Re: TheMatrixTemplateLibrary - 2 questions

On Tue, 12 Nov 2002, Gunter Winkler wrote:

> On Friday, 8. November 2002 23:05, you wrote:
> > Hello, I have 2 questions about MTL:
> >
> > 2) Is there a function that computes the rank of a
> >    matrix?
> 
> There is the LU-Decomposition. If it aborts early, the column (row) 
> number (minus 1) gives you the rank of the matrix. You could probably 
> change the code provided by O. König to return the rank if LU fails.
> 
> mfg
> Gunter

That is not necessarily true. The failure may be much earlier than the
true rank, unless you do full pivoting. Think about a NxN matrix
consisting of all zeroes in the first column (and row), and a unity
submatrix in the rest. This has definitely rank N-1, but LU fails in the
very first step. 
Furthermore, rank computation by decomposition is a badly conditioned
process. Rounding errors can changing the rank considerably, in
either direction. Better use SVD (singular value decomposition) and decide
yourself whether a singular value is close enough to zero to be considered
as a rank defect. That decision is highly dependant on what you need the
rank for.

Ciao,
	Manuel

______________________________________________________________________
  
Dr. Manuel Kessler, Dipl.-Phys.

Institut fuer Aerodynamik und Gasdynamik
Universitaet Stuttgart
Pfaffenwaldring 21           ( ( ( ( ___________.^.___________ ) ) ) )
70550 Stuttgart / Germany                      _\I/_                
                                              /\_|_/\
Phone:      +49 711 685 3435                  \_(_)_/ 
Fax:        +49 711 685 3438                 ./     \.
E-Mail:     [email protected]               
WWW:        http://www.iag.uni-stuttgart.de/people/manuel.kessler
______________________________________________________________________

_______________________________________________
This list is archived at http://www.osl.iu.edu/MailArchives/mtl-devel/