perm_matrix: Permutation matrices

Description

Given a permutation, coerce to word form and return the corresponding permutation matrix

Usage

perm_matrix(p)
is.perm_matrix(M)
pm_to_perm(M)

Arguments

Permutation, coerced to word form, of length 1

Permutation matrix

Value

Given a permutation p of size $s$, function perm_matrix() returns a square matrix with $s$ rows and $s$ columns. Entries are either 0 or 1; each row and each column has exactly one entry of 1 and the rest zero.

Row and column names of the permutation matrix are integers; this makes the printed version more compact.

Function pm_to_perm() takes a permutation matrix and returns the equivalend permutation in word form.

Details

Given a word p with size s, the idiom for perm_matrix() boils down to

    M <- diag(s)
    M[p,]

This is used explicitly in the representations vignette. There is another way:

    M <- diag(s)
    M[cbind(seq_len(s),p)] <- 1
    M

which might be useful sometime.

Examples

Run this code

# NOT RUN {
perm_matrix(rperm(1,9))


p1 <- rperm(1,40)
M1 <- perm_matrix(p1)
p2 <- rperm(1,40)
M2 <- perm_matrix(p2)

stopifnot(is.perm_matrix(M1))

stopifnot(all(solve(M1) == perm_matrix(inverse(p1))))
stopifnot(all(M1 %*% M2 == perm_matrix(p1*p2)))


stopifnot(p1 == pm_to_perm(perm_matrix(p1)))

data("megaminx")
image(perm_matrix(permprod(megaminx)),asp=1,axes=FALSE)

# }