should be greater than zero and smaller
than 0.5.
A coefficient for the Wolfe condition.
This parameter is valid only when the backtracking line-search algorithm is used
with the Wolfe condition,
or . The default value
is 0.9. This parameter should be greater the
and smaller than 1.0.
A parameter to control the accuracy of the line search routine.
The default value is 0.9. If the function and gradient evaluations are
inexpensive with respect to the cost of the iteration (which is sometimes the
case when solving very large problems) it may be advantageous to set this parameter
to a small value. A typical small value is 0.1. This parameter should be
greater than the (1e-4) and smaller than
1.0.
The machine precision for floating-point values.
This parameter must be a positive value set by a client program to
estimate the machine precision. The line search routine will terminate
with the status code (::LBFGSERR_ROUNDING_ERROR) if the relative width
of the interval of uncertainty is less than this parameter.
Coefficient for the L1 norm of variables.
This parameter should be set to zero for standard minimization problems. Setting this
parameter to a positive value activates Orthant-Wise Limited-memory Quasi-Newton (OWL-QN)
method, which minimizes the objective function F(x) combined with the L1 norm |x| of the
variables, {F(x) + C |x|}. This parameter is the coefficient for the |x|, i.e., C.
As the L1 norm |x| is not differentiable at zero, the library modifies function and
gradient evaluations from a client program suitably; a client program thus have only
to return the function value F(x) and gradients G(x) as usual. The default value is zero.
Start index for computing L1 norm of the variables.
This parameter is valid only for OWL-QN method (i.e., != 0).
This parameter b (0 <= b < N) specifies the index number from which the library
computes the L1 norm of the variables x,
|x| := |x_{b}| + |x_{b+1}| + ... + |x_{N}|.
In other words, variables x_1, ..., x_{b-1} are not used for
computing the L1 norm. Setting b (0 < b < N), one can protect
variables, x_1, ..., x_{b-1} (e.g., a bias term of logistic
regression) from being regularized. The default value is zero.
End index for computing L1 norm of the variables.
This parameter is valid only for OWL-QN method (i.e., != 0).
This parameter e (0 < e <= N) specifies the index number at which the library stops
computing the L1 norm of the variables x,
|x| := |x_{b}| + |x_{b+1}| + ... + |x_{N}|.
Occurs when progress is made during the optimization.
Get the exit code returned in the last call to the
or
methods.
Creates a new instance of the L-BFGS optimization algorithm.
Creates a new instance of the L-BFGS optimization algorithm.
The number of free parameters in the optimization problem.
Creates a new instance of the L-BFGS optimization algorithm.
The function to be optimized.
Creates a new instance of the L-BFGS optimization algorithm.
The number of free parameters in the function to be optimized.
The function to be optimized.
The gradient of the function.
Called when the property has changed.
The number of variables.
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
Line Search Failed Exception.
This exception may be thrown by the L-BFGS Optimizer
when the line search routine used by the optimization method fails.
Gets the error code information returned by the line search routine.
The error code information returned by the line search routine.
Initializes a new instance of the class.
Initializes a new instance of the class.
The error code information of the line search routine.
Message providing some additional information.
Initializes a new instance of the class.
Message providing some additional information.
Initializes a new instance of the class.
Message providing some additional information.
The exception that is the cause of the current exception.
Initializes a new instance of the class.
The that holds the serialized object data about the exception being thrown.
The that contains contextual information about the source or destination.
The parameter is null.
The class name is null or is zero (0).
When overridden in a derived class, sets the with information about the exception.
The that holds the serialized object data about the exception being thrown.
The that contains contextual information about the source or destination.
The parameter is a null reference (Nothing in Visual Basic).
Optimization progress event arguments.
Gets the current iteration of the method.
Gets the number of function evaluations performed.
Gets the current gradient of the function being optimized.
Gets the norm of the current .
Gets the current solution parameters for the problem.
Gets the norm of the current .
Gets the value of the function to be optimized
at the current proposed .
Gets the current step size.
Gets or sets a value indicating whether the
optimization process is about to terminate.
true if finished; otherwise, false.
An user-defined value associated with this object.
Initializes a new instance of the class.
The current iteration of the optimization method.
The number of function evaluations performed.
The current gradient of the function.
The norm of the current gradient
The norm of the current parameter vector.
The current solution parameters.
The value of the function evaluated at the current solution.
The current step size.
True if the method is about to terminate, false otherwise.
Status codes for the
constrained quadratic programming solver.
Convergence was attained.
The quadratic problem matrix is not positive definite.
The posed constraints cannot be fulfilled.
Goldfarb-Idnani Quadratic Programming Solver.
References:
-
Goldfarb D., Idnani A. (1982) Dual and Primal-Dual Methods for Solving Strictly Convex Quadratic Programs.
Available on: http://www.javaquant.net/papers/GoldfarbIdnani.pdf .
-
Berwin A Turlach. QuadProg, Quadratic Programming Solver (implementation in Fortran).
Available on: http://school.maths.uwa.edu.au/~berwin/software/quadprog.html .
There are three ways to state a quadratic programming problem in this framework.
-
The first is to state the problem in its canonical form, explicitly stating the
matrix Q and vector d specifying the quadratic function and the matrices A and
vector b specifying the problem constraints.
-
The second is to state the problem with lambda expressions using symbolic variables.
-
The third is to state the problem using text strings.
In the following section we will provide examples for those ways.
This is an example stating the problem using lambdas:
-
R.P. Brent (1973). Algorithms for Minimization without Derivatives, Chapter 4.
Prentice-Hall, Englewood Cliffs, NJ. ISBN 0-13-022335-2.
-
Wikipedia contributors. "Brent's method." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 11 May. 2012. Web. 22 Jun. 2012.
The following example shows how to compute the maximum,
minimum and a single root of a univariate function.
double[] a = { 5.3, 2.3, 4.2 };
int[] idx = a.GetIndices(); // output will be { 0, 1, 2 }
Creates a zero-valued vector.
The type of the vector to be created.
The number of elements in the vector.
A vector of the specified size.
Creates a zero-valued vector.
The type of the vector to be created.
The number of elements in the vector.
A vector of the specified size.
Creates a vector with ones at the positions where
is true, and zero when they
are false.
The type of the vector to be created.
The boolean mask determining where ones will be placed.
Creates a zero-valued vector.
The number of elements in the vector.
A vector of the specified size.
Creates a one-valued vector.
The number of elements in the vector.
A vector of the specified size.
Creates a vector with ones at the positions where
is true, and zero when they
are false.
The boolean mask determining where ones will be placed.
Creates a vector with the given dimension and starting value.
The number of elements in the vector.
The initial values for the vector.
Creates a vector with the given dimension and starting value.
The number of elements in the vector.
The initial values for the vector.
Creates a vector with the given value at the positions where
is true, and zero when they are false.
The initial values for the vector.
The boolean mask determining where the values will be placed.
Creates a vector with the given starting values.
The initial values for the vector.
Creates a vector with the shape of the given vector.
The vector whose shape should be copied.
Creates a one-hot vector, where all values are zero except for the indicated
, which is set to one.
The data type for the vector.
The vector's dimension which will be marked as one.
The size (length) of the vector.
A one-hot vector where only a single position is one and the others are zero.
Creates a vector with the given value at the positions where
is true, and zero when they are false.
The boolean mask determining where the values will be placed.
Creates a vector with the given value at the positions where
is true, and zero when they are false.
The boolean mask determining where the values will be placed.
The vector where the one-hot should be marked.
Creates a one-hot vector, where all values are zero except for the indicated
, which is set to one.
The vector's dimension which will be marked as one.
The size (length) of the vector.
A one-hot vector where only a single position is one and the others are zero.
Creates a one-hot vector, where all values are zero except for the indicated
, which is set to one.
The data type for the vector.
The vector's dimension which will be marked as one.
The vector where the one-hot should be marked.
A one-hot vector where only a single position is one and the others are zero.
Creates a one-hot vector, where all values are zero except for the indicated
, which is set to one.
The vector's dimension which will be marked as one.
The vector where the one-hot should be marked.
A one-hot vector where only a single position is one and the others are zero.
Creates a k-hot vector, where all values are zero except for the elements
at the indicated , which are set to one.
The vector's dimensions which will be marked as ones.
The size (length) of the vector.
A k-hot vector where the indicated positions are one and the others are zero.
Creates a k-hot vector, where all values are zero except for the elements
at the positions where is true, which are set to one.
The boolean mask determining where the values will be placed.
A k-hot vector where the indicated positions are one and the others are zero.
Creates a k-hot vector, where all values are zero except for the elements
at the indicated , which are set to one.
The vector's dimensions which will be marked as ones.
The size (length) of the vector.
A k-hot vector where the indicated positions are one and the others are zero.
Creates a k-hot vector, where all values are zero except for the elements
at the indicated , which are set to one.
The vector's dimensions which will be marked as ones.
The vector where the k-hot should be marked.
A k-hot vector where the indicated positions are one and the others are zero.
Creates a k-hot vector, where all values are zero except for the elements
at the positions where is true, which are set to one.
The boolean mask determining where the values will be placed.
The vector where the k-hot should be marked.
A k-hot vector where the indicated positions are one and the others are zero.
Creates a k-hot vector, where all values are zero except for the elements
at the indicated , which are set to one.
The vector's dimensions which will be marked as ones.
The vector where the k-hot should be marked.
A k-hot vector where the indicated positions are one and the others are zero.
Counts how many times an integer label appears in a vector (i.e. creates
an histogram of integer values assuming possible values start at zero and
go up to the maximum value of in the vector).
An array containing the integer labels to be counted.
An integer array of size corresponding to the maximum label in the vector
, containing how many times each possible label
appears in .
Counts how many times an integer label appears in a vector (i.e. creates
an histogram of integer values assuming possible values start at zero and
go up to the value of ).
An array containing the integer labels to be counted.
The number of labels (will be the size of the generated histogram).
An integer array of size containing how many
times each possible label appears in .
Counts how many times an integer label appears in a vector (i.e. creates
an histogram of integer values assuming possible values start at zero and
go up to the maximum value of in the vector).
An array containing the integer labels to be counted.
The histogram to were the counts will be added. This
vector should have been zeroed out before being passed to this method.
The same vector passed as an argument.
Creates a shallow copy of the array.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(a, b, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(range, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(range, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(range, stepSize) instead.
Creates an interval vector (like NumPy's linspace function).
The Range methods should be equivalent to NumPy's np.linspace function. For
a similar method that accepts a step size instead of a number of steps, see
.
Obsolete. Please use Vector.Range(range, stepSize) instead.
Shuffles an array.
Shuffles a collection.
Sorts the elements of an entire one-dimensional array using the given comparison.
Sorts the elements of an entire one-dimensional array using the given comparison.
Sorts the elements of an entire one-dimensional array using the given comparison.
Shuffles an array.
Shuffles a collection.
Sorts the elements of an entire one-dimensional array using the given comparison.
Sorts the elements of an entire one-dimensional array using the given comparison.
Sorts the elements of an entire one-dimensional array using the given comparison.
Sorts the elements of an entire one-dimensional array using the given comparison.
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Returns a vector containing indices (0, 1, 2, ..., n - 1) in random
order. The vector grows up to to , but does not
include size among its values.
The size of the sample vector to be generated.
var a = Vector.Sample(3); // a possible output is { 2, 1, 0 };
var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5))
{
// ...
}
Returns a vector of the specified containing
non-repeating indices in the range [0, populationSize) in random order.
The size of the sample vector to be generated.
The non-inclusive maximum number an index can have.
In other words, this return a sample of size k from a population
of size N, where k is the parameter
and N is the parameter .
var a = Vector.Sample(3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(5, 6))
{
// ...
}
Returns a vector of the specified of the
containing non-repeating indices in the
range [0, populationSize) in random order.
The percentage of the population to sample.
The non-inclusive maximum number an index can have.
var a = Vector.Sample(0.3, 10); // a possible output is { 1, 7, 4 };
var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };
foreach (var i in Vector.Sample(0.2, 6))
{
// ...
}
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a vector with uniformly distributed random data.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Enumerates through a range (like Python's xrange function).
The inclusive lower bound of the range.
The exclusive upper bound of the range.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Creates a range vector (like NumPy's arange function).
The range from where values should be created.
The step size to be taken between elements.
This parameter can be negative to create a decreasing range.
The Range methods should be equivalent to NumPy's np.arange method, with one
single difference: when the intervals are inverted (i.e. a > b) and the step
size is negative, the framework still iterates over the range backwards, as
if the step was negative.
This function never includes the upper bound of the range. For methods
that include it, please see the methods.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts a value from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Converts values from one scale to another scale.
Comparison methods that can be used in sort
algorithms such as .
This namespace contains different methods for comparing elements. For
example, using the classes in this namespace makes it possible to sort
arrays of arrays,
sort arrays into any direction, or perform
stable sorts.
The namespace class diagram is shown below.
Elementwise comparer for integer arrays.
Please use ArrayComparer{T} instead.
Elementwise comparer for arrays.
Determines whether two instances are equal.
The first object to compare.
The second object to compare.
true if the specified object is equal to the other; otherwise, false.
Returns a hash code for a given instance.
The instance.
A hash code for the instance, suitable for use
in hashing algorithms and data structures like a hash table.
Element-at-position comparer.
This class compares arrays by checking the value
of a particular element at a given array index.
// We sort the arrays according to the
// elements at their second column.
double[][] values =
{ // v
new double[] { 0, 3, 0 },
new double[] { 0, 4, 1 },
new double[] { -1, 1, 1 },
new double[] { -1, 5, 4 },
new double[] { -2, 2, 6 },
};
// Sort the array considering only the second column
Array.Sort(values, new ElementComparer() { Index = 1 });
// The result will be
double[][] result =
{
new double[] { -1, 1, 1 },
new double[] { -2, 2, 6 },
new double[] { 0, 3, 0 },
new double[] { 0, 4, 1 },
new double[] { -1, 5, 4 },
};
Element-at-position comparer.
