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\alias{coerce,pMatrix,matrix-method}
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\alias{coerce,pMatrix,matrix-method}
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\alias{solve,pMatrix,missing-method}
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\alias{solve,pMatrix,missing-method}
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\alias{t,pMatrix-method}
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\alias{t,pMatrix-method}
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\title{Permutation matrices}
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\title{Permutation matrices}
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\description{The \code{"pMatrix"} class is the class of permutation
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\description{The \code{"pMatrix"} class is the class of permutation
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  matrices stored as 1-based integer permutation vectors.}
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  matrices, stored as 1-based integer permutation vectors.}
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\section{Objects from the Class}{
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\section{Objects from the Class}{
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  Objects can be created by calls of the form \code{new("pMatrix", ...)}
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  Objects can be created by calls of the form \code{new("pMatrix", ...)}
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  or by coercion from an integer permutation vector.
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  or by coercion from an integer permutation vector, see below.
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}
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}
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\section{Slots}{
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\section{Slots}{
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  \describe{
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  \describe{
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    \item{\code{perm}:}{An integer, 1-based permutation vector, i.e.
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    \item{\code{perm}:}{An integer, 1-based permutation vector, i.e.
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      an integer vector of length \code{Dim[1]} whose elements form a
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      an integer vector of length \code{Dim[1]} whose elements form a
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      containing NULL or a \code{\link{character}} vector length
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      containing NULL or a \code{\link{character}} vector length
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      equal the corresponding \code{Dim} element.}
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      equal the corresponding \code{Dim} element.}
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  }
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  }
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}
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}
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\section{Extends}{
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\section{Extends}{
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Class \code{"Matrix"}, directly.
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  Class \code{"Matrix"}, directly.
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}
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}
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\section{Methods}{
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\section{Methods}{
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  \describe{
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  \describe{
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    \item{\%*\%}{\code{signature(x = "matrix", y = "pMatrix")} and other
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    \item{\%*\%}{\code{signature(x = "matrix", y = "pMatrix")} and other
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      signatures (use \code{showMethods("\%*\%", class="pMatrix")}): ... }
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      signatures (use \code{showMethods("\%*\%", class="pMatrix")}): ... }
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    \item{coerce}{\code{signature(from = "integer", to = "pMatrix")}: ... }
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    \item{coerce}{\code{signature(from = "integer", to = "pMatrix")}:
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      This is enables typical \code{"pmatrix"} construction, given
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      a permutation vector of \code{1:n}, see the first example.}
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    \item{coerce}{\code{signature(from = "pMatrix", to = "matrix")}: ... }
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    \item{coerce}{\code{signature(from = "pMatrix", to = "matrix")}: ... }
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    \item{solve}{\code{signature(a = "pMatrix", b = "missing")}: return
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    \item{solve}{\code{signature(a = "pMatrix", b = "missing")}: return
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      the inverse permutation matrix.}
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      the inverse permutation matrix.}
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    \item{t}{\code{signature(x = "pMatrix")}: return the transpose of
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    \item{t}{\code{signature(x = "pMatrix")}: return the transpose of
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      the permuation matrix (which is also the inverse of the
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      the permuation matrix (which is also the inverse of the
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  }
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  }
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}
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}
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%\seealso{}
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%\seealso{}
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\examples{
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\examples{
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(pm1 <- as(as.integer(c(2,3,1)), "pMatrix"))
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(pm1 <- as(as.integer(c(2,3,1)), "pMatrix"))
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t(pm1)
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t(pm1) # is the same as
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solve(pm1)
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solve(pm1)
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pm1 \%*\% as(t(pm1), "matrix")   # check that the transpose is the inverse
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pm1 \%*\% t(pm1) # check that the transpose is the inverse
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stopifnot(identical(diag(3), as(pm1 \%*\% t(pm1), "matrix")))
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(mm <- round(array(rnorm(3 * 3), c(3, 3)), 2))
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(mm <- round(array(rnorm(3 * 3), c(3, 3)), 2))
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mm \%*\% pm1
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mm \%*\% pm1
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pm1 \%*\% mm
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pm1 \%*\% mm
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try(as(as.integer(c(3,3,1)), "pMatrix"))
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try(as(as.integer(c(3,3,1)), "pMatrix"))# Error: not a permutation
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}
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}
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\keyword{classes}
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\keyword{classes}