Fast simulation of multivariate normal random variables

rmvn(n, mu, sigma, ncores = 1, isChol = FALSE, A = NULL,
  kpnames = FALSE)

Arguments

n	number of random vectors to be simulated.
mu	vector of length d, representing the mean.
sigma	covariance matrix (d x d). Alternatively is can be the cholesky decomposition of the covariance. In that case `isChol` should be set to `TRUE`.
ncores	Number of cores used. The parallelization will take place only if OpenMP is supported.
isChol	boolean set to true is `sigma` is the cholesky decomposition of the covariance matrix.
A	an (optional) numeric matrix of dimension (n x d), which will be used to store the output random variables. It is useful when n and d are large and one wants to call `rmvn()` several times, without reallocating memory for the whole matrix each time. NB: the element of `A` must be of class "numeric".
kpnames	if `TRUE` the dimensions' names are preserved. That is, the i-th column of the output has the same name as the i-th entry of `mu` or the i-th column of `sigma`. `kpnames==FALSE` by default.

Value

If A==NULL (default) the output is an (n x d) matrix where the i-th row is the i-th simulated vector. If A!=NULL then the random vector are store in A, which is provided by the user, and the function returns NULL.

Details

Notice that this function does not use one of the Random Number Generators (RNGs) provided by R, but one of the parallel cryptographic RNGs described in (Salmon et al., 2011). It is important to point out that this RNG can safely be used in parallel, without risk of collisions between parallel sequence of random numbers. The initialization of the RNG depends on R's seed, hence the set.seed() function can be used to obtain reproducible results. Notice though that changing ncores causes most of the generated numbers to be different even if R's seed is the same (see example below). NB: at the moment the RNG does not work properly on Solaris OS when ncores>1. Hence, rmvn() checks if the OS is Solaris and, if this the case, it imposes ncores==1.

References

John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw (2011). Parallel Random Numbers: As Easy as 1, 2, 3. D. E. Shaw Research, New York, NY 10036, USA.

Examples

# NOT RUN {
d <- 5
mu <- 1:d

# Creating covariance matrix
tmp <- matrix(rnorm(d^2), d, d)
mcov <- tcrossprod(tmp, tmp)

set.seed(414)
rmvn(4, 1:d, mcov)

set.seed(414)
rmvn(4, 1:d, mcov)

set.seed(414)
rmvn(4, 1:d, mcov, ncores = 2) # r.v. generated on the second core are different

###### Here we create the matrix that will hold the simulated random variables upfront.
A <- matrix(NA, 4, d)
class(A) <- "numeric" # This is important. We need the elements of A to be of class "numeric". 

set.seed(414)
rmvn(4, 1:d, mcov, ncores = 2, A = A) # This returns NULL ...
A                                     # ... but the result is here

# }