\name{pMatrix-class} \docType{class} \alias{pMatrix-class} \alias{-,pMatrix,missing-method} \alias{\%*\%,matrix,pMatrix-method} \alias{\%*\%,pMatrix,matrix-method} \alias{\%*\%,pMatrix,pMatrix-method} \alias{\%*\%,Matrix,pMatrix-method} \alias{\%*\%,pMatrix,Matrix-method} \alias{coerce,integer,pMatrix-method} \alias{coerce,numeric,pMatrix-method} \alias{coerce,pMatrix,matrix-method} \alias{coerce,pMatrix,ngTMatrix-method} \alias{coerce,pMatrix,TsparseMatrix-method} \alias{solve,pMatrix,missing-method} \alias{t,pMatrix-method} \title{Permutation matrices} \description{The \code{"pMatrix"} class is the class of permutation matrices, stored as 1-based integer permutation vectors.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("pMatrix", ...)} or by coercion from an integer permutation vector, see below. } \section{Slots}{ \describe{ \item{\code{perm}:}{An integer, 1-based permutation vector, i.e. an integer vector of length \code{Dim[1]} whose elements form a permutation of \code{1:Dim[1]}.} \item{\code{Dim}:}{Object of class \code{"integer"}. The dimensions of the matrix which must be a two-element vector of equal, non-negative integers.} \item{\code{Dimnames}:}{list of length two; each component containing NULL or a \code{\link{character}} vector length equal the corresponding \code{Dim} element.} } } \section{Extends}{ Class \code{"Matrix"}, directly. } \section{Methods}{ \describe{ \item{\%*\%}{\code{signature(x = "matrix", y = "pMatrix")} and other signatures (use \code{showMethods("\%*\%", class="pMatrix")}): ... } \item{coerce}{\code{signature(from = "integer", to = "pMatrix")}: This is enables typical \code{"pMatrix"} construction, given a permutation vector of \code{1:n}, see the first example.} \item{coerce}{\code{signature(from = "numeric", to = "pMatrix")}: a user convenience, to allow \code{as(perm, "pMatrix")} for numeric \code{perm} with integer values.} \item{coerce}{\code{signature(from = "pMatrix", to = "matrix")}: ... } \item{coerce}{\code{signature(from = "pMatrix", to = "ngTMatrix")}: coercion to sparse logical matrix of class \code{\linkS4class{ngTMatrix}}.} \item{solve}{\code{signature(a = "pMatrix", b = "missing")}: return the inverse permutation matrix.} \item{t}{\code{signature(x = "pMatrix")}: return the transpose of the permuation matrix (which is also the inverse of the permutation matrix).} } } \note{ The inverse of the typical \code{"pMatrix"} constructor, \code{P <- as(ip, "pMatrix")} is simply \code{ip <- P@perm}. } %\seealso{} \examples{ (pm1 <- as(as.integer(c(2,3,1)), "pMatrix")) t(pm1) # is the same as solve(pm1) pm1 \%*\% t(pm1) # check that the transpose is the inverse stopifnot(identical(diag(3), as(pm1 \%*\% t(pm1), "matrix"))) set.seed(11) ## random permutation matrix : (p10 <- as(sample(10),"pMatrix")) ## Permute rows / columns of a numeric matrix : (mm <- round(array(rnorm(3 * 3), c(3, 3)), 2)) mm \%*\% pm1 pm1 \%*\% mm try(as(as.integer(c(3,3,1)), "pMatrix"))# Error: not a permutation as(pm1, "ngTMatrix") p10[1:7, 1:4] # gives an "ngTMatrix" (most economic!) } \keyword{classes}