maximizing matrix diagonal elements in R

Question

Edit : a related question is How to move larger values close to matrix diagonal in a correlation matrix This question is about achieving same but in R

Given a matrix (or table in R )

m <- matrix(c(5,25,8,4,2,10,20,3,1),ncol=3,byrow=TRUE)
colnames(m) <- c("L","M","H")
rownames(m) <- c("A","B","C")
tax <- as.table(m)
tax
   L  M  H
A  5 25  8
B  4  2 10
C 20  3  1

I want to rearrange the matrix such that the diagonal elements are maximum.

   H  L  M
B 10  4  2
C  1 20  3
A  8  5 25

Is there any easy to use function in R ?

Answer 1

matrix.sort <- function(matrix) {

    if (nrow(matrix) != ncol(matrix)) stop("Not diagonal")
    if(is.null(rownames(matrix))) rownames(matrix) <- 1:nrow(matrix)

    row.max <- apply(matrix,1,which.max)
    if(all(table(row.max) != 1)) stop("Ties cannot be resolved")

    matrix[names(sort(row.max)),]
}

Answer 2

I don't think Rohit Arora's solution is doing exactly what you want because it will be led by the maximum value of the preceding row. As a result, it's not in fact maximising the diagonal in a optimisation sense.

I found this answer to a similar question elsewhere and I thought it might be useful:

http://r.789695.n4.nabble.com/reordering-of-matrix-rows-to-maximize-the-sum-of-the-diagonal-tt2062867.html#a2065679

pMatrix.min <- function(A, B) { 
#finds the permutation P of A such that ||PA - B|| is minimum in Frobenius norm 
# Uses the linear-sum assignment problem (LSAP) solver in the "clue" package 

# Returns P%*%A and the permutation vector `pvec' such that 
# A[pvec, ] is the permutation of A closest to B 
    n <- nrow(A) 
    D <- matrix(NA, n, n) 
    for (i in 1:n) { 
        for (j in 1:n) { 
        D[j, i] <- (sum((B[j, ] - A[i, ])^2)) 
        }
    } 
    vec <- c(solve_LSAP(D)) 
    list(A=A[vec,], pvec=vec) 
} 

require(clue)  # need this package to solve the LSAP 

#An example
A <- matrix(sample(1:25, size=25, rep=FALSE),  5,  5) 

B <- diag(1, nrow(A)) # this choice of B maximizes the trace of permuted A 

X <- pMatrix.min(A,B) 

A  # original square matrix 

X$A  # permuted A such that its trace is maximum among all permutations 

It uses the Hungarian method to optimise the reordering of the matrix A to the target matrix B.

NB This is my first post so I don't have the reputation to comment on the previous answer, but I hope this helps!