#10802: Singular values of matrices over CDF
------------------------------+---------------------------------------------
Reporter: rbeezer | Owner: jason, was
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-4.7
Component: linear algebra | Keywords:
Author: Rob Beezer | Upstream: N/A
Reviewer: Martin Raum | Merged:
Work_issues: |
------------------------------+---------------------------------------------
Changes (by rbeezer):
* status: needs_work => needs_review
Old description:
> This method serves two purposes:
>
> (a) a convenience for getting singular values and clipping small values
> to zero.
>
> (b) a starting point for reasonable quality control on numerical
> approximations from CDF matrices. This will make a rank computation easy
> (though not fool-proof) and this can be used in other situations as a
> consistency check. See #7392.
>
> '''Apply:'''
> 1. [attachment:trac_10802-singular-values-CDF.patch]
New description:
This method serves two purposes:
(a) a convenience for getting singular values and clipping small values to
zero.
(b) a starting point for reasonable quality control on numerical
approximations from CDF matrices. This will make a rank computation easy
(though not fool-proof) and this can be used in other situations as a
consistency check. See #7392.
----
'''Depends:'''
1. #10837
'''Apply:'''
1. [attachment:trac_10802-singular-values-CDF-v2.patch]
--
Comment:
v2 patch rebases to depend on #10837 on 4.7.alpha3 and reworks the
doctests.
One new doctest at the beginning that is a full-rank matrix (no zero
singular values!) and should be stable numerically. includes a confidence
building test on correctness.
All the other matrices stay the same, including the difficult Hilbert
matrix. Using rounding liberally, plus ellipsis (...) and inequalities in
a few places to get everything to behave, without obscuring the real
nature of the method.
No changes to the code. New doctests pass on my Intel i7-2600 machine and
on sage.math.
The changes to the doctests should be reviewed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10802#comment:7>
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