Re: [Lapackpp-devel] Problem finding Null space using LaSVD_IP()

[Christian S. <sti...@tu...>]

(Please send your message to "lapackpp-devel", not -owner. Thanks.)

Am Donnerstag, 14. Dezember 2006 21:18 schrieb Sonia Singhal:
> Hi,
> I am using the LAPACKPP on Windows with Visual Studio. I downloaded it a
> couple of days back and am using the 2.5.0 version.
>
> I am using LaSVD_IP() to find the null space of a matrix. My matrix is with
> m<n. I was getting wrong answers.
> I dumped the U, S, VT matrices generated by the above call and checked it
> with Matlab results.
> Apparently, the U and V( orVT) matrix columns are fine upto the rank of the
> matrix. Beyond that they are all messed up, hence my null space is
> incorrect.

I'm not so sure you are expecting the right thing here. As you said, the 
singular vectors for the non-null singular values are as expected. However, 
the rest of the U and VT matrices, as I understand SVD, are quite ambiguous, 
given that they only have to span the null space. So as long as these vectors 
span that space, they can be totally different. As far as I understand it, 
you would have to check whether the spanned space of all these vectors from 
lapackpp is identical to the space spanned by the matlab vectors (I don't 
have a good check for that at hand, but surely one can think of something 
appropriate). 

> Has this been observed by someone else ? Am I doing something wrong here ?
> the way I set up my matrices is
> U - m*m
> VT - n*n
> S - min(m,n) . I have tried n also as in my case m<n.
> A matrix is m*n

I think everything is working fine here - you would have gotten clear error 
messages if any of these matrices were of wrong dimension. 

Christian