clever_trace function

Calculate trace of various matrix products.

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.

Returns

A number

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))

Author(s)

Søren Højsgaard, sorenh@math.aau.dk