https://github.com/cran/pracma
Tip revision: 10ae2bb8daa6ba60ffc49143525900a7978d54b7 authored by HwB on 08 August 2013, 00:00:00 UTC
version 1.5.0
version 1.5.0
Tip revision: 10ae2bb
lu.Rd
\name{lu}
\alias{lu}
\title{
LU Matrix Factorization
}
\description{
LU decomposition of a positive definite matrix as Gaussian factorization
(without pivoting).
}
\usage{
lu(A, scheme = c("kji", "jki", "ijk"))
}
\arguments{
\item{A}{square positive definite numeric matrix (will not be checked).}
\item{scheme}{order of row and column operations.}
}
\details{
For a given matrix \code{A}, the LU decomposition exists and is unique iff
its principal submatrices of order \code{i=1,...,n-1} are nonsingular. The
procedure here is a simple Gauss elimination without pivoting.
The scheme abbreviations refer to the order in which the cycles of row- and
column-oriented operations are processed. The ``ijk'' scheme is one of the
two compact forms, here the Doolite factorization (the Crout factorization
would be similar).
}
\value{
Returns a list with components \code{L} and \code{U}, the two lower and
upper triangular matrices such that \code{A=L\%*\%U}.
}
\references{
Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics.
Second edition, Springer-Verlag, Berlin Heidelberg.
}
\note{
This function is not meant to process huge matrices or linear systems of
equations.
Without pivoting it may also be harmed by considerable inaccuracies.
}
\seealso{
\code{\link{qr}}
}
\examples{
A <- magic(5)
LU <- lu(A, scheme = "ijk") # Doolittle scheme
LU$L \%*\% LU$U
## [,1] [,2] [,3] [,4] [,5]
## [1,] 17 24 1 8 15
## [2,] 23 5 7 14 16
## [3,] 4 6 13 20 22
## [4,] 10 12 19 21 3
## [5,] 11 18 25 2 9
}
\keyword{ array }