gRc (version 0.4-3.2)

tr: Calculate trace of various matrix products

Description

Calculate trace of various matrix products.

Usage

trA(A)
trAW(A,W)
trAWB(A,W,B)
trAWBW(A,W,B)
trAWBV(A,W,B,V)

Arguments

A,B

Square matrices represented as matrices or lists (see examples below).

W,V

Square matrices

Value

A number

Examples

# NOT RUN {
d <- 5
W <- matrix(rnorm(d*d),nr=d,nc=d); 
V <- W <- W+t(W)

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

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


## Just for checking the calculations
##
symMat <- function(A,d){
  ans <- matrix(0,nr=d,nc=d)
  for (i in 1:length(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)
}

trAW(A1, W)
#sum(diag(symMat(A1,d=d) %*% W))

trAW(A2, W)
#sum(diag(symMat(A2,d=d) %*% W))

trAWB(A1, W, A2)
#sum(diag(symMat(A1,d=d) %*% W %*% symMat(A2,d=d)))

trAWBV(A1, W, A2, V)
#sum(diag(symMat(A1,d=d) %*% W %*% symMat(A2,d=d) %*% V))
# }