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