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is to be computed. Logical matrices are coerced to numeric.}
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is to be computed. Logical matrices are coerced to numeric.}
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\item{nu}{the number of left singular vectors to be computed.
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\item{nu}{the number of left singular vectors to be computed.
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This must between \code{0} and \code{n = nrow(x)}.}
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This must between \code{0} and \code{n = nrow(x)}.}
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\item{nv}{the number of right singular vectors to be computed.
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\item{nv}{the number of right singular vectors to be computed.
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This must be between \code{0} and \code{p = ncol(x)}.}
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This must be between \code{0} and \code{p = ncol(x)}.}
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\item{LINPACK}{logical. Defunct and ignored (with a warning for true values).}
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\item{LINPACK}{logical. Defunct and ignored.}
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}
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}
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\details{
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27 |
\details{
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The singular value decomposition plays an important role in many
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The singular value decomposition plays an important role in many
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statistical techniques. \code{svd} and \code{La.svd} provide two
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statistical techniques. \code{svd} and \code{La.svd} provide two
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slightly different interfaces.
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slightly different interfaces.
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35 |
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Unsuccessful results from the underlying LAPACK code will result in an
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36 |
Unsuccessful results from the underlying LAPACK code will result in an
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| 37 |
error giving a positive error code (most often \code{1}): these can
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37 |
error giving a positive error code (most often \code{1}): these can
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only be interpreted by detailed study of the FORTRAN code but mean
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38 |
only be interpreted by detailed study of the FORTRAN code but mean
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| 39 |
that the algorithm failed to converge.
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that the algorithm failed to converge.
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|
- |
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The LINPACK interface is restricted to matrices \code{x} with less
|
- |
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| 42 |
than \eqn{2^{31}}{2^31} elements.
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- |
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| 43 |
}
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40 |
}
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\value{
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41 |
\value{
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| 45 |
The SVD decomposition of the matrix as computed by LAPACK/LINPACK,
|
42 |
The SVD decomposition of the matrix as computed by LAPACK,
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| 46 |
\deqn{ \bold{X = U D V'},} where \eqn{\bold{U}} and \eqn{\bold{V}} are
|
43 |
\deqn{ \bold{X = U D V'},} where \eqn{\bold{U}} and \eqn{\bold{V}} are
|
| 47 |
orthogonal, \eqn{\bold{V'}} means \emph{V transposed}, and
|
44 |
orthogonal, \eqn{\bold{V'}} means \emph{V transposed}, and
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\eqn{\bold{D}} is a diagonal matrix with the singular
|
45 |
\eqn{\bold{D}} is a diagonal matrix with the singular
|
| 49 |
values \eqn{D_{ii}}{D[i,i]}. Equivalently, \eqn{\bold{D = U' X V}},
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46 |
values \eqn{D_{ii}}{D[i,i]}. Equivalently, \eqn{\bold{D = U' X V}},
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which is verified in the examples, below.
|
47 |
which is verified in the examples, below.
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