randomNormalMultivariate¶

Generates pseudorandom numbers from a multivariate normal distribution.

Synopsis¶

randomNormalMultivariate (nVectors, covariances)

Required Arguments¶

int nVectors (Input): Number of random multivariate normal vectors to generate.
float covariances (Input): Array of size length × length containing the variance-covariance matrix.

Return Value¶

An array of length nVectors × length containing the random multivariate normal vectors stored consecutively.

Description¶

Function randomNormalMultivariate generates pseudorandom numbers from a multivariate normal distribution with mean vector consisting of all zeros and variance-covariance matrix covariances. First, the Cholesky factor of the variance-covariance matrix is computed. Then, independent random normal deviates with mean 0 and variance 1 are generated, and the matrix containing these deviates is postmultiplied by the Cholesky factor. Because the Cholesky factorization is performed in each invocation, it is best to generate as many random vectors as needed at once.

Deviates from a multivariate normal distribution with means other than 0 can be generated by using randomNormalMultivariate and then by adding the vectors of means to each row of the result.

Example¶

In this example, randomNormalMultivariate generates five pseudorandom normal vectors of length 2 with variance-covariance matrix equal to the following:

\[\begin{split}\begin{bmatrix} 0.500 & 0.375 \\ 0.375 & 0.500 \\ \end{bmatrix}\end{split}\]

from numpy import *
from pyimsl.stat.randomNormalMultivariate import randomNormalMultivariate
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

n_random = 5
length = 2
covariances = [[.5, .375], [.375, .5]]
randomSeedSet(123457)
r = randomNormalMultivariate(n_random, covariances)
writeMatrix("multivariate normal random deviates", r)

Output¶

 
multivariate normal random deviates
                 1            2
      1.451        1.595
      0.058        0.641
     -0.867       -0.492
     -0.933       -1.413
     -0.325       -0.527