This class compares arrays by checking the value
of a particular element at a given array index.
// We sort the arrays according to the
// elements at their second column.
double[][] values =
{ // v
new double[] { 0, 3, 0 },
new double[] { 0, 4, 1 },
new double[] { -1, 1, 1 },
new double[] { -1, 5, 4 },
new double[] { -2, 2, 6 },
};
// Sort the array considering only the second column
Array.Sort(values, new ElementComparer() { Index = 1 });
// The result will be
double[][] result =
{
new double[] { -1, 1, 1 },
new double[] { -2, 2, 6 },
new double[] { 0, 3, 0 },
new double[] { 0, 4, 1 },
new double[] { -1, 5, 4 },
};
Gets or sets the element index to compare.
Compares two objects and returns a value indicating
whether one is less than, equal to, or greater than the other.
The first object to compare.
The second object to compare.
Determines whether two instances are equal.
The first object to compare.
The second object to compare.
true if the specified object is equal to the other; otherwise, false.
Returns a hash code for a given instance.
The instance.
A hash code for the instance, suitable for use
in hashing algorithms and data structures like a hash table.
Custom comparer which accepts any delegate or
anonymous function to perform value comparisons.
The type of objects to compare.
// Assume we have values to sort
double[] values = { 0, 5, 3, 1, 8 };
// We can create an ad-hoc sorting rule using
Array.Sort(values, new CustomComparer<double>((a, b) => -a.CompareTo(b)));
// Result will be { 8, 5, 3, 1, 0 }.
Constructs a new .
The comparer function.
Compares two objects and returns a value indicating
whether one is less than, equal to, or greater than
the other.
The first object to compare.
The second object to compare.
A signed integer that indicates the relative values of x and y.
Determines whether the specified objects are equal.
The first object of type T to compare.
The second object of type T to compare.
true if the specified objects are equal; otherwise, false.
Returns a hash code for the given object.
The object.
A hash code for the given object, suitable for use in
hashing algorithms and data structures like a hash table.
Directions for the General Comparer.
Sorting will be performed in ascending order.
Sorting will be performed in descending order.
General comparer which supports multiple
directions and comparison of absolute values.
// Assume we have values to sort
double[] values = { 0, -5, 3, 1, 8 };
// We can create an ad-hoc sorting rule considering only absolute values
Array.Sort(values, new GeneralComparer(ComparerDirection.Ascending, Math.Abs));
// Result will be { 0, 1, 3, 5, 8 }.
Gets or sets the sorting direction
used by this comparer.
Constructs a new General Comparer.
The direction to compare.
Constructs a new General Comparer.
The direction to compare.
True to compare absolute values, false otherwise. Default is false.
Constructs a new General Comparer.
The direction to compare.
The mapping function which will be applied to
each vector element prior to any comparisons.
Compares two objects and returns a value indicating whether one is less than,
equal to, or greater than the other.
The first object to compare.
The second object to compare.
Compares two objects and returns a value indicating whether one is less than,
equal to, or greater than the other.
The first object to compare.
The second object to compare.
General comparer which supports multiple sorting directions.
// Assume we have values to sort
double[] values = { 0, -5, 3, 1, 8 };
// We can create an ad-hoc sorting rule
Array.Sort(values, new GeneralComparer<double>(ComparerDirection.Descending));
// Result will be { 8, 5, 3, 1, 0 }.
Gets or sets the sorting direction
used by this comparer.
Constructs a new General Comparer.
The direction to compare.
Compares two objects and returns a value indicating whether one is less than,
equal to, or greater than the other.
The first object to compare.
The second object to compare.
Stable comparer for stable sorting algorithm.
The type of objects to compare.
This class helps sort the elements of an array without swapping
elements which are already in order. This comprises a stable
sorting algorithm. This class is used by the method to produce a stable sort
of its given arguments.
In order to use this class, please use .
Constructs a new instance of the class.
The comparison function.
Compares two objects and returns a value indicating
whether one is less than, equal to, or greater than
the other.
The first object to compare.
The second object to compare.
A signed integer that indicates the relative values of x and y.
Common interface for convergence detection algorithms.
Please use MaxIterations instead.
Gets or sets the watched value after the iteration.
Common interface for convergence detection algorithms.
Gets or sets the maximum relative change in the watched value
after an iteration of the algorithm used to detect convergence.
Gets or sets the maximum number of iterations
performed by the iterative algorithm.
Gets the current iteration number.
Gets or sets whether the algorithm has converged.
Resets this instance, reverting all iteration statistics
statistics (number of iterations, last error) back to zero.
General convergence options.
Creates a new object.
The number of variables to be tracked.
Gets or sets the number of variables in the problem.
Gets or sets the relative function tolerance that should
be used as convergence criteria. This tracks the relative
amount that the function output changes after two consecutive
iterations. Setting this value to zero disables those checks.
Default is 0.
Gets or sets the absolute function tolerance that should
be used as convergence criteria. This tracks the absolute
amount that the function output changes after two consecutive
iterations. Setting this value to zero disables those checks.
Default is 0.
Gets or sets the relative parameter tolerance that should
be used as convergence criteria. This tracks the relative
amount that the model parameters changes after two consecutive
iterations. Setting this value to zero disables those checks.
Default is 0.
Gets or sets the absolute parameter tolerance that should
be used as convergence criteria. This tracks the absolute
amount that the model parameters changes after two consecutive
iterations. Setting this value to zero disables those checks.
Default is 0.
Gets or sets the number of function evaluations
performed by the optimization algorithm.
Gets or sets the maximum number of function evaluations to
be used as convergence criteria. This tracks how many times
the function to be optimized has been called, and stops the
algorithm when the number of times specified in this property
has been reached. Setting this value to zero disables this check.
Default is 0.
Gets or sets the maximum amount of time that an optimization
algorithm is allowed to run. This property must be set together
with in order to function correctly.
Setting this value to disables this
check. Default is .
Gets or sets the time when the algorithm started running. When
time will be tracked with the property,
this property must also be set to a correct value.
Gets or sets whether the algorithm should
be forced to terminate. Default is false.
Owen's T function and related functions.
In mathematics, Owen's T function T(h, a), named after statistician Donald Bruce Owen,
is defined by
1 a exp{-0.5 h²(1+x²)
T(h, a) = ---- ∫ ------------------- dx
2π 0 1 + x²
The function T(h, a) gives the probability of the event (X > h and 0 < Y < aX)
where X and Y are independent standard normal random variables. This function can
be used to calculate bivariate normal distribution probabilities
and, from there, in the calculation of multivariate normal distribution probabilities. It also
frequently appears in various integrals involving Gaussian functions.
The code is based on the original FORTRAN77 version by Mike Patefield, David Tandy;
and the C version created by John Burkardt. The original code for the C version can
be found at http://people.sc.fsu.edu/~jburkardt/c_src/owens/owens.html and is valid
under the LGPL.
References:
-
http://people.sc.fsu.edu/~jburkardt/c_src/owens/owens.html
-
Mike Patefield, David Tandy, Fast and Accurate Calculation of Owen's T Function,
Journal of Statistical Software, Volume 5, Number 5, 2000, pages 1-25.
// Computes Owens' T function
double t = OwensT.Function(h: 2, a: 42); // 0.011375065974089608
Computes Owen's T function for arbitrary H and A.
Owen's T function argument H.
Owen's T function argument A.
The value of Owen's T function.
Owen's T function for a restricted range of parameters.
Owen's T function argument H (where 0 <= H).
Owen's T function argument A (where 0 <= A <= 1).
The value of A*H.
The value of Owen's T function.
Numerical methods for approximating integrals.
This namespace contains different methods for numerically approximating
integrals, such as the Trapezoidal Rule,
Romberg method, up to more advanced versions
such as the Infinite Adaptive Gauss
Kronrod for improper integrals or
Monte Carlo integration for multivariate integrals.
The namespace class diagram is shown below.
Common interface for multidimensional integration methods.
Gets the number of parameters expected by
the to be integrated.
Gets or sets the multidimensional function
whose integral should be computed.
Gets or sets the range of each input variable
under which the integral must be computed.
Common interface for multidimensional integration methods.
Gets or sets the unidimensional function
whose integral should be computed.
Gets or sets the input range under
which the integral must be computed.
Common interface for numeric integration methods.
Gets the numerically computed result of the
definite integral for the specified function.
Computes the area of the function under the selected
range. The computed value will be available at this
class's property.
True if the integration method succeeds, false otherwise.
Common interface for numeric integration methods.
Get the exit code returned in the last call to the
method.
Status codes for the
integration method.
The integration calculation has been completed with success.
The obtained result is under the selected convergence criteria.
Maximum number of allowed subdivisions has been reached.
The maximum number of subdivisions allowed has been achieved. One can allow
more subdivisions by increasing the value of limit (and taking the according
dimension adjustments into account). However, if this yields no improvement
it is advised to analyze the integrand in order to determine the integration
difficulties. If the position of a local difficulty can be determined (e.g.
singularity, discontinuity within the interval) one will probably gain from
splitting up the interval at this point and calling the integrator on the
subranges. if possible, an appropriate special-purpose integrator should be
used, which is designed for handling the type of difficulty involved.
Roundoff errors prevent the tolerance from being reached.
The occurrence of roundoff error is detected, which prevents the requested
tolerance from being achieved. The error may be under-estimated.
There are severe discontinuities in the integrand function.
Extremely bad integrand behaviour occurs at some points of the
integration interval.
The algorithm cannot converge.
The algorithm does not converge. Roundoff error is detected in the
extrapolation table. It is assumed that the requested tolerance cannot
be achieved, and that the returned result is the best which can be obtained.
The integral is divergent or slowly convergent.
The integral is probably divergent, or slowly convergent. It must be
noted that divergence can occur with any other error code.
Infinite Adaptive Gauss-Kronrod integration method.
In applied mathematics, adaptive quadrature is a process in which the
integral of a function f(x) is approximated using static quadrature rules
on adaptively refined subintervals of the integration domain. Generally,
adaptive algorithms are just as efficient and effective as traditional
algorithms for "well behaved" integrands, but are also effective for
"badly behaved" integrands for which traditional algorithms fail.
The algorithm implemented by this class has been based on the original FORTRAN
implementation from QUADPACK. The function implemented the Non-adaptive Gauss-
Kronrod integration is qagi(f,bound,inf,epsabs,epsrel,result,abserr,neval,
ier,limit,lenw,last,iwork,work). The original source code is in the public
domain, but this version is under the LGPL. The original authors, as long as the
original routine description, are listed below:
Robert Piessens, Elise de Doncker; Applied Mathematics and Programming Division,
K.U.Leuven, Leuvenappl. This routine calculates an approximation result to a given
integral i = integral of f over (bound,+infinity) or i = integral of f over
(-infinity,bound) or i = integral of f over (-infinity,+infinity) hopefully satisfying
following claim for accuracy abs(i-result).le.max(epsabs,epsrel*abs(i)).
References:
-
Wikipedia, The Free Encyclopedia. Adaptive quadrature. Available on:
http://en.wikipedia.org/wiki/Adaptive_quadrature
-
Wikipedia, The Free Encyclopedia. QUADPACK. Available on:
http://en.wikipedia.org/wiki/QUADPACK
-
Robert Piessens, Elise de Doncker; Non-adaptive integration standard fortran
subroutine (qng.f). Applied Mathematics and Programming Division, K.U.Leuven,
Leuvenappl. Available at: http://www.netlib.no/netlib/quadpack/qagi.f
Let's say we would like to compute the definite integral of the function
f(x) = cos(x) in the interval -1 to +1 using a variety of integration
methods, including the ,
and . Those methods can compute definite
integrals where the integration interval is finite:
// Declare the function we want to integrate
Func<double, double> f = (x) => Math.Cos(x);
// We would like to know its integral from -1 to +1
double a = -1, b = +1;
// Integrate!
double trapez = TrapezoidalRule.Integrate(f, a, b, steps: 1000); // 1.6829414
double romberg = RombergMethod.Integrate(f, a, b); // 1.6829419
double nagk = NonAdaptiveGaussKronrod.Integrate(f, a, b); // 1.6829419
Moreover, it is also possible to calculate the value of improper integrals
(it is, integrals with infinite bounds) using ,
as shown below. Let's say we would like to compute the area under the Gaussian
curve from -infinite to +infinite. While this function has infinite bounds, this
function is known to integrate to 1.
// Declare the Normal distribution's density function (which is the Gaussian's bell curve)
Func<double, double> g = (x) => (1 / Math.Sqrt(2 * Math.PI)) * Math.Exp(-(x * x) / 2);
// Integrate!
double iagk = InfiniteAdaptiveGaussKronrod.Integrate(g,
Double.NegativeInfinity, Double.PositiveInfinity); // Result should be 0.99999...
Get the maximum number of subintervals to be utilized in the
partition of the integration interval.
Gets or sets the function to be differentiated.
Gets or sets the input range under
which the integral must be computed.
Desired absolute accuracy. If set to zero, this parameter
will be ignored and only other requisites will be taken
into account. Default is zero.
Desired relative accuracy. If set to zero, this parameter
will be ignored and only other requisites will be taken
into account. Default is 1e-3.
Get the exit code returned in the last call to the
method.
Gets the numerically computed result of the
definite integral for the specified function.
Gets the integration error for the
computed value.
Gets the number of function evaluations performed in
the last call to the method.
Creates a new integration algorithm.
Maximum number of subintervals in the
partition of the given integration interval. Default is 100.
Creates a new integration algorithm.
Maximum number of subintervals in the
partition of the given integration interval. Default is 100.
The function to be integrated.
Creates a new integration algorithm.
Maximum number of subintervals in the
partition of the given integration interval. Default is 100.
The function to be integrated.
The lower limit of integration.
The upper limit of integration.
Computes the area of the function under the selected .
The computed value will be available at this object's .
If the integration method fails, the reason will be available at .
True if the integration method succeeds, false otherwise.
Computes the area under the integral for the given function, in the given
integration interval, using the Infinite Adaptive Gauss Kronrod algorithm.
