Permutation matrices
Given a permutation, coerce to word form and return the corresponding permutation matrix
perm_matrix(p) is.perm_matrix(M) pm_to_perm(M)
p |
Permutation, coerced to word form, of length 1 |
M |
Permutation matrix |
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 equivalent permutation in word form.
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
Mwhich might be useful sometime.
Robin K. S. Hankin
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.