rmnorm function

Random number generator for (conditional) multivariate normal distribution

This function generates random numbers (i.e. variates) from (conditional) multivariate normal distribution.

rmnorm(
  n,
  mean,
  sigma,
  given_ind = numeric(),
  given_x = numeric(),
  dependent_ind = numeric(),
  is_validation = TRUE,
  n_cores = 1L
)

Arguments

• n: positive integer representing the number of random variates to be generated from (conditional) multivariate normal distribution. If given_ind is not empty vector then n should be be equal to nrow(given_x).
• mean: numeric vector representing expectation of multivariate normal vector (distribution).
• sigma: positively defined numeric matrix representing covariance matrix of multivariate normal vector (distribution).
• given_ind: numeric vector representing indexes of multivariate normal vector which are conditioned at values given by given_x argument.
• given_x: numeric vector which i-th element corresponds to the given value of the given_ind[i]-th element (component) of multivariate normal vector. If given_x is numeric matrix then it's rows are such vectors of given values.
• dependent_ind: numeric vector representing indexes of unconditional elements (components) of multivariate normal vector.
• is_validation: logical value indicating whether input arguments should be validated. Set it to FALSE to get performance boost (default value is TRUE).
• n_cores: positive integer representing the number of CPU cores used for parallel computing. Currently it is not recommended to set n_cores > 1 if vectorized arguments include less then 100000 elements.

Returns

This function returns a numeric matrix which rows a random variates from (conditional) multivariate normal distribution with mean equal to mean and covariance equal to sigma. If given_x and given_ind are also provided then random variates will be from conditional multivariate normal distribution. Please, see details section of cmnorm to get additional information on the conditioning procedure.

Details

This function uses Cholesky decomposition to generate multivariate normal variates from independent standard normal variates.

Examples

# Consider multivariate normal vector:
# X = (X1, X2, X3, X4, X5) ~ N(mean, sigma)

# Prepare multivariate normal vector parameters
  # expected value
mean <- c(-2, -1, 0, 1, 2)
n_dim <- length(mean)
  # correlation matrix
cor <- c(   1,  0.1,  0.2,   0.3,  0.4,
          0.1,    1, -0.1,  -0.2, -0.3,
          0.2, -0.1,    1,   0.3,  0.2,
          0.3, -0.2,  0.3,     1, -0.05,
          0.4, -0.3,  0.2, -0.05,     1)
cor <- matrix(cor, ncol = n_dim, nrow = n_dim, byrow = TRUE)
  # covariance matrix
sd_mat <- diag(c(1, 1.5, 2, 2.5, 3))
sigma <- sd_mat %*% cor %*% t(sd_mat)

# Simulate random variates from this distribution
rmnorm(n = 3, mean = mean, sigma = sigma)

# Simulate random variate from (X1, X3, X5 | X1 = -1, X4 = 1)
given_x <- c(-1, 1)
given_ind = c(1, 4)
rmnorm(n = 1, mean = mean, sigma = sigma, 
       given_x = given_x, given_ind = given_ind)

# Simulate random variate from (X1, X3, X5 | X1 = -1, X4 = 1)
# and (X1, X3, X5 | X1 = 2, X4 = 3)
given_x = rbind(c(-1, 1), c(2, 3))
rmnorm(n = nrow(given_x), mean = mean, sigma = sigma, 
       given_x = given_x, given_ind = given_ind)