David,
Thank you for your reply.
Note that there is an inversion in the signal of the third eigenvector of U
when we use eigvec function compared with U1 obtained from SVD routine (call
svd).
So, with the following code, which have this change,
==========================================================
proc iml;
reset print;
U1 ={
0.6829111 0.729794 0.032144 0,
0.379184 0.3917486 0.838303 0,
0.6243813 0.560298 0.5442556 0};
Q1={
15.63108,
6.2868832,
1.0697839,
0};
V1={
0.123579 0.0621615 0.987458 0.0760974,
0.4240811 0.5518147 0.142056 0.7039005,
0.7466757 0.2119602 0.058408 0.627803,
0.4973518 0.804182 0.036542 0.3234137};
AA=U1*diag(Q1)*T(V1);
QUIT;
=========================================================
we have in output the matrix AA:
AA 3 rows 4 cols (numeric)
1.0679119 1.99023 6.9959835 8.9974851
1.7711111 3.7452081 4.8952398 0.9344588
0.8501328 6.1654201 8.0680142 2.0425536
so different of original one:
A={1 2 7 9,
0 4 5 1,
2 6 8 2};
I can not understand why the eigvec and eigval functions do not give the
correct singular value decomposition. Is it a wrong calculation in this
functions?
Obviously, both sets of eigenvectors form an orthonormal basis, as noted by
Dale (not post here). I don't know what determines whether
one should employ the positive or the negative eigenvector.
TIA
Carlos
 Original Message 
From: David L. Cassell <cassell.david@EPAMAIL.EPA.GOV>
Newsgroups: bit.listserv.sasl
To: <SASL@LISTSERV.UGA.EDU>
Sent: Friday, April 11, 2003 9:01 PM
Subject: Re: svd in iml again
> Carlos Tadeu <ctsdias@CARPA.CIAGRI.USP.BR> wrote:
> > I am trying to do a singular value decomposition of matrix A in IML
> using eigvec and eigval functions, but I can not reproduce the original
> matrix A.
> > What is wrong? Does anyone have had the same problem?
> > I know that SVD routine operates well. It sound like inversion in the
> signal of the eigvector.
> > The code that I am using eigvec function is:
> > proc iml;
> > reset print;
> > A={1 2 7 9,
> > 0 4 5 1,
> > 2 6 8 2};
> > n=nrow(A);
> > p=ncol(A);
> > AAL=A*t(A);
> > ALA=t(A)*A;
> > U=eigvec(AAL);
> > V=eigvec(ALA);
> > L=eigval(AAL);
> > D=sqrt(diag(L));
>
> Things are fine down to here...
>
> > U=U[1:3,1:3];
> > V=V[1:4,1:3];
>
> Uhoh. Here's where your code goes astray.
>
> Your original *square* matrices U and V are the correct matrices
> for the SVD. Try using:
>
> call svd (U1,Q1,V1,A);
>
> and compare the results to your U and V matrices.
> Just don't cut V (or U in the m<n case) down.
>
> HTH,
> David
> 
> David Cassell, CSC
> Cassell.David@epa.gov
> Senior computing specialist
> mathematical statistician