The unidimensional function whose integral should be computed.
The integral's value in the current interval.
Computes the area under the integral for the given function, in the given
integration interval, using the Infinite Adaptive Gauss Kronrod algorithm.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The integral's value in the current interval.
Computes the area under the integral for the given function, in the given
integration interval, using the Infinite Adaptive Gauss Kronrod algorithm.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The relative tolerance under which the solution has to be found. Default is 1e-3.
The integral's value in the current interval.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Status codes for the
integration method.
The integration calculation has been completed with success.
The obtained result is under the selected convergence criteria.
Maximum number of steps has been reached.
The maximum number of steps has been executed. The integral
is probably too difficult to be calculated by dqng.
Non-Adaptive Gauss-Kronrod integration method.
The algorithm implemented by this class has been based on the original FORTRAN
implementation from QUADPACK. The function implemented the Non-adaptive Gauss-
Kronrod integration is qng(f,a,b,epsabs,epsrel,result,abserr,neval,ier).
The original source code is in the public domain, but this version is under the
LGPL. The original authors, as long as the original routine description, are
listed below:
Robert Piessens, Elise de Doncker; Applied Mathematics and Programming Division,
K.U.Leuven, Leuvenappl. This routine calculates an approximation result to a given
definite integral i = integral of f over (a,b), hopefully satisfying following claim
for accuracy abs(i-result).le.max(epsabs,epsrel*abs(i)).
References:
-
Wikipedia, The Free Encyclopedia. QUADPACK. Available on:
http://en.wikipedia.org/wiki/QUADPACK
-
Robert Piessens, Elise de Doncker; Non-adaptive integration standard fortran
subroutine (qng.f). Applied Mathematics and Programming Division, K.U.Leuven,
Leuvenappl. Available at: http://www.netlib.no/netlib/quadpack/qng.f
Let's say we would like to compute the definite integral of the function
f(x) = cos(x) in the interval -1 to +1 using a variety of integration
methods, including the ,
and . Those methods can compute definite
integrals where the integration interval is finite:
// Declare the function we want to integrate
Func<double, double> f = (x) => Math.Cos(x);
// We would like to know its integral from -1 to +1
double a = -1, b = +1;
// Integrate!
double trapez = TrapezoidalRule.Integrate(f, a, b, steps: 1000); // 1.6829414
double romberg = RombergMethod.Integrate(f, a, b); // 1.6829419
double nagk = NonAdaptiveGaussKronrod.Integrate(f, a, b); // 1.6829419
Moreover, it is also possible to calculate the value of improper integrals
(it is, integrals with infinite bounds) using ,
as shown below. Let's say we would like to compute the area under the Gaussian
curve from -infinite to +infinite. While this function has infinite bounds, this
function is known to integrate to 1.
// Declare the Normal distribution's density function (which is the Gaussian's bell curve)
Func<double, double> g = (x) => (1 / Math.Sqrt(2 * Math.PI)) * Math.Exp(-(x * x) / 2);
// Integrate!
double iagk = InfiniteAdaptiveGaussKronrod.Integrate(g,
Double.NegativeInfinity, Double.PositiveInfinity); // Result should be 0.99999...
Gets or sets the function to be differentiated.
Gets or sets the input range under
which the integral must be computed.
Desired absolute accuracy. If set to zero, this parameter
will be ignored and only other requisites will be taken
into account. Default is zero.
Desired relative accuracy. If set to zero, this parameter
will be ignored and only other requisites will be taken
into account. Default is 1e-3.
Gets the numerically computed result of the
definite integral for the specified function.
Gets the integration error for the
computed value.
Get the exit code returned in the last call to the
method.
Gets the number of function evaluations performed in
the last call to the method.
Creates a new integration algorithm.
Creates a new integration algorithm.
The function to be integrated.
Creates a new integration algorithm.
The function to be integrated.
The lower limit of integration.
The upper limit of integration.
Computes the area of the function under the selected .
The computed value will be available at this object's .
If the integration method fails, the reason will be available at .
True if the integration method succeeds, false otherwise.
Computes the area under the integral for the given function,
in the given integration interval, using Gauss-Kronrod method.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The integral's value in the current interval.
Computes the area under the integral for the given function, in the given
integration interval, using the Non-Adaptive Gauss Kronrod algorithm.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The relative tolerance under which the solution has to be found. Default is 1e-3.
The integral's value in the current interval.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Monte Carlo method for multi-dimensional integration.
In mathematics, Monte Carlo integration is a technique for numerical
integration using random numbers. It is a particular Monte Carlo method
that numerically computes a definite integral. While other algorithms
usually evaluate the integrand at a regular grid, Monte Carlo randomly
choose points at which the integrand is evaluated. This method is
particularly useful for higher-dimensional integrals. There are different
methods to perform a Monte Carlo integration, such as uniform sampling,
stratified sampling and importance sampling.
References:
-
Wikipedia, The Free Encyclopedia. Monte Carlo integration. Available on:
http://en.wikipedia.org/wiki/Monte_Carlo_integration
A common Monte-Carlo integration example is to compute the value of Pi. This is the
same example given in Wikipedia's page for Monte-Carlo Integration, available at
https://en.wikipedia.org/wiki/Monte_Carlo_integration#Example
// Define a function H that tells whether two points
// are inside a unit circle (a circle of radius one):
//
Func<double, double, double> H =
(x, y) => (x * x + y * y <= 1) ? 1 : 0;
// We will check how many points in the square (-1,-1), (-1,+1),
// (+1, -1), (+1, +1) fall into the circle defined by function H.
//
double[] from = { -1, -1 };
double[] to = { +1, +1 };
int samples = 100000;
// Integrate it!
double area = MonteCarloIntegration.Integrate(x => H(x[0], x[1]), from, to, samples);
// Output should be approximately 3.14.
Gets the number of parameters expected by
the to be integrated.
Gets or sets the range of each input variable
under which the integral must be computed.
Gets or sets the multidimensional function
whose integral should be computed.
Gets or sets the random generator algorithm to be used within
this Monte Carlo method.
Gets the numerically computed result of the
definite integral for the specified function.
Gets the integration error for the
computed value.
Gets or sets the number of random samples
(iterations) generated by the algorithm.
Constructs a new Monte Carlo integration method.
The function to be integrated.
The number of parameters expected by the .
Constructs a new Monte Carlo integration method.
The number of parameters expected by the integrand.
Manually resets the previously computed area and error
estimates, so the integral can be computed from scratch
without reusing previous computations.
Computes the area of the function under the selected .
The computed value will be available at this object's .
True if the integration method succeeds, false otherwise.
Computes the area of the function under the selected .
The computed value will be available at this object's .
True if the integration method succeeds, false otherwise.
Computes the area of the function under the selected .
The computed value will be available at this object's .
True if the integration method succeeds, false otherwise.
Computes the area under the integral for the given function, in the
given integration interval, using a Monte Carlo integration algorithm.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The number of points that should be sampled.
The integral's value in the current interval.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Romberg's method for numerical integration.
In numerical analysis, Romberg's method (Romberg 1955) is used to estimate
the definite integral ∫_a^b(x) dx by applying Richardson extrapolation
repeatedly on the trapezium rule or the rectangle rule (midpoint rule). The
estimates generate a triangular array. Romberg's method is a Newton–Cotes
formula – it evaluates the integrand at equally spaced points. The integrand
must have continuous derivatives, though fairly good results may be obtained
if only a few derivatives exist. If it is possible to evaluate the integrand
at unequally spaced points, then other methods such as Gaussian quadrature
and Clenshaw–Curtis quadrature are generally more accurate.
References:
-
Wikipedia, The Free Encyclopedia. Romberg's method. Available on:
http://en.wikipedia.org/wiki/Romberg's_method
Let's say we would like to compute the definite integral of the function
f(x) = cos(x) in the interval -1 to +1 using a variety of integration
methods, including the ,
and . Those methods can compute definite
integrals where the integration interval is finite:
// Declare the function we want to integrate
Func<double, double> f = (x) => Math.Cos(x);
// We would like to know its integral from -1 to +1
double a = -1, b = +1;
// Integrate!
double trapez = TrapezoidalRule.Integrate(f, a, b, steps: 1000); // 1.6829414
double romberg = RombergMethod.Integrate(f, a, b); // 1.6829419
double nagk = NonAdaptiveGaussKronrod.Integrate(f, a, b); // 1.6829419
Moreover, it is also possible to calculate the value of improper integrals
(it is, integrals with infinite bounds) using ,
as shown below. Let's say we would like to compute the area under the Gaussian
curve from -infinite to +infinite. While this function has infinite bounds, this
function is known to integrate to 1.
// Declare the Normal distribution's density function (which is the Gaussian's bell curve)
Func<double, double> g = (x) => (1 / Math.Sqrt(2 * Math.PI)) * Math.Exp(-(x * x) / 2);
// Integrate!
double iagk = InfiniteAdaptiveGaussKronrod.Integrate(g,
Double.NegativeInfinity, Double.PositiveInfinity); // Result should be 0.99999...
Gets or sets the unidimensional function
whose integral should be computed.
Gets the numerically computed result of the
definite integral for the specified function.
Gets or sets the number of steps used
by Romberg's method. Default is 6.
Gets or sets the input range under
which the integral must be computed.
Constructs a new Romberg's integration method.
Constructs a new Romberg's integration method.
The unidimensional function whose integral should be computed.
Constructs a new Romberg's integration method.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
Constructs a new Romberg's integration method.
The number of steps used in Romberg's method. Default is 6.
Constructs a new Romberg's integration method.
The number of steps used in Romberg's method. Default is 6.
The unidimensional function whose integral should be computed.
Constructs a new Romberg's integration method.
The number of steps used in Romberg's method. Default is 6.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
Computes the area of the function under the selected .
The computed value will be available at this object's .
True if the integration method succeeds, false otherwise.
Computes the area under the integral for the given function,
in the given integration interval, using Romberg's method.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The integral's value in the current interval.
Computes the area under the integral for the given function,
in the given integration interval, using Romberg's method.
The number of steps used in Romberg's method. Default is 6.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The integral's value in the current interval.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Trapezoidal rule for numerical integration.
In numerical analysis, the trapezoidal rule (also known as the trapezoid rule
or trapezium rule) is a technique for approximating the definite integral
∫_a^b(x) dx. The trapezoidal rule works by approximating the region
under the graph of the function f(x) as a trapezoid and calculating its area.
It follows that ∫_a^b(x) dx ~ (b - a) [f(a) - f(b)] / 2.
References:
-
Wikipedia, The Free Encyclopedia. Trapezoidal rule. Available on:
http://en.wikipedia.org/wiki/Trapezoidal_rule
Let's say we would like to compute the definite integral of the function
f(x) = cos(x) in the interval -1 to +1 using a variety of integration
methods, including the ,
and . Those methods can compute definite
integrals where the integration interval is finite:
// Declare the function we want to integrate
Func<double, double> f = (x) => Math.Cos(x);
// We would like to know its integral from -1 to +1
double a = -1, b = +1;
// Integrate!
double trapez = TrapezoidalRule.Integrate(f, a, b, steps: 1000); // 1.6829414
double romberg = RombergMethod.Integrate(f, a, b); // 1.6829419
double nagk = NonAdaptiveGaussKronrod.Integrate(f, a, b); // 1.6829419
Moreover, it is also possible to calculate the value of improper integrals
(it is, integrals with infinite bounds) using ,
as shown below. Let's say we would like to compute the area under the Gaussian
curve from -infinite to +infinite. While this function has infinite bounds, this
function is known to integrate to 1.
// Declare the Normal distribution's density function (which is the Gaussian's bell curve)
Func<double, double> g = (x) => (1 / Math.Sqrt(2 * Math.PI)) * Math.Exp(-(x * x) / 2);
// Integrate!
double iagk = InfiniteAdaptiveGaussKronrod.Integrate(g,
Double.NegativeInfinity, Double.PositiveInfinity); // Result should be 0.99999...
Gets or sets the unidimensional function
whose integral should be computed.
Gets the numerically computed result of the
definite integral for the specified function.
Gets or sets the number of steps into which the
integration interval will
be divided. Default is 6.
Gets or sets the input range under
which the integral must be computed.
Constructs a new integration method.
Constructs a new integration method.
The unidimensional function whose integral should be computed.
Constructs a new integration method.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
Constructs a new integration method.
The number of steps into which the integration
interval will be divided.
Constructs a new integration method.
The number of steps into which the integration
interval will be divided.
The unidimensional function
whose integral should be computed.
Constructs a new integration method.
The number of steps into which the integration
interval will be divided.
The unidimensional function
whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
Computes the area of the function under the selected .
The computed value will be available at this object's .
True if the integration method succeeds, false otherwise.
Creates a new object that is a copy of the current instance.
A new object that is a copy of this instance.
Computes the area under the integral for the given function,
in the given integration interval, using the Trapezoidal rule.
The number of steps into which the integration interval will be divided.
The unidimensional function whose integral should be computed.
The beginning of the integration interval.
The ending of the integration interval.
The integral's value in the current interval.
Derivative approximation by finite differences.
Numerical differentiation is a technique of numerical analysis to produce an estimate
of the derivative of a mathematical function or function subroutine using values from
the function and perhaps other knowledge about the function.
A finite difference is a mathematical expression of the form f(x + b) − f(x + a). If a
finite difference is divided by b − a, one gets a difference quotient. The approximation
of derivatives by finite differences plays a central role in finite difference methods
for the numerical solution of differential equations, especially boundary value problems.
This class implements Newton's finite differences method for approximating the derivatives
of a multivariate function. A simplified version of the class is also available for
univariate functions through
its Derivative static methods.
References:
-
Wikipedia, The Free Encyclopedia. Finite difference. Available on:
http://en.wikipedia.org/wiki/Finite_difference
-
Trent F. Guidry, Calculating derivatives of a function numerically. Available on:
http://www.trentfguidry.net/post/2009/07/12/Calculate-derivatives-function-numerically.aspx
int length = 3; // The number of variables; or number
// of columns in the generated table.
