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From Sean Owen <sro...@gmail.com>
Subject Re: [MATH] Repurposing a deprecated constructor in EigenDecomposition
Date Wed, 23 Oct 2013 18:33:52 GMT
Ah I see so you can just stop computing the eigenvectors when the
eigenvalues are too small. That does seem more efficient and then the
zero values are left as literally 0. I think I should back up and
implement the patch that way.

The original question stands then -- what to do about the singularity
threshold parameter given the existence of a constructor with the
signature already? because that is where it belongs. Adding an extra
boolean flag dodges that question; it feels a little funny just
because then we should have similar logic for other decompositions. I
think I remember the LU one stops early, always.

On Wed, Oct 23, 2013 at 4:50 PM, Ted Dunning <ted.dunning@gmail.com> wrote:
> On Wed, Oct 23, 2013 at 3:14 PM, Sean Owen <srowen@gmail.com> wrote:
>
>> EigenDecomposition resembles QR in this respect, as far as they are
>> implemented here. This argues for them to treat arguments similarly.
>>
>
> Actually not.  It is quite reasonable for the EigenDecomposition to stop
> when singularity is reached.  This affects the shape of the eigenvector
> matrix.
>
> Perhaps add a new constructor with a double tolerance and a boolean that
> says to stop early.  QR is subject to the same logic since partial QR is
> often more useful than full QR with singular R.  This is the same logic as
> with Cholesky since QR and Cholesky are two sides of the same coin in many
> respects.

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