clever_trace {gRc}

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))