[SciPy-dev] Why does orth use svd instead of QR ?
Charles R Harris
Thu Feb 4 23:58:23 CST 2010
On Thu, Feb 4, 2010 at 8:45 PM, David Cournapeau <firstname.lastname@example.org>wrote:
> 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.
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