[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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