[SciPy-dev] Why does orth use svd instead of QR ?

David Cournapeau david@silveregg.co...
Fri Feb 5 01:18:02 CST 2010


Charles R Harris wrote:
> 
> 
> On Thu, Feb 4, 2010 at 8:45 PM, David Cournapeau <david@silveregg.co.jp 
> <mailto:david@silveregg.co.jp>> wrote:
> 
>     Hi,
> 
>     I wanted to know if there was a rationale for using svd to
>     orthonormalize the columns of a matrix (in scipy.linalg). QR-based
>     methods are likely to be much faster, and I thought this was the
>     standard, numerically-stable method to orthonormalize a basis ? If the
>     reason is to deal with rank-deficient matrices, maybe we could add an
>     option to choose between them ?
> 
> 
> QR with column rotation would deal with rank-deficient matrices and 
> routines for that are available in LAPACK 
> <http://netlib.org/lapack/lug/node42.html>. The SVD was probably used 
> because it was available. The diagonal elements of the R matrix can 
> somewhat take the place of the singular values when column rotation is used.

So would be it ok to use this column-rotated QR in place of svd for 
every case in orth ? I would have to check that QR with column rotation 
is still significantly faster than svd, but I would surprised if if were 
not the case. QR has also the advantage of being implemented in PLASMA 
already contrary to eigen/svd solvers,

cheers,

David


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