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\name{lu}
\title{Triangular Decomposition of a Square Matrix}
\usage{
lu(x, \dots)
}
\alias{lu}
\description{
Computes triangular decompositions of square matrices.
}
\arguments{
\item{x}{a matrix. No missing values or IEEE special values are allowed.}
\item{\dots}{further arguments passed to or from other methods.}
}
\value{
an object of class \code{"LU"}, i.e., \code{"\linkS4class{denseLU}"} or
\code{"sparseLU"}, see \code{\linkS4class{sparseLU}}; this is
a representation of a triangular decomposition of \code{x}.
}
\details{
This is a generic function with special methods for different types
of matrices. Use \code{\link{showMethods}("lu")} to list all the methods
for the \code{\link{lu}} generic.
The method for class \code{\linkS4class{dgeMatrix}} is based on
LAPACK's \code{"dgetrf"} subroutine.
The method for class \code{\linkS4class{dgCMatrix}} of sparse matrices
is based on functions from the CSparse library.
}
\references{
Golub, G., and Van Loan, C. F. (1989).
\emph{Matrix Computations,}
2nd edition, Johns Hopkins, Baltimore.
Tim Davis (2005)
\url{http://www.cise.ufl.edu/research/sparse/CSparse/}
Timothy A. Davis (2006)
\emph{Direct Methods for Sparse Linear Systems}, SIAM Series
\dQuote{Fundamentals of Algorithms}.
}
\seealso{
Class definitions \code{\linkS4class{LU}} and \code{\linkS4class{sparseLU}}
and function \code{\link{expand}};
\code{\link{qr}}, \code{\link{chol}}.
}
\examples{
x <- Matrix(rnorm(9), 3, 3)
lu(x)
pm <- as(readMM(system.file("external/pores_1.mtx",
package = "Matrix")),
"CsparseMatrix")
str(pmLU <- lu(pm)) # p is a 0-based permutation of the rows
# q is a 0-based permutation of the columns
## permute rows and columns of original matrix
ppm <- pm[pmLU@p + 1:1, pmLU@q + 1:1]
ppm[1:14, 1:5]
(pmLU@L \%*\% pmLU@U)[1:14, 1:5] # product can have extra zeros
}
\keyword{array}
\keyword{algebra}
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