# AW: [R] General Matrix Inverse

Trenkler, Dietrich dtrenkler at nts6.oec.uni-osnabrueck.de
Thu Oct 18 11:11:42 CEST 2001

```Thorsten is right. There is a direct formula for computing the Moore-Penrose
inverse
using the singular value composition of a matrix. This is incorporated in
the following:

mpinv <- function(A, eps = 1e-13) {
s <- svd(A)
e <- s\$d
e[e > eps] <- 1/e[e > eps]
return(s\$v %*% diag(e) %*% t(s\$u))
}

Hope it helps.

Dietrich

****************************************************************************
*****
Dr. Dietrich Trenkler        (dtrenkler at nts6.oec.uni-osnabrueck.de)
Statistik / Empirische Wirtschaftsforschung
Universitaet Osnabrueck
Rolandstrasse 8                                Phone: +49(0) 541-969-2753
D-49069 Osnabrueck                          Fax  : +49(0) 541-969-2744
GERMANY
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*****

> -----Ursprüngliche Nachricht-----
> Von:	Torsten Hothorn
> Gesendet am:	Thursday, October 18, 2001 9:52 AM
> An:	Philippe Grosjean
> Cc:	r-help at stat.math.ethz.ch
> Betreff:	RE: [R] General Matrix Inverse
>
>
>
> > I use solve(x) to find the inverse of a matrix (don't know what a
> "general
> > inverse" is). By the way, what is better: solve(x), qr.solve(x) or
> ginv(x)?
> > ginv(x) seems to give results for matrices where solve and qr.solve
> return
> > an error:
> >
> > > x <- matrix(1:9, 3, 3)
> > > x
> >      [,1] [,2] [,3]
> > [1,]    1    4    7
> > [2,]    2    5    8
> > [3,]    3    6    9
> > > solve(x)
> > Error in solve.default(x) : singular matrix `x' in solve
> > > qr.solve(x)
> > Error in qr.solve(x) : singular matrix `x' in solve
> > > ginv(x)
> >            [,1]          [,2]       [,3]
> > [1,] -0.6388889 -5.555556e-02  0.5277778
> > [2,] -0.1666667  4.163336e-17  0.1666667
> > [3,]  0.3055556  5.555556e-02 -0.1944444
> >
>
> if A is singular, A^-1 is not defined but a generalized inverse G is,
> namely
>
> G is generalized inverse of A <=>
>
> A G A = A  (sometimes G is written as A^-)
>
> G is not unique, but adding 3 conditions
>
> - G A G = G
>
> - t(G A) = G A
>
> - t(A G) = A G
>
> makes G unique (Moore-Penrose-Inverse)
>
> Torsten
>
>
> > Regards,
> >
> > Philippe Grosjean
> >
> >
> > ...........]<(({?<...............<?}))><...............................
> >  ) ) ) ) )	 __               	 __
> > ( ( ( ( ( 	|__)              	|  _
> >  ) ) ) ) )	|   hilippe       	|__)rosjean
> > ( ( ( ( ( 	Marine Biol. Lab., ULB, Belgium
> >  ) ) ) ) )	                  	 __
> > ( ( ( ( ( 	|\  /|            	|__)
> >  ) ) ) ) )	| \/ |ariculture &	|__)iostatistics
> > ( ( ( ( (
> >  ) ) ) ) )	e-mail: phgrosje at ulb.ac.be or phgrosjean at sciviews.org
> > ( ( ( ( ( 	SciViews project coordinator (http://www.sciviews.org)
> >  ) ) ) ) )      tel: 00-32-2-650.29.70 (lab), 00-32-2-673.31.33 (home)
> > ( ( ( ( (
> >  ) ) ) ) )      "I'm 100% confident that p is between 0 and 1"
> > ( ( ( ( (                                  L. Gonick & W. Smith (1993)
> >  ) ) ) ) )
> > .......................................................................
> >
> >
> > -----Message d'origine-----
> > De : owner-r-help at stat.math.ethz.ch
> > [mailto:owner-r-help at stat.math.ethz.ch]De la part de Prof Brian Ripley
> > Envoye : jeudi 18 octobre 2001 04:25
> > A : Randall Skelton
> > Cc : r-help at stat.math.ethz.ch
> > Objet : Re: [R] General Matrix Inverse
> >
> >
> > On Wed, 17 Oct 2001, Randall Skelton wrote:
> >
> > > What is the easiest (not the fastest) way to find the general inverse
> of a
> > > matrix in R?
> >
> > If you mean the generalized inverse, ginv() in package MASS.  Otherwise,
> > pleae tell us what a `general inverse' is.
> >
> >
> > --
> > Brian D. Ripley,                  ripley at stats.ox.ac.uk
> > Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> > University of Oxford,             Tel:  +44 1865 272861 (self)
> > 1 South Parks Road,                     +44 1865 272860 (secr)
> > Oxford OX1 3TG, UK                Fax:  +44 1865 272595
> >
> >
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