Cholesky.Rd
\name{Cholesky}
\docType{genericFunction}
\alias{Cholesky}
\alias{Cholesky,dsCMatrix-method}
\title{Cholesky Decomposition of a Sparse Matrix}
\usage{
Cholesky(A, perm, LDL, super, \dots)
}
\description{
Computes the Cholesky decomposition of a sparse, symmetric,
positive-definite matrix.
}
\arguments{
\item{A}{sparse symmetric matrix. No missing values or IEEE special
values are allowed.}
\item{perm}{logical scalar indicating if a fill-reducing permutation
should be computed and applied to the rows and columns of \code{A}.
Default is \code{TRUE}.}
\item{LDL}{logical scalar indicating if the decomposition should be
computed as LDL' where \code{L} is a unit lower triangular matrix.
The alternative is LL' where \code{L} is lower triangular with
arbitrary diagonal elements. Default is \code{TRUE}.}
\item{super}{logical scalar indicating is a supernodal decomposition
should be created. The alternative is a simplicial decomposition.
Default is \code{FALSE}.}
\item{\dots}{further arguments passed to or from other methods.}
}
\value{
an object inheriting from either
\code{"\linkS4class{CHMsuper}"}, or
\code{"\linkS4class{CHMsimpl}"}, depending on the \code{super}
argument; both classes extend \code{"\linkS4class{CHMfactor}"}.
}
\details{
This is a generic function with special methods for different types
of matrices. Use \code{\link{showMethods}("Cholesky")} to list all
the methods for the \code{\link{Cholesky}} generic.
The method for class \code{\linkS4class{dsCMatrix}} of sparse matrices
is based on functions from the CHOLMOD library.
}
\references{
Tim Davis (2005)
\emph{{CHOLMOD}: sparse supernodal {Cholesky} factorization and
update/downdate}
\url{http://www.cise.ufl.edu/research/sparse/cholmod/}
Timothy A. Davis (2006)
\emph{Direct Methods for Sparse Linear Systems}, SIAM Series
\dQuote{Fundamentals of Algorithms}.
}
\seealso{
Class definitions \code{\linkS4class{CHMfactor}} and \code{\linkS4class{dsCMatrix}}
and function \code{\link{expand}}.
Note that \code{\link{chol}()} returns matrices (inheriting from
\code{"\linkS4class{Matrix}"}) whereas \code{Cholesky()} returns a
\code{"\linkS4class{CHMfactor}"} object.
}
\examples{
data(KNex)
mtm <- with(KNex, crossprod(mm))
Cholesky(mtm) # uses show(<MatrixFactorization>)
(Cm <- Cholesky(mtm, super = TRUE))
str(cmat <- as(Cm, "sparseMatrix"))
cmat[1:20, 1:20]
}
\keyword{array}
\keyword{algebra}