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\name{runExactSVD}
\alias{runExactSVD}
\title{Exact SVD}
\description{Perform an exact singular value decomposition.}
\usage{
runExactSVD(x, k=min(dim(x)), nu=k, nv=k, center=FALSE, scale=FALSE,
deferred=FALSE, fold=Inf, BPPARAM=SerialParam())
}
\arguments{
\item{x}{A numeric matrix-like object to use in the SVD.}
\item{k}{Integer scalar specifying the number of singular values to return.}
\item{nu}{Integer scalar specifying the number of left singular vectors to return.}
\item{nv}{Integer scalar specifying the number of right singular vectors to return.}
\item{center}{A logical scalar indicating whether columns should be centered.
Alternatively, a numeric vector or \code{NULL} - see \code{?"\link{BiocSingular-options}"}.}
\item{scale}{A logical scalar indicating whether columns should be scaled.
Alternatively, a numeric vector or \code{NULL} - see \code{?"\link{BiocSingular-options}"}.}
\item{deferred}{Logical scalar indicating whether centering/scaling should be deferred, see \code{?"\link{BiocSingular-options}"}.}
\item{fold}{Numeric scalar specifying the minimum fold difference between dimensions of \code{x} to compute the cross-product,
see \code{?"\link{BiocSingular-options}"}.}
\item{BPPARAM}{A \linkS4class{BiocParallelParam} object specifying how parallelization should be performed.}
}
\details{
If any of \code{k}, \code{nu} or \code{nv} exceeds \code{min(dim(x))}, they will be capped and a warning will be raised.
The exception is when they are explicitly set to \code{Inf}, in which case all singular values/vectors of \code{x} are returned without any warning.
Note that parallelization via \code{BPPARAM} is only applied to the calculation of the cross-product.
It has no effect for near-square matrices where the SVD is computed directly.
}
\value{
A list containing:
\itemize{
\item \code{d}, a numeric vector of the first \code{k} singular values.
\item \code{u}, a numeric matrix with \code{nrow(x)} rows and \code{nu} columns.
Each column contains a left singular vector.
\item \code{u}, a numeric matrix with \code{ncol(x)} rows and \code{nv} columns.
Each column contains a right singular vector.
}
}
\author{
Aaron Lun
}
\seealso{
\code{\link{svd}} for the underlying algorithm.
}
\examples{
a <- matrix(rnorm(100000), ncol=20)
out <- runExactSVD(a)
str(out)
}
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