Re: SVD, EIG and CHOL of a matrix

[Carlo de Falco]

Hi,

On 19 Jan 2010, at 16:16, Alberto Frigerio wrote:

> Hello world, I'm a neofite in Octave and I'm trying to find the  
> eigenvalues /
> eigenvectors, the singular value decomposition and the Cholesky
> factorization of a square matrix A.
> I've seen that Octave has functions for doing all these things, but  
> I would
> see HOW they work. I tried to make the SVD using the QR  
> decomposition of A,
> but in doing QR I got completely different results ... may someone  
> help me?

Octave uses lapack routines for most of these tasks, for example for  
double precision, real, full matrices
SVD is performed via a call to the lapack routine 'DGESVD'
to find out what DGESVD does, you can inspect the source code:

http://www.netlib.org/lapack/explore-html/dgesvd.f.html
or read the lapack documentation:
http://www.netlib.org/lapack/lug/node53.html

To find this information I just went through the code of SVD.cc and  
dbleSVD.cc in the Octave sources.
Assuming you are interested in algorithms for real double precision   
matrices, to find out about what is done for eigenvalues you should  
look at the files EIG.cc and eig.cc, while for Cholesky you should  
look at chol.cc and dbleCHOL.cc

> Thanks in advance,
>    Alberto

HTH,
c.