clever-trace: Calculate trace of various matrix products.

In gRc: Inference in Graphical Gaussian Models with Edge and Vertex Symmetries

Calculate trace of various matrix products.

Description

Calculate trace of various matrix products.

Usage

trA(A)

trAW(rA, rW)

trAWB(rA, rW, rB)

trAWBW(rA, rW, rB)

trAWBV(rA, rW, rB, rV)

trAWBlist(Alist, W, Blist, mode = 0L)

trAWBWlist(Alist, W, Blist, mode = 0L)

Arguments

A	A matrix
rA, rB	Square matrices represented as "sparse" matrices. The dimension is inferred from dimension of V,W.
rW, rV, W	Square matrices; must be of same dimension.
Alist, Blist	Lists of such "sparse" matrices.
mode	0 or 1.

Value

A number

Author(s)

Søren Højsgaard, [e-mail]

Examples

## Turn list into "sparse" matrix
to_sp <- function(x){
  ans <- do.call("rbind", x)
  storage.mode(ans)<-"double"
  return(ans)
}

## Turn "sparse" matrix into dense matrix
##
to_de <- function(A,d){
  if (nrow(A) < 1) stop("need non-empty matrix\n")
  ans <- matrix(0,nr=d,nc=d)
  for (i in 1:nrow(A)){
    e <- A[i,]
    if (length(e) == 1){
      ans[e,e] <- 1
    } else { 
      ans[e[1],e[2]] <-   ans[e[2],e[1]] <- 1 
    }
  }  
  return(ans)
}

d <- 5
W <- matrix(rnorm(d * d), nr=d, nc=d);
V <- matrix(rnorm(d * d), nr=d, nc=d); 
W <- W + t(W)
V <- V + t(V)


A1.lst <- list(c(1,2),c(1,3))
A2.lst <- list(1,3,5)

A1.sp <- to_sp(A1.lst)
A2.sp <- to_sp(A2.lst)

A1.de <- to_de(A1.sp, d)
A2.de <- to_de(A2.sp, d)

trAW(A1.sp, W)
sum(diag(A1.de %*% W))

trAW(A2.sp, W)
sum(diag(A2.de %*% W))

trAWB(A1.sp, W, A2.sp)
trAWB(A2.sp, W, A1.sp)
sum(diag(A1.de %*% W %*% A2.de))

trAWBW(A1.sp, W, A2.sp)
trAWBW(A2.sp, W, A1.sp)
sum(diag(A1.de %*% W %*% A2.de %*% W))

trAWBV(A1.sp, W, A2.sp, V)
trAWBV(A2.sp, W, A1.sp, V)
sum(diag(A1.de %*% W %*% A2.de %*% V))

gRc documentation built on April 30, 2023, 9:09 a.m.