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% $Id: fast.prcomp.Rd 1466 2011-01-16 22:17:17Z warnes $
%
\name{fast.prcomp}
\alias{fast.prcomp}
\alias{fast.svd}
\title{Efficient computation of principal components and singular value
decompositions.}
\description{
The standard \code{\link[stats]{prcomp}} and \code{\link{svd}}
function are very inefficient for wide matrixes. \code{fast.prcomp}
and \code{fast.svd} are modified versions which are efficient even
for matrixes that are very wide.
}
\usage{
fast.prcomp(x, retx = TRUE, center = TRUE, scale. = FALSE, tol = NULL)
fast.svd( x, nu = min(n, p), nv = min(n, p), ...)
}
\arguments{
\item{x}{data matrix}
\item{retx, center, scale., tol}{ See documetation for
\code{\link[stats]{prcomp}}
}
\item{nu, nv, ...}{ See documetation for \code{\link{svd}} }
}
\details{
The current implementation of the function \code{\link{svd}} in S-Plus
and R is much slower when operating on a matrix with a large number of
columns than on the transpose of this matrix, which has a large
number of rows. As a consequence, \code{\link[stats]{prcomp}}, which uses
\code{\link{svd}}, is also very slow when applied to matrixes with a
large number of rows.
For R, the simple solution is to use \code{\link{La.svd}} instead of
\code{\link{svd}}. A suitable patch to \code{\link[stats]{prcomp}} has
been submitted. In the mean time, the function \code{fast.prcomp} has
been provided as a short-term work-around.
For S-Plus the solution is to replace the standard \code{\link{svd}}
with a version that checks the dimensions of the matrix, and performs
the computation on the transposed the matrix if it is wider than tall.
For R:
\describe{
\item{\code{fast.prcomp}}{is a modified versiom of
\code{\link[stats]{prcomp}} that calls \code{\link{La.svd}} instead
of \code{\link{svd}}
}
\item{\code{fast.svd}}{is simply a wrapper around \code{\link{La.svd}}.
}
}
For S-Plus:
\describe{
\item{\code{fast.prcomp}}{is a modified versiom of
\code{\link{prcomp}} that calls \code{fast.svd} instead
of \code{\link{svd}}
}
\item{\code{fast.svd}}{checks the dimensions of the
matrix. When it is wider than tall, it transposes the input matrix
and calls \code{\link{svd}}. It then swaps \code{u} and \code{v}
and returns the result. Otherwise, it just calls \code{\link{svd}}
and returns the results unchanged.
}
}
}
\value{
See the documetation for \code{\link[stats]{prcomp}} or
\code{\link{svd}} .
}
\author{Modifications by Gregory R. Warnes
\email{greg@warnes.net} }
\seealso{
\code{\link[stats]{prcomp}}, \code{\link{svd}}, \code{\link{La.svd}}
}
\examples{
# create test matrix
set.seed(4943546)
nr <- 50
nc <- 2000
x <- matrix( rnorm( nr*nc), nrow=nr, ncol=nc )
tx <- t(x)
# SVD directly on matrix is SLOW:
system.time( val.x <- svd(x)$u )
# SVD on t(matrix) is FAST:
system.time( val.tx <- svd(tx)$v )
# and the results are equivalent:
max( abs(val.x) - abs(val.tx) )
# Time gap dissapears using fast.svd:
system.time( val.x <- fast.svd(x)$u )
system.time( val.tx <- fast.svd(tx)$v )
max( abs(val.x) - abs(val.tx) )
library(stats)
# prcomp directly on matrix is SLOW:
system.time( pr.x <- prcomp(x) )
# prcomp.fast is much faster
system.time( fast.pr.x <- fast.prcomp(x) )
# and the results are equivalent
max( pr.x$sdev - fast.pr.x$sdev )
max( abs(pr.x$rotation[,1:49]) - abs(fast.pr.x$rotation[,1:49]) )
max( abs(pr.x$x) - abs(fast.pr.x$x) )
# (except for the last and least significant component):
max( abs(pr.x$rotation[,50]) - abs(fast.pr.x$rotation[,50]) )
}
\keyword{multivariate}
\keyword{algebra}
\keyword{array}
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