#10795: Fix and upgrade double dense matrix QR decomposition
----------------------------------+-----------------------------------------
Reporter: rbeezer | Owner: jason, was
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-5.1
Component: linear algebra | Resolution:
Keywords: sd40.5 | Work issues:
Report Upstream: N/A | Reviewers: Martin Raum
Authors: Rob Beezer | Merged in:
Dependencies: | Stopgaps:
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Old description:
> The Q matrix of a QR decomposition should be unitary, hence invertible.
> For zero-column trivial cases, this is broken.
>
> {{{
> sage: A = zero_matrix(CDF, 5, 0)
> sage: Q, R = A.QR()
> sage: Q
> [0 0 0 0 0]
> [0 0 0 0 0]
> [0 0 0 0 0]
> [0 0 0 0 0]
> [0 0 0 0 0]
> }}}
>
> Besides a bugfix this patch will upgrade the documentation to make it
> clear how this routine works over the complex numbers. In particular,
> `SciPy` routines are using a Hermitian inner product - documentation
> upgrade will reflect that.
>
> '''Apply''':
> 1. [attachment:trac_10795-QR-decomposition-double-dense-v2.patch]
New description:
The Q matrix of a QR decomposition should be unitary, hence invertible.
For zero-column trivial cases, this is broken.
{{{
sage: A = zero_matrix(CDF, 5, 0)
sage: Q, R = A.QR()
sage: Q
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
}}}
Besides a bugfix this patch will upgrade the documentation to make it
clear how this routine works over the complex numbers. In particular,
`SciPy` routines are using a Hermitian inner product - documentation
upgrade will reflect that.
'''Apply''':
1. [attachment:trac_10795-QR-decomposition-double-dense-v2.patch]
1. [attachment:trac_10795-QR-decomposition-formatting.patch]
--
Comment (by rbeezer):
Dear Martin,
Thanks for participating remotely in Sage Days 40.5. ;-)
"formatting" patch is an add-on, so you can see the changes. I did the
"OUTPUT" section entirely with math quotes, other than the result objects.
The rest is in code quotes.
Updated the output description, which needed work. Added some left kernel
explanation for Dan Drake, who was also looking at this here at SD 40.5.
Thanks again,
Rob
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10795#comment:22>
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