// Generate the table using Combinatorics.TruthTable(3)
int[][] table = Combinatorics.TruthTable(length);
// The generated table will be:
{
new int[] { 0, 0, 0 },
new int[] { 0, 0, 1 },
new int[] { 0, 1, 0 },
new int[] { 0, 1, 1 },
new int[] { 1, 0, 0 },
new int[] { 1, 0, 1 },
new int[] { 1, 1, 0 },
new int[] { 1, 1, 1 },
};
Generates all possible ordered permutations
with repetitions allowed (a truth table).
The number of symbols.
The length of the sequence to generate.
Suppose we would like to generate a truth table for a binary
problem. In this case, we are only interested in two symbols:
0 and 1. Let's then generate the table for three binary values
int symbols = 2; // Binary variables: either 0 or 1
int length = 3; // The number of variables; or number
// of columns in the generated table.
// Generate the table using Combinatorics.TruthTable(2,3)
int[][] table = Combinatorics.TruthTable(symbols, length);
// The generated table will be:
{
new int[] { 0, 0, 0 },
new int[] { 0, 0, 1 },
new int[] { 0, 1, 0 },
new int[] { 0, 1, 1 },
new int[] { 1, 0, 0 },
new int[] { 1, 0, 1 },
new int[] { 1, 1, 0 },
new int[] { 1, 1, 1 },
};
Generates all possible ordered permutations
with repetitions allowed (a truth table).
The number of symbols for each variable.
Suppose we would like to generate a truth table (i.e. all possible
combinations of a set of discrete symbols) for variables that contain
different numbers symbols. Let's say, for example, that the first
variable may contain symbols 0 and 1, the second could contain either
0, 1, or 2, and the last one again could contain only 0 and 1. Thus
we can generate the truth table in the following way:
// Number of symbols for each variable
int[] symbols = { 2, 3, 2 };
// Generate the truth table for the given symbols
int[][] table = Combinatorics.TruthTable(symbols);
// The generated table will be:
{
new int[] { 0, 0, 0 },
new int[] { 0, 0, 1 },
new int[] { 0, 1, 0 },
new int[] { 0, 1, 1 },
new int[] { 0, 2, 0 },
new int[] { 0, 2, 1 },
new int[] { 1, 0, 0 },
new int[] { 1, 0, 1 },
new int[] { 1, 1, 0 },
new int[] { 1, 1, 1 },
new int[] { 1, 2, 0 },
new int[] { 1, 2, 1 },
};
Provides a way to enumerate all possible ordered permutations
with repetitions allowed (i.e. a truth table), without using
many memory allocations.
The length of the sequence to generate.
If set to true, the different generated sequences will be stored in
the same array, thus preserving memory. However, this may prevent the
samples from being stored in other locations without having to clone
them. If set to false, a new memory block will be allocated for each
new object in the sequence.
Suppose we would like to generate the same sequences shown
in the example,
however, without explicitly storing all possible combinations
in an array. In order to iterate over all possible combinations
efficiently, we can use:
int length = 3; // The number of variables; or number
// of columns in the generated table.
foreach (int[] row in Combinatorics.Sequences(length))
{
// The following sequences will be generated in order:
//
// new int[] { 0, 0, 0 },
// new int[] { 0, 0, 1 },
// new int[] { 0, 1, 0 },
// new int[] { 0, 1, 1 },
// new int[] { 1, 0, 0 },
// new int[] { 1, 0, 1 },
// new int[] { 1, 1, 0 },
// new int[] { 1, 1, 1 },
}
Provides a way to enumerate all possible ordered permutations
with repetitions allowed (i.e. a truth table), without using
many memory allocations.
The number of symbols.
The length of the sequence to generate.
If set to true, the different generated sequences will be stored in
the same array, thus preserving memory. However, this may prevent the
samples from being stored in other locations without having to clone
them. If set to false, a new memory block will be allocated for each
new object in the sequence.
Suppose we would like to generate the same sequences shown
in the example,
however, without explicitly storing all possible combinations
in an array. In order to iterate over all possible combinations
efficiently, we can use:
int symbols = 2; // Binary variables: either 0 or 1
int length = 3; // The number of variables; or number
// of columns in the generated table.
foreach (int[] row in Combinatorics.Sequences(symbols, length))
{
// The following sequences will be generated in order:
//
// new int[] { 0, 0, 0 },
// new int[] { 0, 0, 1 },
// new int[] { 0, 1, 0 },
// new int[] { 0, 1, 1 },
// new int[] { 1, 0, 0 },
// new int[] { 1, 0, 1 },
// new int[] { 1, 1, 0 },
// new int[] { 1, 1, 1 },
}
Provides a way to enumerate all possible ordered permutations
with repetitions allowed (i.e. a truth table), without using
many memory allocations.
The number of symbols for each variable.
If set to true, the different generated permutations will be stored in
the same array, thus preserving memory. However, this may prevent the
samples from being stored in other locations without having to clone
them. If set to false, a new memory block will be allocated for each
new object in the sequence.
Suppose we would like to generate the same sequences shown
in the example,
however, without explicitly storing all possible combinations
in an array. In order to iterate over all possible combinations
efficiently, we can use:
foreach (int[] row in Combinatorics.Sequences(new[] { 2, 2 }))
{
// The following sequences will be generated in order:
//
// new int[] { 0, 0, 0 },
// new int[] { 0, 0, 1 },
// new int[] { 0, 1, 0 },
// new int[] { 0, 1, 1 },
// new int[] { 1, 0, 0 },
// new int[] { 1, 0, 1 },
// new int[] { 1, 1, 0 },
// new int[] { 1, 1, 1 },
}
Enumerates all possible value combinations for a given array.
The array whose combinations need to be generated.
If set to true, the different generated combinations will be stored in
the same array, thus preserving memory. However, this may prevent the
samples from being stored in other locations without having to clone
them. If set to false, a new memory block will be allocated for each
new object in the sequence.
// Create a new convergence criteria for a maximum of 10 iterations
var criteria = new AbsoluteConvergence(iterations: 10, tolerance: 0.1);
int progress = 1;
do
{
// Do some processing...
// Update current iteration information:
criteria.NewValue = 12345.6 / progress++;
} while (!criteria.HasConverged);
// The method will converge after reaching the
// maximum of 10 iterations with a final value
// of 1371.73:
int iterations = criteria.CurrentIteration; // 10
double value = criteria.OldValue; // 1371.7333333
Gets or sets the maximum change in the watched value
after an iteration of the algorithm used to detect
convergence. Default is 0.
Please use MaxIterations instead.
Gets or sets the maximum number of iterations
performed by the iterative algorithm. Default
is 100.
Initializes a new instance of the class.
Initializes a new instance of the class.
The maximum number of iterations which should be
performed by the iterative algorithm. Setting to zero indicates there
is no maximum number of iterations. Default is 0.
The maximum change in the watched value
after an iteration of the algorithm used to detect convergence.
Default is 0.
The initial value for the and
properties.
Gets the watched value before the iteration.
Gets or sets the watched value after the iteration.
Gets or sets the current iteration number.
Gets whether the algorithm has converged.
Clears this instance.
Common interface for convergence detection algorithms that
depend solely on a single value (such as the iteration error).
Relative convergence criteria.
This class can be used to track progress and convergence
of methods which rely on the relative change of a value.
// Create a new convergence criteria with unlimited iterations
var criteria = new RelativeConvergence(iterations: 0, tolerance: 0.1);
int progress = 1;
do
{
// Do some processing...
// Update current iteration information:
criteria.NewValue = 12345.6 / progress++;
} while (!criteria.HasConverged);
// The method will converge after reaching the
// maximum of 11 iterations with a final value
// of 1234.56:
int iterations = criteria.CurrentIteration; // 11
double value = criteria.OldValue; // 1234.56
Gets or sets the maximum relative change in the watched value
after an iteration of the algorithm used to detect convergence.
Default is zero.
Gets or sets the maximum number of iterations
performed by the iterative algorithm. Default
is 100.
Please use MaxIterations instead.
Initializes a new instance of the class.
Initializes a new instance of the class.
The maximum number of iterations which should be
performed by the iterative algorithm. Setting to zero indicates there
is no maximum number of iterations. Default is 100.
The maximum relative change in the watched value
after an iteration of the algorithm used to detect convergence.
Default is 0.
Initializes a new instance of the class.
The maximum number of iterations which should be
performed by the iterative algorithm. Setting to zero indicates there
is no maximum number of iterations. Default is 0.
The maximum relative change in the watched value
after an iteration of the algorithm used to detect convergence.
Default is 0.
The minimum number of convergence checks that the
iterative algorithm should pass before convergence can be declared
reached.
Initializes a new instance of the class.
The maximum number of iterations which should be
performed by the iterative algorithm. Setting to zero indicates there
is no maximum number of iterations. Default is 0.
The maximum relative change in the watched value
after an iteration of the algorithm used to detect convergence.
Default is 0.
The minimum number of convergence checks that the
iterative algorithm should pass before convergence can be declared
reached.
The initial value for the and
properties.
Gets or sets the watched value before the iteration.
Gets or sets the watched value after the iteration.
Gets the current iteration number.
Gets whether the algorithm has converged.
Gets the absolute difference between the and
as as Math.Abs(OldValue - NewValue).
Gets the relative difference between the and
as Math.Abs(OldValue - NewValue) / Math.Abs(OldValue).
Gets the initial value for the
and properties.
Resets this instance, reverting all iteration statistics
statistics (number of iterations, last error) back to zero.
Returns a that represents this instance.
A that represents this instance.
Relative parameter change convergence criteria.
This class can be used to track progress and convergence
of methods which rely on the maximum relative change of
the values within a parameter vector.
// Converge if the maximum change amongst all parameters is less than 0.1:
var criteria = new RelativeParameterConvergence(iterations: 0, tolerance: 0.1);
int progress = 1;
double[] parameters = { 12345.6, 952.12, 1925.1 };
do
{
// Do some processing...
// Update current iteration information:
criteria.NewValues = parameters.Divide(progress++);
} while (!criteria.HasConverged);
// The method will converge after reaching the
// maximum of 11 iterations with a final value
// of { 1234.56, 95.212, 192.51 }:
int iterations = criteria.CurrentIteration; // 11
var v = criteria.OldValues; // { 1234.56, 95.212, 192.51 }
Gets or sets the maximum change in the watched value
after an iteration of the algorithm used to detect convergence.
Gets or sets the maximum number of iterations
performed by the iterative algorithm.
Please use MaxIterations instead.
Initializes a new instance of the class.
Initializes a new instance of the class.
The maximum number of iterations which should be
performed by the iterative algorithm. Setting to zero indicates there
is no maximum number of iterations. Default is 0.
The maximum relative change in the watched value
after an iteration of the algorithm used to detect convergence.
Default is 0.
Gets the maximum relative parameter
change after the last iteration.
Gets or sets the watched value before the iteration.
Gets or sets the watched value after the iteration.
Gets or sets the current iteration number.
Gets whether the algorithm has diverged.
Gets whether the algorithm has converged.
Clears this instance.
GNU R algorithm environment. Work in progress.
Creates a new vector.
Creates a new matrix.
Placeholder vector definition
Vector definition operator.
Inner vector object
Initializes a new instance of the class.
Implements the operator -.
Implements the operator <.
Implements the operator >.
Performs an implicit conversion from
to .
Performs an implicit conversion from
to .
Matrix definition operator.
Inner matrix object.
Initializes a new instance of the class.
Implements the operator -.
Implements the operator <.
Implements the operator >.
Performs an implicit conversion from
to
.
Performs an implicit conversion from
to .
Programming environment for Octave.
This class implements a Domain Specific Language (DSL) for
C# which is remarkably similar to Octave. Please take a loook
on what is possible to do using this class in the examples
section.
To use this class, inherit from .
After this step, all code written inside your child class will
be able to use the syntax below:
Using the mat and ret keywords, it is possible
to replicate most of the Octave environment inside plain C#
code. The example below demonstrates how to compute the
Singular Value Decomposition of a matrix, which in turn was
generated using .
// Declare local matrices
mat u = _, s = _, v = _;
// Compute a new mat
mat M = magic(3) * 5;
// Compute the SVD
ret [u, s, v] = svd(M);
// Write the matrix
string str = u;
/*
0.577350269189626 -0.707106781186548 0.408248290463863
u = 0.577350269189626 -1.48007149071427E-16 -0.816496580927726
0.577350269189626 0.707106781186548 0.408248290463863
*/
It is also possible to ignore certain parameters by
providing a wildcard in the return structure:
// Declare local matrices
mat u = _, v = _;
// Compute a new mat
mat M = magic(3) * 5;
// Compute the SVD
ret [u, _, v] = svd(M); // the second argument is omitted
Standard matrix operations are also supported:
mat I = eye(3); // 3x3 identity matrix
mat A = I * 2; // matrix-scalar multiplication
Console.WriteLine(A);
//
// 2 0 0
// A = 0 2 0
// 0 0 2
mat B = ones(3, 6); // 3x6 unit matrix
Console.WriteLine(B);
//
// 1 1 1 1 1 1
// B = 1 1 1 1 1 1
// 1 1 1 1 1 1
mat C = new double[,]
{
{ 2, 2, 2, 2, 2, 2 },
{ 2, 0, 0, 0, 0, 2 },
{ 2, 2, 2, 2, 2, 2 },
};
mat D = A * B - C;
Console.WriteLine(D);
//
// 0 0 0 0 0 0
// C = 0 2 2 2 2 0
// 0 0 0 0 0 0
Whether to use octave indexing or not.
Pi.
Machine epsilon.
Creates an identity matrix.
Inverts a matrix.
Inverts a matrix.
Creates a unit matrix.
Creates a unit matrix.
Creates a unit matrix.
Creates a unit matrix.
Random vector.
Size of a matrix.
Rank of a matrix.
Matrix sum vector.
Sum of vector elements.
Product of vector elements.
Matrix sum vector.
Rounding.
Ceiling.
Flooring.
Rounding.
Ceiling.
