kipedia.org/wiki/Multivariate_normal_distribution"> Multivariate Normal Distribution. The approach using a Cholesky decomposition is quite usual in this case. However, it can be extended to other cases as long as the underlying random generator provides {@link NormalizedRandomGenerator normalized values} like {@link GaussianRandomGenerator} or {@link UniformRandomGenerator}.
Sometimes, the covariance matrix for a given simulation is not strictly positive definite. This means that the correlations are not all independent from each other. In this case, however, the non strictly positive elements found during the Cholesky decomposition of the covariance matrix should not be negative either, they should be null. Another non-conventional extension handling this case is used here. Rather than computing C = UT.U
where C
is the covariance matrix and U
is an upper-triangular matrix, we compute C = B.BT
where B
is a rectangular matrix having more rows than columns. The number of columns of B
is the rank of the covariance matrix, and it is the dimension of the uncorrelated random vector that is needed to compute the component of the correlated vector. This class handles this situation automatically.
@since 1.2