Compute density from multivariate normal distribution

dmvn.sparse(x, mu, CH, prec = TRUE, log = TRUE)

Arguments

x	numeric matrix, where each row is an MVN sample.
mu	mean (numeric vector)
CH	An object of class dCHMsimpl or dCHMsuper that represents the Cholesky factorization of either the precision (default) or covariance matrix. See details.
prec	If TRUE, CH is the Cholesky decomposition of the precision matrix. If false, it is the decomposition for the covariance matrix.
log	If TRUE (default), returns the log density, else returns density.

Value

A density or log density for each row of x

Details

This function use sparse matrix operations to compute the log density of a multivariate normal distribution. The user must compute the Cholesky decomposition first, using the Cholesky function in the Matrix package. This function operates on a sparse symmetric matrix, and returns an object of class dCHMsimpl or dCHMsuper (this depends on the algorithm that was used for the decomposition). This object contains information about any fill-reducing permutations that were used to preserve sparsity. The rmvn.sparse and dmvn.sparse functions use this permutation information, even if pivoting was turned off.

Examples

   require(Matrix)
#> Loading required package: Matrix
   m <- 20
   p <- 2
   k <- 4

## build sample sparse covariance matrix
   Q1 <- tril(kronecker(Matrix(seq(0.1,p,length=p*p),p,p),diag(m)))
   Q2 <- cbind(Q1,Matrix(0,m*p,k))
   Q3 <- rbind(Q2,cbind(Matrix(rnorm(k*m*p),k,m*p),Diagonal(k)))
   V <- tcrossprod(Q3)
   CH <- Cholesky(V)

   x <- rmvn.sparse(10,rep(0,p*m+k),CH, FALSE)
   y <- dmvn.sparse(x[1,],rep(0,p*m+k), CH, FALSE)