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From Chris Nix <chris....@gmail.com>
Subject Re: [MATH] Re: Pivoting QR Decomposition: Take Two!
Date Wed, 05 Oct 2011 07:34:51 GMT
Greg,

Apologies that I've not had more time on this, I started a new job that
doesn't afford it at the moment, :(.

I would say that a single implementation, with or without pivoting, makes
sense to save confusion.  Your clearer code would be a good choice for
maintainability.

One possible word of caution with replacing the current implementation with
a pivoting version is that current users of the QRDecomposition may not
expect a third factor, namely P, particularly in the solvers.  This is not
really a problem, but it should be well documented as a change to v2 to save
confusion and perhaps method names, ie testAEqualQR should be changed to
make this clear.

Additionally, any pivoting QRDecomposition class should also have a
getRank() method since it is after all 'rank-revealing' and in most (or
all?) cases it would be more efficient than
SingularValueDecomposition.getRank().

Chris.


On 5 October 2011 05:05, Greg Sterijevski <gsterijevski@gmail.com> wrote:

> My apologies! Forgot to tag the subject line.
>
> On Tue, Oct 4, 2011 at 8:35 PM, Greg Sterijevski <gsterijevski@gmail.com
> >wrote:
>
> > Hello all,
> >
> > A while back I was interested in being able to do pivoting qr
> > decomposition. I noticed that Chris Nix submitted a patch, but he
> indicated
> > that he had more work to do (testing and filling in functionality). In
> the
> > discussion around this, Luc suggested that I look at the QR decomposition
> in
> > Levenberg-Marquardt. I did just that a few days ago. The code was very
> clear
> > and nicely written (kudos to Luc). So, I copied the routine and made a
> new
> > PivotingQRDecomposition class. The class is intended as a "drop in
> > replacement" for QRDecomposition. I also copied the QRSolverTest and
> > QRDecompositionTest. With the exception of testUnderdetermined in the
> solver
> > test and testAEqualQR in QRDecompositionTest, the tests are unchanged
> (and
> > all pass!). With testUndertermined, the "zeroed" rows of the solution
> matrix
> > are interspersed throughout the matrix (because of pivoting). So I change
> > the test to count all the rows that have zero norms, and check that it is
> > the correct number. In testAEqualQR, I added a multiplication by the
> > permutation matrix.
> >
> > What is the best way to proceed? I don't want to trounce the additions
> that
> > Chris made, but it looks like Chris has more sophisticated classes in
> mind.
> > I don't see this proposed change competing with his. Does it make sense
> to
> > bring back QRDecomposition interface (sorry Sebastien)? We can then keep
> > both implementations until we are satisfied the pivoting one works.
> >
> > Thoughts?
> >
> > -Greg
> >
>

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