Date:         Sat, 12 Apr 1997 20:00:55 -0300
Reply-To:     Carlos Tadeu <ctsdias@CARPA.CIAGRI.USP.BR>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Carlos Tadeu <ctsdias@CARPA.CIAGRI.USP.BR>
Subject:      Re: svd in iml again
Comments: To: cassell.david@EPAMAIL.EPA.GOV
Content-Type: text/plain; charset="iso-8859-1"

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.sas-l
To: <SAS-L@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];
>
> Uh-oh.  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