Fast computation of the multivariate normal density.

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Description

Fast computation of the multivariate normal density.

Usage

1
dmvn(X, mu, sigma, log = FALSE, ncores = 1, isChol = FALSE)

Arguments

X

matrix n by d where each row is a d dimensional random vector. Alternatively X can be a d-dimensional vector.

mu

vector of length d, representing the mean of the distribution.

sigma

covariance matrix (d x d). Alternatively it can be the cholesky decomposition of the covariance. In that case isChol should be set to TRUE.

log

boolean set to true the logarithm of the pdf is required.

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.

Value

A vector of length n where the i-the entry contains the pdf of the i-th random vector.

Author(s)

Matteo Fasiolo <matteo.fasiolo@gmail.com>

Examples

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N <- 100
d <- 5
mu <- 1:d
X <- t(t(matrix(rnorm(N*d), N, d)) + mu)
tmp <- matrix(rnorm(d^2), d, d)
mcov <- tcrossprod(tmp, tmp)  + diag(0.5, d)
myChol <- chol(mcov)

head(dmvn(X, mu, mcov), 10)
head(dmvn(X, mu, myChol, isChol = TRUE), 10)

## Not run: 
# Performance comparison
library(mvtnorm)
library(microbenchmark)

a <- cbind(
      dmvn(X, mu, mcov),
      dmvn(X, mu, myChol, isChol = TRUE),
      dmvnorm(X, mu, mcov))
      
# Check if we get the same output as dmvnorm()
a[ , 1] / a[, 3]
a[ , 2] / a[, 3]

microbenchmark(dmvn(X, mu, myChol, isChol = TRUE), 
               dmvn(X, mu, mcov), 
               dmvnorm(X, mu, mcov))
               
detach("package:mvtnorm", unload=TRUE)

## End(Not run)