Date:         Thu, 30 Jul 2009 14:04:22 -0400
Reply-To:     msz03@albany.edu
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Mike Zdeb <msz03@ALBANY.EDU>
Subject:      Re: matrix inverse without IML
Content-Type: text/plain;charset=iso-8859-1

hi ... wow, a reference to a post from 2001 !!!

well, since then, if you don't have IML, you can use some matrix functions PROC FCMP

as was pointed out by a couple postings by  Dale McLerran in a few postings, among them ...

http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0812B&L=sas-l&P=R31866

http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0905A&L=sas-l&P=R24270


data x;
input m1-m3;
datalines;
1 3 3
1 4 3
1 3 4
;
run;

proc fcmp;
array temp[3,3] / nosymbols;
array im[3,3];
rc = read_array('work.x',temp);
call inv(temp, inverse);
rc = write_array('work.y',im);
quit;

title 'matrix';
proc print data=x noobs;
run;

title 'inverse';
proc print data=y noobs;
run;

matrix
m1    m2    m3
 1     3     3
 1     4     3
 1     3     4

inverse
im1    im2    im3
  7     -3     -3
 -1      1      0
 -1      0      1

--
Mike Zdeb
U@Albany School of Public Health
One University Place
Rensselaer, New York 12144-3456
P/518-402-6479 F/630-604-1475

> by understanding the operations behind a matrix inversion, we certainly can
> resort to SVD algorithm
>
> SVD on a square matrix X is
> X=UEV'
> and once we got matrix U, E, V, we can obtain the inverse of X as
> inv(X)=UE^{-1}V'
>
> since matrix E is an diagonal matrix, its inverse is simply inversion of
> its diagonal scalar elements which can be easily done, taking numerical
> stability into consideration.
>
> Well, I've also point out a way in SAS to do SVD (hence generalized
> inverse) without IML (but you do need SAS/STAT) at
> sas-programming.blogspot.com
>
> now you don't IML or other software and the overhead in exchange data
> between them.
>
> On Thu, 7 Jun 2001 14:21:18 -0700, David L. Cassell
> <Cassell.David@EPAMAIL.EPA.GOV> wrote:
>
>>Howard Schreier wrote [ in part]:
>>>Here's an alternative.
>>>
>>> You probably have Excel.
>>>
>>> Excel has a function (MINVERSE) for inverting matrices.
>>>
>>> You could put the data into Excel, do the calculation, then get the data
>>> back into SAS.
>>
>>Very clever [as usual].  But are you aware that Excel does *not* do a
>>good job on some matrix and stat functions?  I believe there is an ACM
>>paper of last year in which two authors tested Excel on NIST test data
>>sets for stats and it did wretchedly.  I wouldn't use Excel to invert a
>>matrix
>>without substantial testing first.  And if the matrix is ill-conditioned,
>>Excel [or most non-matrix/stat software for that matter] may do a *ghastly*
>>job of inverting the matrix properly.  BTW, this is not just another MS
>>slam,
>>because I wouldn't trust any of the popular spreadsheets to do this well
>>without
>>testing first.
>>
>>OTOH, there are realtively inexpensive matrix mainpulation and stats
>>packages
>>which could be used in place of Excel here.  GLIM comes to mind, as does
>>Perl's PDL module [which is free - if you can get it to compile on your
>>OS!]
>>and the R system [also free].
>>
>>David
>>--
>>David Cassell, CSC
>>Cassell.David@epa.gov
>>Senior computing specialist
>>mathematical statistician
>