Flooring.
Rounding.
Ceiling.
Flooring.
Sin.
Cos.
Exponential value.
Absolute value.
Logarithm.
Sin.
Cos.
Exponential value.
Absolute value.
Logarithm.
Sin.
Cos.
Exponential value.
Absolute value.
Logarithm.
Creates a magic square matrix.
Singular value decomposition.
QR decomposition.
QR decomposition.
Eigenvalue decomposition.
Eigenvalue decomposition.
Eigenvalue decomposition.
Eigenvalue decomposition.
Eigenvalue decomposition.
Eigenvalue decomposition.
Cholesky decomposition.
Matrix placeholder.
Return setter keyword.
Return definition operator.
Can be used to set output arguments
to the output of another function.
Matrix definition operator.
Inner matrix object.
Initializes a new instance of the class.
Multiplication operator
Multiplication operator
Multiplication operator
Addition operator
Addition operator
Addition operator
Subtraction operator
Subtraction operator
Subtraction operator
Equality operator.
Inequality operator.
Implicit conversion from double[,].
Implicit conversion to double[,].
Implicit conversion to string.
Implicit conversion from list.
Transpose operator.
Determines whether the specified is equal to this instance.
Returns a hash code for this instance.
Initializes a new instance of the class.
Gabor kernel types.
Creates kernel based on the real part of the Gabor function.
Creates a kernel based on the imaginary part of the Gabor function.
Creates a kernel based on the Magnitude of the Gabor function.
Creates a kernel based on the Squared Magnitude of the Gabor function.
Gabor functions.
This class has been contributed by Diego Catalano, author of the Catalano
Framework, a native port of AForge.NET and Accord.NET for Java and Android.
1-D Gabor function.
2-D Gabor function.
Real part of the 2-D Gabor function.
Imaginary part of the 2-D Gabor function.
Computes the 2-D Gabor kernel.
Computes the 2-D Gabor kernel.
Computes the 2-D Gabor kernel.
Computes the 2-D Gabor kernel.
3D Plane class with normal vector and distance from origin.
Creates a new object
passing through the .
The first component of the plane's normal vector.
The second component of the plane's normal vector.
The third component of the plane's normal vector.
Creates a new object
passing through the .
The plane's normal vector.
Initializes a new instance of the class.
The first component of the plane's normal vector.
The second component of the plane's normal vector.
The third component of the plane's normal vector.
The distance from the plane to the origin.
Initializes a new instance of the class.
The plane's normal vector.
The distance from the plane to the origin.
Constructs a new object from three points.
The first point.
The second point.
The third point.
A passing through the three points.
Gets the plane's normal vector.
Gets or sets the constant a in the plane
definition a * x + b * y + c * z + d = 0.
Gets or sets the constant b in the plane
definition a * x + b * y + c * z + d = 0.
Gets or sets the constant c in the plane
definition a * x + b * y + c * z + d = 0.
Gets or sets the distance offset
between the plane and the origin.
Computes the distance from point to plane.
The point to have its distance from the plane computed.
The distance from to this plane.
Normalizes this plane by dividing its components
by the vector's norm.
Implements the operator !=.
Implements the operator !=.
Determines whether the specified is equal to this instance.
The to compare with this instance.
The acceptance tolerance threshold to consider the instances equal.
true if the specified is equal to this instance; otherwise, false.
Determines whether the specified is equal to this instance.
The to compare with this instance.
true if the specified is equal to this instance; otherwise, false.
Determines whether the specified is equal to this instance.
The to compare with this instance.
true if the specified is equal to this instance; otherwise, false.
Returns a hash code for this instance.
A hash code for this instance, suitable for use in hashing
algorithms and data structures like a hash table.
Returns a that represents this instance.
A that represents this instance.
Returns a that represents this instance.
The format.
The format provider.
A that represents this instance.
Returns a that represents this instance.
The variable to put on the left hand side. Can
be either 'x', 'y' or 'z'.
A that represents this instance.
Returns a that represents this instance.
The variable to put on the left hand side. Can
be either 'x', 'y' or 'z'.
The format provider.
A that represents this instance.
3D point structure with X, Y, and coordinates.
Creates a new
structure from the given coordinates.
The x coordinate.
The y coordinate.
The z coordinate.
Creates a new
structure from the given coordinates.
The point coordinates.
Gets or sets the point's X coordinate.
Gets or sets the point's Y coordinate.
Gets or sets the point's Z coordinate.
Performs an implicit conversion from
to .
The point to be converted.
The result of the conversion.
Performs an implicit conversion from
to .
The vector to be converted.
The result of the conversion.
Performs a conversion from
to .
Gets whether three points lie on the same line.
The first point.
The second point.
The third point.
True if there is a line passing through all
three points; false otherwise.
Gets the point at the 3D space origin: (0, 0, 0)
Implements the operator !=.
Implements the operator !=.
Determines whether the specified is equal to this instance.
The to compare with this instance.
The acceptance tolerance threshold to consider the instances equal.
true if the specified is equal to this instance; otherwise, false.
Determines whether the specified is equal to this instance.
The to compare with this instance.
true if the specified is equal to this instance; otherwise, false.
Determines whether the specified is equal to this instance.
The to compare with this instance.
true if the specified is equal to this instance; otherwise, false.
Returns a hash code for this instance.
A hash code for this instance, suitable for use in hashing
algorithms and data structures like a hash table.
Denavit Hartenberg matrix (commonly referred as T).
Gets or sets the transformation matrix T (as in T = Z * X).
Gets or sets the matrix regarding X axis transformations.
Gets or sets the matrix regarding Z axis transformations.
Executes the transform calculations (T = Z*X).
Transform matrix T.
Calling this method also updates the Transform property.
Denavit Hartenberg model for joints.
This class represents either a model itself or a submodel
when used with a
DenavitHartenbergModelCombinator instance.
References:
-
Wikipedia contributors, "Denavit-Hartenberg parameters," Wikipedia,
The Free Encyclopedia, available at:
http://en.wikipedia.org/wiki/Denavit%E2%80%93Hartenberg_parameters
The following example shows the creation and animation
of a 2-link planar manipulator.
// Create the DH-model at location (0, 0, 0)
DenavitHartenbergModel model = new DenavitHartenbergModel();
// Add the first joint
model.Joints.Add(alpha: 0, theta: Math.PI / 4, radius: 35, offset: 0);
// Add the second joint
model.Joints.Add(alpha: 0, theta: -Math.PI / 3, radius: 35, offset: 0);
// Now move the arm
model.Joints[0].Parameters.Theta += Math.PI / 10;
model.Joints[1].Parameters.Theta -= Math.PI / 10;
// Calculate the model
model.Compute();
Gets the model kinematic chain.
Gets or sets the model position.
Gets the transformation matrix T for the full model, given
as T = T_0 * T_1 * T_2 ...T_n in which T_i is the transform
matrix for each joint in the model.
Initializes a new instance of the
class given a specified model position in 3D space.
The model's position in 3D space. Default is (0,0,0).
Initializes a new instance of the
class at the origin of the space (0,0,0).
Computes the entire model, calculating the
final position for each joint in the model.
The model transformation matrix
Calculates the entire model given it is attached to a parent model and computes each joint position.
Parent model this model is attached to.
Model transform matrix of the whole chain (parent + model).
This function assumes the parent model has already been calculated.
Returns an enumerator that iterates through a collection.
An object that can be used to iterate through the collection.
Returns an enumerator that iterates through a collection.
An object that can be used to iterate through the collection.
Denavit Hartenberg Model Combinator class to make combination
of models to create a complex model composed of multiple chains.
The following example shows the creation and animation of a
2-link planar manipulator with a dual 2-link planar gripper.
// Create the DH-model at (0, 0, 0) location
DenavitHartenbergModel model = new DenavitHartenbergModel();
// Add the first joint
model.Joints.Add(alpha: 0, theta: Math.PI / 4, radius: 35, offset: 0);
// Add the second joint
model.Joints.Add(alpha: 0, theta: -Math.PI / 3, radius: 35, offset: 0);
// Create the top finger
DenavitHartenbergModel model_tgripper = new DenavitHartenbergModel();
model_tgripper.Joints.Add(alpha: 0, theta: Math.PI / 4, radius: 20, offset: 0);
model_tgripper.Joints.Add(alpha: 0, theta: -Math.PI / 3, radius: 20, offset: 0);
// Create the bottom finger
DenavitHartenbergModel model_bgripper = new DenavitHartenbergModel();
model_bgripper.Joints.Add(0, -Math.PI / 4, 20, 0);
model_bgripper.Joints.Add(0, Math.PI / 3, 20, 0);
// Create the model combinator from the parent model
DenavitHartenbergModelCombinator arm = new DenavitHartenbergModelCombinator(model);
// Add the top finger
arm.Children.Add(model_tgripper);
// Add the bottom finger
arm.Children.Add(model_bgripper);
// Calculate the whole model (parent model + children models)
arm.Compute();
Gets the parent of this node.
Gets the model contained at this node.
Gets the collection of models attached to this node.
Initializes a new instance of the class.
The inner model contained at this node.
Calculates the whole combined model (this model plus all its
children plus all the children of the children and so on)
Collection of Denavit-Hartenberg model nodes.
Gets the owner of this collection (i.e. the parent
which owns the
children contained at this collection.
Initializes a new instance of the class.
The owner.
Adds a children model to the end of this .
Inserts an element into the Collection<T> at the specified index.
Denavit Hartenberg joint-description parameters.
Angle in radians about common normal, from
old z axis to the new z axis.
Angle in radians about previous z,
from old x to the new x.
Length of the joint (also known as a).
Offset along previous z to the common normal (also known as d).
Initializes a new instance of the class.
Angle (in radians) of the Z axis relative to the last joint.
Angle (in radians) of the X axis relative to the last joint.
Length or radius of the joint.
Offset along Z axis relatively to the last joint.
Denavit Hartenberg parameters constructor
Denavit-Hartenberg Model Joint.
Gets or sets the current associated with this joint.
Gets or sets the position of this joint.
Gets or sets the parameters for this joint.
Initializes a new instance of the class.
The
parameters to be used to create the joint.
Initializes a new instance of the class.
Angle in radians on the Z axis relatively to the last joint.
Angle in radians on the X axis relatively to the last joint.
Length or radius of the joint.
Offset along Z axis relatively to the last joint.
Updates the joint transformation matrix and position
given a model transform matrix and reference position.
Collection of Denavit Hartenberg Joints.
Adds an object to the end of this .
The
parameters specifying the joint to be added.
Adds an object to the end of this .
Angle in radians on the Z axis relatively to the last joint.
Angle in radians on the X axis relatively to the last joint.
Length or radius of the joint.
Offset along Z axis relatively to the last joint.
Taylor series expansions for common functions.
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms
that are calculated from the values of the function's derivatives at a single point.
The concept of a Taylor series was discovered by the Scottish mathematician James Gregory and
formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor series is
centered at zero, then that series is also called a Maclaurin series, named after the Scottish
mathematician Colin Maclaurin, who made extensive use of this special case of Taylor series in
the 18th century.
It is common practice to approximate a function by using a finite number of terms of its Taylor
series. Taylor's theorem gives quantitative estimates on the error in this approximation. Any
finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.
The Taylor series of a function is the limit of that function's Taylor polynomials, provided that
the limit exists. A function may not be equal to its Taylor series, even if its Taylor series
converges at every point. A function that is equal to its Taylor series in an open interval (or
a disc in the complex plane) is known as an analytic function in that interval.
References:
-
Wikipedia, The Free Encyclopedia. Taylor series. Available at:
http://en.wikipedia.org/wiki/Taylor_series
-
Anne Fry, Amy Plofker, Sarah-marie Belcastro, Lyle Roelofs. A Set of Appendices on Mathematical
Methods for Physics Students: Taylor Series Expansions and Approximations. Available at:
http://www.haverford.edu/physics/MathAppendices/Taylor_Series.pdf
Returns the sine of a specified angle by evaluating a Taylor series.
An angle, measured in radians.
The number of terms to be evaluated.
The sine of the angle .
Returns the cosine of a specified angle by evaluating a Taylor series.
An angle, measured in radians.
The number of terms to be evaluated.
The cosine of the angle .
Returns the hyperbolic sine of a specified angle by evaluating a Taylor series.
An angle, measured in radians.
The number of terms to be evaluated.
The hyperbolic sine of the angle .
Returns the hyperbolic cosine of a specified angle by evaluating a Taylor series.
An angle, measured in radians.
The number of terms to be evaluated.
The hyperbolic cosine of the angle .
Returns e raised to the specified power by evaluating a Taylor series.
A number specifying a power.
The number of terms to be evaluated.
Euler's constant raised to the specified power .
Fourier Transform (for arbitrary size matrices).
The transforms in this class accept arbitrary-length matrices and are not restricted to
only matrices that have dimensions which are powers of two. It also provides results which
are more equivalent with other mathematical packages, such as MATLAB and Octave.
This class had been created as an alternative to AForge.NET's
original FourierTransform class that would provide more expected results.
1-D Discrete Fourier Transform.
The data to transform.
The transformation direction.
-
Wikipedia contributors, "Hartley transform," Wikipedia, The Free Encyclopedia,
available at: http://en.wikipedia.org/w/index.php?title=Hartley_transform
-
K. R. Castleman, Digital Image Processing. Chapter 13, p.289.
Prentice. Hall, 1998.
-
Poularikas A. D. “The Hartley Transform”. The Handbook of Formulas and
Tables for Signal Processing. Ed. Alexander D. Poularikas, 1999.
Forward Hartley Transform.
Forward Hartley Transform.
Discrete Sine Transform
In mathematics, the discrete sine transform (DST) is a Fourier-related transform
similar to the discrete Fourier transform (DFT), but using a purely real matrix. It
is equivalent to the imaginary parts of a DFT of roughly twice the length, operating
on real data with odd symmetry (since the Fourier transform of a real and odd function
is imaginary and odd), where in some variants the input and/or output data are shifted
by half a sample.
