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\name{LU-class}
\docType{class}
\alias{LU-class}
\alias{denseLU-class}
\alias{expand,denseLU-method}
\title{LU (dense) Matrix Decompositions}
\description{
The \code{"LU"} class is the \emph{virtual} class of LU decompositions of
real matrices. \code{"denseLU"} the class of LU decompositions of
dense real matrices.
}
\section{Objects from the Class}{
Objects can be created by calls of the form \code{new("denseLU", ...)}.
More commonly the objects are created explicitly from calls of the form
\code{\link{lu}(mm)} where \code{mm} is an object that inherits from the
\code{"dgeMatrix"} class or as a side-effect of other functions applied
to \code{"dgeMatrix"} objects.
}
\section{Extends}{
\code{"LU"} directly extends the virtual class
\code{"\linkS4class{MatrixFactorization}"}.
\code{"denseLU"} directly extends \code{"LU"}.
}
\section{Slots}{
\describe{
\item{\code{x}:}{object of class \code{"numeric"}. The \code{"L"}
(unit lower triangular) and \code{"U"} (upper triangular) factors
of the original matrix. These are stored in a packed format
described in the Lapack manual.}
\item{\code{perm}:}{Object of class \code{"integer"} - a vector of
length \code{min(Dim)} that describes the permutation applied to
the rows of the original matrix. The contents of this vector are
described in the Lapack manual.}
\item{\code{Dim}:}{the dimension of the original matrix; inherited
from class \code{\linkS4class{MatrixFactorization}} .}
}
}
\section{Methods}{
\describe{
\item{expand}{\code{signature(x = "denseLU")}: Produce the \code{"L"} and
\code{"U"} factors as a named list of matrices.}
}
}
% \references{}
% \author{}
% \note{}
\seealso{
class \code{\linkS4class{sparseLU}} for LU decompositions of
\emph{sparse} matrices;
further, class \code{\linkS4class{dgeMatrix}} and functions \code{\link{lu}},
\code{\link{expand}}.
}
\examples{
set.seed(1)
mm <- Matrix(round(rnorm(9),2), nrow = 3)
mm
str(lum <- lu(mm))
elu <- expand(lum)
elu # three components: "L", "U", and "P", the permutation
elu$L \%*\% elu$U
(m2 <- with(elu, P \%*\% L \%*\% U)) # the same as 'mm'
stopifnot(all.equal(as(mm, "matrix"),
as(m2, "matrix")))
}
\keyword{classes}
\keyword{algebra}
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