rmatrixnorm: Matrix variate Normal distribution functions

In MixMatrix: Classification with Matrix Variate Normal and t Distributions

Matrix variate Normal distribution functions

Description

Density and random generation for the matrix variate normal distribution

Usage

rmatrixnorm(
  n,
  mean,
  L = diag(dim(as.matrix(mean))[1]),
  R = diag(dim(as.matrix(mean))[2]),
  U = L %*% t(L),
  V = t(R) %*% R,
  list = FALSE,
  array = NULL,
  force = FALSE
)

dmatrixnorm(
  x,
  mean = matrix(0, p, n),
  L = diag(p),
  R = diag(n),
  U = L %*% t(L),
  V = t(R) %*% R,
  log = FALSE
)

Arguments

n	number of observations to generate - must be a positive integer.
mean	p \times q matrix of means
L	p \times p matrix specifying relations among the rows. By default, an identity matrix.
R	q \times q matrix specifying relations among the columns. By default, an identity matrix.
U	LL^T - p \times p positive definite variance-covariance matrix for rows, computed from L if not specified.
V	R^T R - q \times q positive definite variance-covariance matrix for columns, computed from R if not specified.
list	Defaults to FALSE . If this is TRUE , then the output will be a list of matrices.
array	If n = 1 and this is not specified and list is FALSE , the function will return a matrix containing the one observation. If n > 1 , should be the opposite of list . If list is TRUE , this will be ignored.
force	If TRUE, will take the input of L and/or R directly - otherwise computes U and V and uses Cholesky decompositions. Useful for generating degenerate normal distributions. Will also override concerns about potentially singular matrices unless they are not, in fact, invertible.
x	quantile for density
log	logical; if TRUE, probabilities p are given as log(p).

Value

rmatrixnorm returns either a list of n p \times q matrices or a p \times q \times n array.

dmatrixnorm returns the density at x.

References

Gupta, Arjun K, and Daya K Nagar. 1999. Matrix Variate Distributions. Vol. 104. CRC Press. ISBN:978-1584880462

See Also

rmatrixt(), rmatrixinvt(), rnorm() and stats::Distributions()

Examples

set.seed(20180202)
# a draw from a matrix variate normal with a certain mean
# and row-wise covariance
rmatrixnorm(
  n = 1, mean = matrix(c(100, 0, -100, 0, 25, -1000), nrow = 2),
  L = matrix(c(2, 1, 0, .1), nrow = 2), list = FALSE
)
set.seed(20180202)
# another way of specifying this - note the output is equivalent
A <- rmatrixnorm(
  n = 10, mean = matrix(c(100, 0, -100, 0, 25, -1000), nrow = 2),
  L = matrix(c(2, 1, 0, .1), nrow = 2), list = TRUE
)
A[[1]]
# demonstrating the dmatrixnorm function
dmatrixnorm(A[[1]],
  mean = matrix(c(100, 0, -100, 0, 25, -1000), nrow = 2),
  L = matrix(c(2, 1, 0, .1), nrow = 2), log = TRUE
)

MixMatrix documentation built on Oct. 1, 2024, 1:07 a.m.