References:
-
Wikipedia contributors, "Discrete sine transform," Wikipedia, The Free Encyclopedia,
available at: http://en.wikipedia.org/w/index.php?title=Discrete_sine_transform
-
K. R. Castleman, Digital Image Processing. Chapter 13, p.288.
Prentice. Hall, 1998.
Forward Discrete Sine Transform.
Inverse Discrete Sine Transform.
Forward Discrete Sine Transform.
Inverse Discrete Sine Transform.
Discrete Cosine Transformation.
A discrete cosine transform (DCT) expresses a finite sequence of data points
in terms of a sum of cosine functions oscillating at different frequencies.
DCTs are important to numerous applications in science and engineering, from
lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small
high-frequency components can be discarded), to spectral methods for the
numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical in these applications:
for compression, it turns out that cosine functions are much more efficient,
whereas for differential equations the cosines express a particular choice of
boundary conditions.
References:
-
Wikipedia contributors, "Discrete sine transform," Wikipedia, The Free Encyclopedia,
available at: http://en.wikipedia.org/w/index.php?title=Discrete_sine_transform
-
K. R. Castleman, Digital Image Processing. Chapter 13, p.288.
Prentice. Hall, 1998.
Forward Discrete Cosine Transform.
Inverse Discrete Cosine Transform.
Forward 2D Discrete Cosine Transform.
Inverse 2D Discrete Cosine Transform.
Common interface for Matrix format providers.
A string denoting the start of the matrix to be used in formatting.
A string denoting the end of the matrix to be used in formatting.
A string denoting the start of a matrix row to be used in formatting.
A string denoting the end of a matrix row to be used in formatting.
A string denoting the start of a matrix column to be used in formatting.
A string denoting the end of a matrix column to be used in formatting.
A string containing the row delimiter for a matrix to be used in formatting.
A string containing the column delimiter for a matrix to be used in formatting.
A string denoting the start of the matrix to be used in parsing.
A string denoting the end of the matrix to be used in parsing.
A string denoting the start of a matrix row to be used in parsing.
A string denoting the end of a matrix row to be used in parsing.
A string denoting the start of a matrix column to be used in parsing.
A string denoting the end of a matrix column to be used in parsing.
A string containing the row delimiter for a matrix to be used in parsing.
A string containing the column delimiter for a matrix to be used in parsing.
Gets the culture specific formatting information
to be used during parsing or formatting.
Base class for IMatrixFormatProvider implementers.
A string denoting the start of the matrix to be used in formatting.
A string denoting the end of the matrix to be used in formatting.
A string denoting the start of a matrix row to be used in formatting.
A string denoting the end of a matrix row to be used in formatting.
A string denoting the start of a matrix column to be used in formatting.
A string denoting the end of a matrix column to be used in formatting.
A string containing the row delimiter for a matrix to be used in formatting.
A string containing the column delimiter for a matrix to be used in formatting.
A string denoting the start of the matrix to be used in parsing.
A string denoting the end of the matrix to be used in parsing.
A string denoting the start of a matrix row to be used in parsing.
A string denoting the end of a matrix row to be used in parsing.
A string denoting the start of a matrix column to be used in parsing.
A string denoting the end of a matrix column to be used in parsing.
A string containing the row delimiter for a matrix to be used in parsing.
A string containing the column delimiter for a matrix to be used in parsing.
Gets the culture specific formatting information
to be used during parsing or formatting.
Initializes a new instance of the class.
The inner format provider.
Returns an object that provides formatting services for the specified
type. Currently, only is supported.
An object that specifies the type of format
object to return.
An instance of the object specified by formatType, if the
IFormatProvider implementation
can supply that type of object; otherwise, null.
Format provider for the matrix format used by Octave.
Converting from a multidimensional matrix to a
string representation:
// Declare a number array
double[,] x =
{
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
};
// Convert the aforementioned array to a string representation:
string str = x.ToString(OctaveArrayFormatProvider.CurrentCulture);
// the final result will be equivalent to
"[ 1, 2, 3, 4]"
Converting from strings to actual matrices:
// Declare an input string
string str = "[ 1, 2, 3, 4]";
// Convert the string representation to an actual number array:
double[] array = Matrix.Parse(str, OctaveArrayFormatProvider.InvariantCulture);
// array will now contain the actual number
// array representation of the given string.
Initializes a new instance of the class.
Gets the IMatrixFormatProvider which uses the CultureInfo used by the current thread.
Gets the IMatrixFormatProvider which uses the invariant system culture.
Gets the default matrix representation, where each row
is separated by a new line, and columns are separated by spaces.
This class can be used to convert to and from C#
arrays and their string representation. Please
see the example for details.
Converting from an array matrix to a
string representation:
// Declare a number array
double[] x = { 5, 6, 7, 8 };
// Convert the aforementioned array to a string representation:
string str = x.ToString(DefaultArrayFormatProvider.CurrentCulture);
// the final result will be equivalent to
"5, 6, 7, 8"
Converting from strings to actual matrices:
// Declare an input string
string str = "5, 6, 7, 8";
// Convert the string representation to an actual number array:
double[] array = Matrix.Parse(str, DefaultArrayFormatProvider.InvariantCulture);
// array will now contain the actual number
// array representation of the given string.
Initializes a new instance of the class.
Gets the IMatrixFormatProvider which uses the CultureInfo used by the current thread.
Gets the IMatrixFormatProvider which uses the invariant system culture.
Gets the matrix representation used in C# multi-dimensional arrays.
This class can be used to convert to and from C#
arrays and their string representation. Please
see the example for details.
Converting from an array to a string representation:
// Declare a number array
double[] x = { 1, 2, 3, 4 };
// Convert the aforementioned array to a string representation:
string str = x.ToString(CSharpArrayFormatProvider.CurrentCulture);
// the final result will be
"double[] x = { 1, 2, 3, 4 }"
Converting from strings to actual arrays:
// Declare an input string
string str = "double[] { 1, 2, 3, 4 }";
// Convert the string representation to an actual number array:
double[] array = Matrix.Parse(str, CSharpArrayFormatProvider.InvariantCulture);
// array will now contain the actual number
// array representation of the given string.
Initializes a new instance of the class.
Gets the IMatrixFormatProvider which uses the CultureInfo used by the current thread.
Gets the IMatrixFormatProvider which uses the invariant system culture.
Gets the matrix representation used in C# multi-dimensional arrays.
This class can be used to convert to and from C#
matrices and their string representation. Please
see the example for details.
Converting from a multidimensional matrix to a
string representation:
// Declare a number array
double[,] x =
{
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
};
// Convert the aforementioned array to a string representation:
string str = x.ToString(CSharpMatrixFormatProvider.CurrentCulture);
// the final result will be equivalent to
"double[,] x = " +
"{ " +
" { 1, 2, 3, 4 }, " +
" { 5, 6, 7, 8 }, " +
"}"
Converting from strings to actual matrices:
// Declare an input string
string str = "double[,] x = " +
"{ " +
" { 1, 2, 3, 4 }, " +
" { 5, 6, 7, 8 }, " +
"}";
// Convert the string representation to an actual number array:
double[,] matrix = Matrix.Parse(str, CSharpMatrixFormatProvider.InvariantCulture);
// matrix will now contain the actual multidimensional
// matrix representation of the given string.
Initializes a new instance of the class.
Gets the IMatrixFormatProvider which uses the CultureInfo used by the current thread.
Gets the IMatrixFormatProvider which uses the invariant system culture.
Gets the matrix representation used in C# jagged arrays.
This class can be used to convert to and from C#
arrays and their string representation. Please
see the example for details.
Converting from a jagged matrix to a string representation:
// Declare a number array
double[][] x =
{
new double[] { 1, 2, 3, 4 },
new double[] { 5, 6, 7, 8 },
};
// Convert the aforementioned array to a string representation:
string str = x.ToString(CSharpJaggedMatrixFormatProvider.CurrentCulture);
// the final result will be equivalent to
"double[][] x = " +
"{ " +
" new double[] { 1, 2, 3, 4 }, " +
" new double[] { 5, 6, 7, 8 }, " +
"}"
Converting from strings to actual arrays:
// Declare an input string
string str = "double[][] x = " +
"{ " +
" new double[] { 1, 2, 3, 4 }, " +
" new double[] { 5, 6, 7, 8 }, " +
"}";
// Convert the string representation to an actual number array:
double[][] array = Matrix.Parse(str, CSharpJaggedMatrixFormatProvider.InvariantCulture);
// array will now contain the actual jagged
// array representation of the given string.
Initializes a new instance of the class.
Gets the IMatrixFormatProvider which uses the CultureInfo used by the current thread.
Gets the IMatrixFormatProvider which uses the invariant system culture.
Gets the default matrix representation, where each row
is separated by a new line, and columns are separated by spaces.
This class can be used to convert to and from C#
matrices and their string representation. Please
see the example for details.
Converting from a multidimensional matrix to a
string representation:
// Declare a number array
double[,] x =
{
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
};
// Convert the aforementioned array to a string representation:
string str = x.ToString(DefaultMatrixFormatProvider.CurrentCulture);
// the final result will be equivalent to
@"1, 2, 3, 4
5, 6, 7, 8";
Converting from strings to actual matrices:
// Declare an input string
string str = @"1, 2, 3, 4
"5, 6, 7, 8";
// Convert the string representation to an actual number array:
double[,] matrix = Matrix.Parse(str, DefaultMatrixFormatProvider.InvariantCulture);
// matrix will now contain the actual multidimensional
// matrix representation of the given string.
Initializes a new instance of the class.
Gets the IMatrixFormatProvider which uses the CultureInfo used by the current thread.
Gets the IMatrixFormatProvider which uses the invariant system culture.
Defines how matrices are formatted and displayed, depending on the
chosen format representation.
Converts the value of a specified object to an equivalent string
representation using specified formatting information.
A format string containing formatting specifications.
An object to format.
An object that supplies
format information about the current instance.
The string representation of the value of ,
formatted as specified by and
.
Converts a jagged or multidimensional array into a System.String representation.
Parses a format string containing the format options for the matrix representation.
Handles formatting for objects other than matrices.
Converts a matrix represented in a System.String into a jagged array.
Converts a matrix represented in a System.String into a multi-dimensional array.
Format provider for the matrix format used by Octave.
This class can be used to convert to and from C#
matrices and their string representation. Please
see the example for details.
This class can be used to convert to and from C#
matrices and their string representation. Please
see the example for details.
Converting from a multidimensional matrix to a
string representation:
// Declare a number array
double[,] x =
{
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
};
// Convert the aforementioned array to a string representation:
string str = x.ToString(OctaveMatrixFormatProvider.CurrentCulture);
// the final result will be equivalent to
"[ 1, 2, 3, 4; 5, 6, 7, 8 ]"
Converting from strings to actual matrices:
// Declare an input string
string str = "[ 1, 2, 3, 4; 5, 6, 7, 8 ]";
// Convert the string representation to an actual number array:
double[,] matrix = Matrix.Parse(str, OctaveMatrixFormatProvider.InvariantCulture);
// matrix will now contain the actual multidimensional
// matrix representation of the given string.
Initializes a new instance of the class.
Gets the IMatrixFormatProvider which uses the CultureInfo used by the current thread.
Gets the IMatrixFormatProvider which uses the invariant system culture.
Normal distribution functions.
References:
-
Cephes Math Library, http://www.netlib.org/cephes/
-
George Marsaglia, Evaluating the Normal Distribution, 2004.
Available in: http://www.jstatsoft.org/v11/a05/paper
The following example shows the normal usages for the Normal functions:
// Compute standard precision functions
double phi = Normal.Function(0.42); // 0.66275727315175048
double phic = Normal.Complemented(0.42); // 0.33724272684824952
double inv = Normal.Inverse(0.42); // -0.20189347914185085
// Compute at the limits
double phi = Normal.Function(16.6); // 1.0
double phic = Normal.Complemented(16.6); // 3.4845465199504055E-62
Normal cumulative distribution function.
The area under the Gaussian p.d.f. integrated
from minus infinity to the given value.
Normal cumulative distribution function.
The area under the Gaussian p.d.f. integrated
from minus infinity to the given value.
Complemented cumulative distribution function.
The area under the Gaussian p.d.f. integrated
from the given value to positive infinity.
Normal (Gaussian) inverse cumulative distribution function.
For small arguments 0 < y < exp(-2), the program computes z =
sqrt( -2.0 * log(y) ); then the approximation is x = z - log(z)/z -
(1/z) P(1/z) / Q(1/z).
There are two rational functions P/Q, one for 0 < y < exp(-32) and
the other for y up to exp(-2). For larger arguments, w = y - 0.5,
and x/sqrt(2pi) = w + w^3 * R(w^2)/S(w^2)).
Returns the value, x, for which the area under the Normal (Gaussian)
probability density function (integrated from minus infinity to x) is
equal to the argument y (assumes mean is zero, variance is one).
High-accuracy Normal cumulative distribution function.
The following formula provide probabilities with an absolute error
less than 8e-16.
References:
- George Marsaglia, Evaluating the Normal Distribution, 2004.
Available in: http://www.jstatsoft.org/v11/a05/paper
High-accuracy Complementary normal distribution function.
This function uses 9 tabled values to provide tail values of the
normal distribution, also known as complementary Phi, with an
absolute error of 1e-14 ~ 1e-16.
References:
- George Marsaglia, Evaluating the Normal Distribution, 2004.
Available in: http://www.jstatsoft.org/v11/a05/paper
The area under the Gaussian p.d.f. integrated
from the given value to positive infinity.
Bivariate normal cumulative distribution function.
The value of the first variate.
The value of the second variate.
The correlation coefficient between x and y. This can be computed
from a covariance matrix C as rho = C_12 / (sqrt(C_11) * sqrt(C_22)).
Complemented bivariate normal cumulative distribution function.
The value of the first variate.
The value of the second variate.
The correlation coefficient between x and y. This can be computed
from a covariance matrix C as rho = C_12 / (sqrt(C_11) * sqrt(C_22)).
A function for computing bivariate normal probabilities.
