Multi-variate normal distribution RNG output N random variates. Each variate’s distribution is N(0, 1), and these variates have a certain correlation. To generate such variates, this RNG needs to set up the lower triangle matrix first, which is the result of the Cholesky decomposition of the correlation matrix. This implementation supports an even number of variate which is 2N. Instead of storing a 2N-by-2N matrix, we only store the N*(2N+1) non-zero elements. The storage scheme is as below. This RNG needs to pre-calculate a certain number of random numbers before it can output the right random number.
Put the storage scheme aside, the basic working principle is using one underlying random number generator to produce several independent random numbers. Every 2N independent random numbers compose a vector. By multiplying this vector with the lower triangle matrix, we get the result vector. Elements of result vector are multi-variate normal distribution random numbers, which have the pre-set correlation.