1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
|
\name{solve-methods}
\docType{methods}
\alias{solve-methods}
\alias{solve}
\alias{solve,ANY,ANY-method}
\alias{solve,PosSemDefSymmMatrix,ANY-method}
\alias{solve,PosDefSymmMatrix,ANY-method}
\alias{solve,ANY-method}
\alias{solve,PosSemDefSymmMatrix-method}
\alias{solve,PosDefSymmMatrix-method}
\title{ Methods for Function solve in Package `distr' }
\description{solve-methods using generalized inverses for various types of matrices}
\usage{solve(a,b, ...)
\S4method{solve}{ANY,ANY}(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
\S4method{solve}{PosSemDefSymmMatrix,ANY}(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
\S4method{solve}{PosDefSymmMatrix,ANY}(a, b, tol = 1e-10)
}
\arguments{
\item{a}{matrix to be inverted / to be solved for RHS.}
\item{b}{a numeric or complex vector or matrix giving the right-hand
side(s) of the linear system. If missing, \code{b} is taken to be
an identity matrix and \code{solve} will return the inverse of
\code{a}.}
\item{\dots}{ further arguments to be passed to specific methods (see \code{\link[base]{solve}}).}
\item{generalized}{ logical: should generalized / Moore-Penrose inverses be used? By default uses
the corresponding global option to be set by \code{\link{distroptions}}.}
\item{tol}{ the tolerance for detecting linear dependencies in the
columns of \code{a}. Default is \code{.Machine$double.eps}.}
}
\section{Methods}{\describe{
\item{solve}{\code{signature(a = "ANY", b = "ANY")}: tries to evaluate \code{solve.default} method from \pkg{base} in classical way;
if this gives an error, this one is returned if \code{generalized} is \code{TRUE}, else it will then
return \eqn{a^-b} where \eqn{a^-} is the pseudo or Moore-Penrose inverse of \eqn{a}.}
\item{solve}{\code{signature(a = "PosSemDefSymmMatrix", b = "ANY")}: evaluates \eqn{a^-b} where \eqn{a^-} is the pseudo or Moore-Penrose
inverse of \eqn{a}.}
\item{solve}{\code{signature(a = "PosDefSymmMatrix", b = "ANY")}: evaluates solve method from \pkg{base} in classical way.}
}}
\details{The method for the Moore-Penrose inverse for
\code{signature(a = "PosSemDefSymmMatrix", b = "ANY")} uses \code{eigen} to find the eigenvalue
decomposition of \code{a} and then simply "pseudo-inverts" the corresponding diagonal matrix built from
\code{eigen(a)$values}, while for \code{signature(a = "ANY", b = "ANY")} it uses the svd
decomposition of \code{a} and then simply "pseudo-inverts" the corresponding diagonal matrix built from
\code{svd(a)$d}.}
\author{Peter Ruckdeschel \email{peter.ruckdeschel@uni-oldenburg.de}}
\seealso{
\code{\link[base]{solve}} for the default method, \code{\link[base]{eigen}} and \code{\link[base]{svd}}
for the pseudo inversion}
\keyword{algebra}
\keyword{array}
\concept{pseudo inverse}
\concept{inverse}
\concept{svd}
\concept{eigenvalue decomposition}
|