BVND calculates the probability that X > DH and Y > DK.
This method is based on the work done by Alan Genz, Department of
Mathematics, Washington State University. Pullman, WA 99164-3113
Email: alangenz@wsu.edu. This work was shared under a 3-clause BSD
license. Please see source file for more details and the actual
license text.
This function is based on the method described by Drezner, Z and G.O.
Wesolowsky, (1989), On the computation of the bivariate normal integral,
Journal of Statist. Comput. Simul. 35, pp. 101-107, with major modifications
for double precision, and for |R| close to 1.
First derivative of Normal cumulative
distribution function, also known as the Normal density
function.
Log of the first derivative of Normal cumulative
distribution function, also known as the Normal density function.
1-D Gaussian function.
The variance parameter σ² (sigma squared).
x value.
Returns function's value at point .
The function calculates 1-D Gaussian function:
f(x) = exp( x * x / ( -2 * s * s ) ) / ( s * sqrt( 2 * PI ) )
2-D Gaussian function.
The variance parameter σ² (sigma squared).
x value.
y value.
Returns function's value at point (, ).
The function calculates 2-D Gaussian function:
f(x, y) = exp( x * x + y * y / ( -2 * s * s ) ) / ( s * s * 2 * PI )
1-D Gaussian kernel.
The variance parameter σ² (sigma squared).
Kernel size (should be odd), [3, 101].
Returns 1-D Gaussian kernel of the specified size.
The function calculates 1-D Gaussian kernel, which is array
of Gaussian function's values in the [-r, r] range of x value, where
r=floor(/2).
Wrong kernel size.
2-D Gaussian kernel.
The variance parameter σ² (sigma squared).
Kernel size (should be odd), [3, 101].
Returns 2-D Gaussian kernel of specified size.
The function calculates 2-D Gaussian kernel, which is array
of Gaussian function's values in the [-r, r] range of x,y values, where
r=floor(/2).
Wrong kernel size.
Reduced row Echelon form
Reduces a matrix to reduced row Echelon form.
The matrix to be reduced.
Pass to perform the reduction in place. The matrix
will be destroyed in the process, resulting in less
memory consumption.
Gets the pivot indicating the position
of the original rows before the swap.
Gets the matrix in row reduced Echelon form.
Gets the number of free variables (linear
dependent rows) in the given matrix.
Matrix major order. The default is to use C-style Row-Major order.
In computing, row-major order and column-major order describe methods for arranging
multidimensional arrays in linear storage such as memory. In row-major order, consecutive
elements of the rows of the array are contiguous in memory; in column-major order,
consecutive elements of the columns are contiguous. Array layout is critical for correctly
passing arrays between programs written in different languages. It is also important for
performance when traversing an array because accessing array elements that are contiguous
in memory is usually faster than accessing elements which are not, due to caching. In some
media such as tape or NAND flash memory, accessing sequentially is orders of magnitude faster
than nonsequential access.
References:
-
Wikipedia contributors. "Row-major order." Wikipedia, The Free Encyclopedia. Wikipedia,
The Free Encyclopedia, 13 Feb. 2016. Web. 22 Mar. 2016.
Row-major order (C, C++, C#, SAS, Pascal, NumPy default).
Column-major oder (Fotran, MATLAB, R).
Default (Row-Major, C/C++/C# order).
Static class ComplexExtensions. Defines a set of extension methods
that operates mainly on multidimensional arrays and vectors of
AForge.NET's data type.
Computes the absolute value of an array of complex numbers.
Computes the sum of an array of complex numbers.
Elementwise multiplication of two complex vectors.
Gets the magnitude of every complex number in an array.
Gets the magnitude of every complex number in a matrix.
Gets the magnitude of every complex number in a matrix.
Gets the phase of every complex number in an array.
Gets the phase of every complex number in a matrix.
Gets the phase of every complex number in a matrix.
Returns the real vector part of the complex vector c.
A vector of complex numbers.
A vector of scalars with the real part of the complex numbers.
Returns the real matrix part of the complex matrix c.
A matrix of complex numbers.
A matrix of scalars with the real part of the complex numbers.
Returns the real matrix part of the complex matrix c.
A matrix of complex numbers.
A matrix of scalars with the real part of the complex numbers.
Returns the imaginary vector part of the complex vector c.
A vector of complex numbers.
A vector of scalars with the imaginary part of the complex numbers.
Returns the imaginary matrix part of the complex matrix c.
A matrix of complex numbers.
A matrix of scalars with the imaginary part of the complex numbers.
Returns the imaginary matrix part of the complex matrix c.
A matrix of complex numbers.
A matrix of scalars with the imaginary part of the complex numbers.
Converts a complex number to a matrix of scalar values
in which the first column contains the real values and
the second column contains the imaginary values.
An array of complex numbers.
Converts a vector of real numbers to complex numbers.
The real numbers to be converted.
A vector of complex number with the given
real numbers as their real components.
Combines a vector of real and a vector of
imaginary numbers to form complex numbers.
The real part of the complex numbers.
The imaginary part of the complex numbers
A vector of complex number with the given
real numbers as their real components and
imaginary numbers as their imaginary parts.
Gets the range of the magnitude values in a complex number vector.
A complex number vector.
The range of magnitude values in the complex vector.
Compares two matrices for equality, considering an acceptance threshold.
Compares two vectors for equality, considering an acceptance threshold.
Gets the squared magnitude of a complex number.
Set of special mathematic functions.
References:
-
Cephes Math Library, http://www.netlib.org/cephes/
-
John D. Cook, http://www.johndcook.com/
Complementary error function of the specified value.
http://mathworld.wolfram.com/Erfc.html
Error function of the specified value.
Inverse error function (.
Inverse complemented error function (.
Evaluates polynomial of degree N
Evaluates polynomial of degree N with assumption that coef[N] = 1.0
Computes the Basic Spline of order n
Computes the binomial coefficients C(n,k).
Computes the binomial coefficients C(n,k).
Computes the log binomial Coefficients Log[C(n,k)].
Computes the log binomial Coefficients Log[C(n,k)].
Returns the extended factorial definition of a real number.
Returns the log factorial of a number (ln(n!))
Returns the log factorial of a number (ln(n!))
Computes the factorial of a number (n!)
Computes log(1-x) without losing precision for small values of x.
Computes log(1+x) without losing precision for small values of x.
References:
- http://www.johndcook.com/csharp_log_one_plus_x.html
Compute exp(x) - 1 without loss of precision for small values of x.
References:
- http://www.johndcook.com/cpp_expm1.html
Estimates unit round-off in quantities of size x.
This is a port of the epslon function from EISPACK.
Returns with the sign of .
This is a port of the sign transfer function from EISPACK,
and is is equivalent to C++'s std::copysign function.
If B > 0 then the result is ABS(A), else it is -ABS(A).
Computes x + y without losing precision using ln(x) and ln(y).
Computes x + y without losing precision using ln(x) and ln(y).
Computes x + y without losing precision using ln(x) and ln(y).
Computes x + y without losing precision using ln(x) and ln(y).
Computes sum(x) without losing precision using ln(x_0) ... ln(x_n).
Secant.
Cosecant.
Cotangent.
Inverse secant.
Inverse cosecant.
Inverse cotangent.
Hyperbolic secant.
Hyperbolic secant.
Hyperbolic cotangent.
Inverse hyperbolic sin.
Inverse hyperbolic cos.
Inverse hyperbolic tangent.
Inverse hyperbolic secant.
Inverse hyperbolic cosecant.
Inverse hyperbolic cotangent.
Computes the Softmax function (also known as normalized Exponencial
function) that "squashes"a vector or arbitrary real values into a
vector of real values in the range (0, 1) that add up to 1.
The real values to be converted into the unit interval.
A vector with the same number of dimensions as
but where values lie between 0 and 1.
Computes the Softmax function (also known as normalized Exponencial
function) that "squashes"a vector or arbitrary real values into a
vector of real values in the range (0, 1) that add up to 1.
The real values to be converted into the unit interval.
The location where to store the result of this operation.
A vector with the same number of dimensions as
but where values lie between 0 and 1.
Computes log(1 + exp(x)) without losing precision.
Discrete Hilbert Transformation.
The discrete Hilbert transform is a transformation operating on the time
domain. It performs a 90 degree phase shift, shifting positive frequencies
by +90 degrees and negative frequencies by -90 degrees. It is useful to
create analytic representation of signals.
The Hilbert transform can be implemented efficiently by using the Fast
Fourier Transform. After transforming a signal from the time-domain to
the frequency domain, one can zero its negative frequency components and
revert the signal back to obtain the phase shifting.
By applying the Hilbert transform to a signal twice, the negative of
the original signal is recovered.
References:
-
Marple, S.L., "Computing the discrete-time analytic signal via FFT," IEEE
Transactions on Signal Processing, Vol. 47, No.9 (September 1999). Available on:
http://classes.engr.oregonstate.edu/eecs/winter2009/ece464/AnalyticSignal_Sept1999_SPTrans.pdf
-
J. F. Culling, Online, cross-indexed dictionary of DSP terms. Available on:
http://www.cardiff.ac.uk/psych/home2/CullingJ/frames_dict.html
Performs the Fast Hilbert Transform over a double[] array.
Performs the Fast Hilbert Transform over a complex[] array.
Special matrix types.
Symmetric matrix.
Lower (left) triangular matrix.
Upper (right) triangular matrix.
Diagonal matrix.
Rectangular matrix.
Square matrix.
Beta functions.
This class offers implementations for the many Beta functions,
such as the Beta function itself,
its logarithm, the
incomplete regularized functions and others
The beta function was studied by Euler and Legendre and was given
its name by Jacques Binet; its symbol Β is a Greek capital β rather
than the similar Latin capital B.
References:
-
Cephes Math Library, http://www.netlib.org/cephes/
-
Wikipedia contributors, "Beta function,". Wikipedia, The Free
Encyclopedia. Available at: http://en.wikipedia.org/wiki/Beta_function
Beta.Function(4, 0.42); // 1.2155480852832423
Beta.Log(4, 15.2); // -9.46087817876467
Beta.Incbcf(4, 2, 4.2); // -0.23046874999999992
Beta.Incbd(4, 2, 4.2); // 0.7375
Beta.PowerSeries(4, 2, 4.2); // -3671.801280000001
Beta.Incomplete(a: 5, b: 4, x: 0.5); // 0.36328125
Beta.IncompleteInverse(0.5, 0.6, 0.1); // 0.019145979066925722
Beta.Multinomial(0.42, 0.5, 5.2 ); // 0.82641912952987062
Beta function as gamma(a) * gamma(b) / gamma(a+b).
Please see
Natural logarithm of the Beta function.
Please see
Incomplete (regularized) Beta function Ix(a, b).
Please see
Continued fraction expansion #1 for incomplete beta integral.
Please see
Continued fraction expansion #2 for incomplete beta integral.
Please see
Inverse of incomplete beta integral.
Please see
Power series for incomplete beta integral. Use when b*x
is small and x not too close to 1.
Please see
Multinomial Beta function.
Please see
Gamma Γ(x) functions.
In mathematics, the gamma function (represented by the capital Greek
letter Γ) is an extension of the factorial function, with its argument
shifted down by 1, to real and complex numbers. That is, if n is
a positive integer:
Γ(n) = (n-1)!
The gamma function is defined for all complex numbers except the negative
integers and zero. For complex numbers with a positive real part, it is
defined via an improper integral that converges:
∞
Γ(z) = ∫ t^(z-1)e^(-t) dt
0
This integral function is extended by analytic continuation to all
complex numbers except the non-positive integers (where the function
has simple poles), yielding the meromorphic function we call the gamma
function.
The gamma function is a component in various probability-distribution
functions, and as such it is applicable in the fields of probability
and statistics, as well as combinatorics.
References:
-
Wikipedia contributors, "Gamma function,". Wikipedia, The Free
Encyclopedia. Available at: http://en.wikipedia.org/wiki/Gamma_function
-
Cephes Math Library, http://www.netlib.org/cephes/
double x = 0.17;
// Compute main Gamma function and variants
double gamma = Gamma.Function(x); // 5.4511741801042106
double gammap = Gamma.Function(x, p: 2); // -39.473585841300675
double log = Gamma.Log(x); // 1.6958310313607003
double logp = Gamma.Log(x, p: 2); // 3.6756317353404273
double stir = Gamma.Stirling(x); // 24.040352622960743
double psi = Gamma.Digamma(x); // -6.2100942259248626
double tri = Gamma.Trigamma(x); // 35.915302055854525
double a = 4.2;
// Compute the incomplete regularized Gamma functions P and Q:
double lower = Gamma.LowerIncomplete(a, x); // 0.000015685073063633753
double upper = Gamma.UpperIncomplete(a, x); // 0.9999843149269364
Maximum gamma on the machine.
Gamma function of the specified value.
Multivariate Gamma function
Digamma function.
Trigamma function.
This code has been adapted from the FORTRAN77 and subsequent
C code by B. E. Schneider and John Burkardt. The code had been
made public under the GNU LGPL license.
Gamma function as computed by Stirling's formula.
Upper incomplete regularized Gamma function Q
(a.k.a the incomplete complemented Gamma function)
This function is equivalent to Q(x) = Γ(s, x) / Γ(s).
Lower incomplete regularized gamma function P
(a.k.a. the incomplete Gamma function).
This function is equivalent to P(x) = γ(s, x) / Γ(s).
Natural logarithm of the gamma function.
Natural logarithm of the multivariate Gamma function.
Inverse of the
incomplete Gamma integral (LowerIncomplete, P).
Inverse of the complemented
incomplete Gamma integral (UpperIncomplete, Q).
Inverse of the complemented
incomplete Gamma integral (UpperIncomplete, Q).
Common mathematical constants.
References:
-
Cephes Math Library, http://www.netlib.org/cephes/
-
http://www.johndcook.com/cpp_expm1.html
Euler-Mascheroni constant.
This constant is defined as 0.5772156649015328606065120.
Double-precision machine round-off error.
