#11027: Schur matrix decomposition over RDF/CDF
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Reporter: rbeezer | Owner: jason, was
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.7.1
Component: linear algebra | Resolution:
Keywords: | Work_issues:
Upstream: N/A | Reviewer: Martin Raum, John Palmieri
Author: Rob Beezer | Merged:
Dependencies: |
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Comment(by rbeezer):
Replying to [comment:34 jdemeyer]:
> *ping* any ideas?
Hi Jeroen. Thanks for the interest.
Ideas? Lots:
(a) Doctesting this numerical stuff is hard.
(b) We should not be relying on Apple's vector libraries.
(c) Organizing Sage Days 31 has me distracted.
But seriously,
(i) I've thinking about taking on eigenvalues and eigenvectors, generally.
There is a lot of inconsistency floating around. Ordering eigenvalues
would be one thing to tackle. Which is the real reason I have not moved
on this one.
(ii) Doctest in question is about verifying the 2x2 blocks along the
diagonal of the real Schur decomposition. It would probably be better to
not force the eigenvalues of the 2x2 blocks to match the usual Sage
output, and instead just sort the "plain" eigenvalues to match the sorted
list from the 2x2 blocks. That would be an easy fix.
(iii) The ordering of eigenvalues under "old" OS X might need to be
investigated separately and fixed up. On Linux and Sage 4.7 I get:
{{{
sage: A = matrix(RDF, 4, 4, [[1, 0, -3, -1],
... [4, -16, -7, 0],
... [1, 21, 1, -2],
... [26, -1, -2, 1]])
sage: A.eigenvalues()
[-0.789826456477 + 2.33693044103*I, -0.789826456477 - 2.33693044103*I,
-5.71017354352 + 8.38264062467*I, -5.71017354352 - 8.38264062467*I]
}}}
which is different from what you are reporting on OS X 10.4 PPC. Probably
happening at the `NumPy` level or further down.
I'll likely make the change mentioned above in a few days, perhaps while
at Sage Days. On vacation at the moment.
Rob
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11027#comment:35>
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