This value is actually different from Double.Epsilon. It
is defined as 1.11022302462515654042E-16.
Double-precision machine round-off error.
This value is actually different from Double.Epsilon. It
is defined as 1.11022302462515654042E-16.
Single-precision machine round-off error.
This value is actually different from Single.Epsilon. It
is defined as 1.1920929E-07f.
Double-precision small value.
This constant is defined as 1.493221789605150e-300.
Single-precision small value.
This constant is defined as 1.493221789605150e-40f.
Fixed-precision small value.
Maximum log on the machine.
This constant is defined as 7.09782712893383996732E2.
Minimum log on the machine.
This constant is defined as -7.451332191019412076235E2.
Catalan's constant.
Log of number pi: log(pi).
This constant has the value 1.14472988584940017414.
Log of two: log(2).
This constant has the value 0.69314718055994530941.
Log of three: log(3).
This constant has the value 1.098612288668109691395.
Log of square root of twice number pi: sqrt(log(2*π).
This constant has the value 0.91893853320467274178032973640562.
Log of twice number pi: log(2*pi).
This constant has the value 1.837877066409345483556.
Square root of twice number pi: sqrt(2*π).
This constant has the value 2.50662827463100050242E0.
Square root of half number π: sqrt(π/2).
This constant has the value 1.25331413731550025121E0.
Square root of 2: sqrt(2).
This constant has the value 1.4142135623730950488016887.
Half square root of 2: sqrt(2)/2.
This constant has the value 7.07106781186547524401E-1.
Bessel functions.
Bessel functions, first defined by the mathematician Daniel
Bernoulli and generalized by Friedrich Bessel, are the canonical
solutions y(x) of Bessel's differential equation.
Bessel's equation arises when finding separable solutions to Laplace's
equation and the Helmholtz equation in cylindrical or spherical coordinates.
Bessel functions are therefore especially important for many problems of wave
propagation and static potentials. In solving problems in cylindrical coordinate
systems, one obtains Bessel functions of integer order (α = n); in spherical
problems, one obtains half-integer orders (α = n+1/2). For example:
-
Electromagnetic waves in a cylindrical waveguide
-
Heat conduction in a cylindrical object
-
Modes of vibration of a thin circular (or annular) artificial
membrane (such as a drum or other membranophone)
-
Diffusion problems on a lattice
-
Solutions to the radial Schrödinger equation (in spherical and
cylindrical coordinates) for a free particle
-
Solving for patterns of acoustical radiation
-
Frequency-dependent friction in circular pipelines
Bessel functions also appear in other problems, such as signal processing
(e.g., see FM synthesis, Kaiser window, or Bessel filter).
This class offers implementations of Bessel's first and second kind
functions, with special cases for zero and for arbitrary n.
References:
-
Cephes Math Library, http://www.netlib.org/cephes/
-
Wikipedia contributors, "Bessel function,". Wikipedia, The Free
Encyclopedia. Available at: http://en.wikipedia.org/wiki/Bessel_function
// Bessel function of order 0
actual = Bessel.J0(1); // 0.765197686557967
actual = Bessel.J0(5); // -0.177596771314338
// Bessel function of order n
double j2 = Bessel.J(2, 17.3); // 0.117351128521774
double j01 = Bessel.J(0, 1); // 0.765197686557967
double j05 = Bessel.J(0, 5); // -0.177596771314338
// Bessel function of the second kind, of order 0.
double y0 = Bessel.Y0(64); // 0.037067103232088
// Bessel function of the second kind, of order n.
double y2 = Bessel.Y(2, 4); // 0.215903594603615
double y0 = Bessel.Y(0, 64); // 0.037067103232088
Bessel function of order 0.
See
Bessel function of order 1.
See
Bessel function of order n.
See
Bessel function of the second kind, of order 0.
See
Bessel function of the second kind, of order 1.
See
Bessel function of the second kind, of order n.
See
Bessel function of the first kind, of order 0.
See
Bessel function of the first kind, of order 1.
See
Bessel function of the first kind, of order n.
See
Set of mathematical tools.
Gets a reference to the random number generator used
internally by the Accord.NET classes and methods.
Sets a random seed for the framework's main
internal number generator.
Gets the angle formed by the vector [x,y].
Gets the angle formed by the vector [x,y].
Gets the displacement angle between two points.
Gets the displacement angle between two points, coded
as an integer varying from 0 to 20.
Gets the greatest common divisor between two integers.
First value.
Second value.
The greatest common divisor.
Returns the next power of 2 after the input value x.
Input value x.
Returns the next power of 2 after the input value x.
Returns the previous power of 2 after the input value x.
Input value x.
Returns the previous power of 2 after the input value x.
Hypotenuse calculus without overflow/underflow
First value
Second value
The hypotenuse Sqrt(a^2 + b^2)
Hypotenuse calculus without overflow/underflow
first value
second value
The hypotenuse Sqrt(a^2 + b^2)
Hypotenuse calculus without overflow/underflow
first value
second value
The hypotenuse Sqrt(a^2 + b^2)
Gets the proper modulus operation for
an integer value x and modulo m.
Gets the proper modulus operation for
a real value x and modulo m.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Converts the value x (which is measured in the scale
'from') to another value measured in the scale 'to'.
Returns the hyperbolic arc cosine of the specified value.
Returns the hyperbolic arc sine of the specified value.
Returns the hyperbolic arc tangent of the specified value.
Returns the factorial falling power of the specified value.
Truncated power function.
Fast inverse floating-point square root.
Sorts the elements of an entire one-dimensional array using the given comparison.
Sorts the elements of an entire one-dimensional array using the given comparison.
Sorts the elements of an entire one-dimensional array using the given comparison.
Interpolates data using a piece-wise linear function.
The value to be calculated.
The input data points x. Those values need to be sorted.
The output data points y.
The value to be returned for values before the first point in .
The value to be returned for values after the last point in .
Computes the output for f(value) by using a piecewise linear
interpolation of the data points and .
Gets the maximum value among three values.
The first value a.
The second value b.
The third value c.
The maximum value among ,
and .
Gets the minimum value among three values.
The first value a.
The second value b.
The third value c.
The minimum value among ,
and .
Calculates power of 2.
Power to raise in.
Returns specified power of 2 in the case if power is in the range of
[0, 30]. Otherwise returns 0.
Checks if the specified integer is power of 2.
Integer number to check.
Returns true if the specified number is power of 2.
Otherwise returns false.
Get base of binary logarithm.
Source integer number.
Power of the number (base of binary logarithm).
Returns the square root of the specified number.
Cohen-Daubechies-Feauveau Wavelet Transform
Constructs a new Cohen-Daubechies-Feauveau Wavelet Transform.
The number of iterations for the 2D transform.
1-D Forward Discrete Wavelet Transform.
2-D Forward Discrete Wavelet Transform.
1-D Backward (Inverse) Discrete Wavelet Transform.
2-D Backward (Inverse) Discrete Wavelet Transform.
Forward biorthogonal 9/7 wavelet transform
Inverse biorthogonal 9/7 wavelet transform
Forward biorthogonal 9/7 2D wavelet transform
Inverse biorthogonal 9/7 2D wavelet transform
Haar Wavelet Transform.
References:
-
Musawir Ali, An Introduction to Wavelets and the Haar Transform.
Available on: http://www.cs.ucf.edu/~mali/haar/
Constructs a new Haar Wavelet Transform.
The number of iterations for the 2D transform.
1-D Forward Discrete Wavelet Transform.
1-D Backward (Inverse) Discrete Wavelet Transform.
2-D Forward Discrete Wavelet Transform.
2-D Backward (Inverse) Discrete Wavelet Transform.
Discrete Haar Wavelet Transform
Inverse Haar Wavelet Transform
Discrete Haar Wavelet 2D Transform
Inverse Haar Wavelet 2D Transform
Common interface for wavelets algorithms.
1-D Forward Discrete Wavelet Transform.
2-D Forward Discrete Wavelet Transform.
1-D Backward (Inverse) Discrete Wavelet Transform.
2-D Backward (Inverse) Discrete Wavelet Transform.
Provides static methods to save and load files saved in NumPy's .npy format.
Saves the specified array to an array of bytes.
The array to be saved to the array of bytes.
A byte array containig the saved array.
Saves the specified array to the disk using the npy format.
The array to be saved to disk.
The disk path under which the file will be saved.
The number of bytes written when saving the file to disk.
Saves the specified array to a stream using the npy format.
The array to be saved to disk.
The stream to which the file will be saved.
The number of bytes written when saving the file to disk.
Loads an array of the specified type from a byte array.
The type to be loaded from the npy-formatted file.
The bytes that contain the matrix to be loaded.
The array to be returned.
Loads an array of the specified type from a file in the disk.
The type to be loaded from the npy-formatted file.
The bytes that contain the matrix to be loaded.
The object to be read. This parameter can be used to avoid the
need of specifying a generic argument to this function.
The array to be returned.
Loads an array of the specified type from a file in the disk.
The type to be loaded from the npy-formatted file.
The path to the file containing the matrix to be loaded.
The object to be read. This parameter can be used to avoid the
need of specifying a generic argument to this function.
The array to be returned.
Loads an array of the specified type from a stream.
The type to be loaded from the npy-formatted file.
The stream containing the matrix to be loaded.
The object to be read. This parameter can be used to avoid the
need of specifying a generic argument to this function.
The array to be returned.
Loads an array of the specified type from a file in the disk.
The path to the file containing the matrix to be loaded.
The array to be returned.
Loads an array of the specified type from a stream.
The type to be loaded from the npy-formatted file.
The stream containing the matrix to be loaded.
The array to be returned.
Loads a multi-dimensional array from an array of bytes.
The bytes that contain the matrix to be loaded.
A multi-dimensional array containing the values available in the given stream.
Loads a multi-dimensional array from a file in the disk.
The path to the file containing the matrix to be loaded.
A multi-dimensional array containing the values available in the given stream.
Loads a jagged array from an array of bytes.
The bytes that contain the matrix to be loaded.
A jagged array containing the values available in the given stream.
Loads a jagged array from a file in the disk.
The path to the file containing the matrix to be loaded.
A jagged array containing the values available in the given stream.
Loads a multi-dimensional array from a stream.
The stream containing the matrix to be loaded.
A multi-dimensional array containing the values available in the given stream.
Loads a jagged array from a stream.
The stream containing the matrix to be loaded.
Pass true to remove null or empty elements from the loaded array.
A jagged array containing the values available in the given stream.
Cell array
Structure
Object
Character array
Sparse array
Double precision array
Single precision array
8-bit, signed integer
8-bit, unsigned integer
16-bit, signed integer
16-bit, unsigned integer
32-bit, signed integer
32-bit, unsigned integer
64-bit, signed integer
64-bit, unsigned integer
8 bit, signed
8 bit, unsigned
16-bit, signed
16-bit, unsigned
32-bit, signed
32-bit, unsigned
IEEE® 754 single format
IEEE 754 double format
64-bit, signed
64-bit, unsigned
MATLAB array
Compressed Data
Unicode UTF-8 Encoded Character Data
Unicode UTF-16 Encoded Character Data
Unicode UTF-32 Encoded Character Data
Node object contained in .MAT file.
A node can contain a matrix object, a string, or another nodes.
Gets the name of this node.
Gets the child nodes contained at this node.
Gets the object value contained at this node, if any.
Its type can be known by checking the
property of this node.
Gets the type of the object value contained in this node.
Gets the object value contained at this node, if any.
Its type can be known by checking the
property of this node.
The object type, if known.
The object stored at this node.
Gets the number of child objects contained in this node.
Gets the child fields contained under the given name.
The name of the field to be retrieved.
Gets the child fields contained under the given name.
The name of the field to be retrieved.
Returns an enumerator that iterates through a collection.
An object that can be used to iterate through the collection.
Returns an enumerator that iterates through a collection.
An object that can be used to iterate through the collection.
Reader for .mat files (such as the ones created by Matlab and Octave).
MAT files are binary files containing variables and structures from mathematical
processing programs, such as MATLAB or Octave. In MATLAB, .mat files can be created
using its save and load functions. For the moment, this reader supports
only version 5 MAT files (Matlab 5 MAT-file).
The MATLAB file format is documented at
http://www.mathworks.com/help/pdf_doc/matlab/matfile_format.pdf
All the examples below involve loading files from the following URL:
https://github.com/accord-net/framework/blob/development/Unit%20Tests/Accord.Tests.Math/Resources/mat/
The first example shows how to read a simple .MAT file containing a single matrix of
integer numbers. It also shows how to discover the names of the variables stored in
the file and how to discover their types:
1-D: f(x) = exp( x * x / ( -2 * s * s ) ) / ( s * sqrt( 2 * PI ) )
2-D: f(x, y) = exp( x * x + y * y / ( -2 * s * s ) ) / ( s * s * 2 * PI )
Sigma value.
Sigma property of Gaussian function.
Default value is set to 1. Minimum allowed value is 0.00000001.
Initializes a new instance of the class.
Initializes a new instance of the class.
Sigma value.
1-D Gaussian function.
x value.
Returns function's value at point .
The function calculates 1-D Gaussian function:
f(x) = exp( x * x / ( -2 * s * s ) ) / ( s * sqrt( 2 * PI ) )
2-D Gaussian function.
x value.
y value.
Returns function's value at point (, ).
The function calculates 2-D Gaussian function:
f(x, y) = exp( x * x + y * y / ( -2 * s * s ) ) / ( s * s * 2 * PI )
1-D Gaussian kernel.
Kernel size (should be odd), [3, 101].
Returns 1-D Gaussian kernel of the specified size.
The function calculates 1-D Gaussian kernel, which is array
of Gaussian function's values in the [-r, r] range of x value, where
r=floor(/2).
Wrong kernel size.
2-D Gaussian kernel.
Kernel size (should be odd), [3, 101].
Returns 2-D Gaussian kernel of specified size.
The function calculates 2-D Gaussian kernel, which is array
of Gaussian function's values in the [-r, r] range of x,y values, where
r=floor(/2).
Wrong kernel size.