#10795: Fix and upgrade double dense matrix QR decomposition
-------------------------------+--------------------------------------------
Reporter: rbeezer | Owner: jason, was
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-4.7.2
Component: linear algebra | Resolution:
Keywords: | Work_issues:
Upstream: N/A | Reviewer: Martin Raum
Author: Rob Beezer | Merged:
Dependencies: |
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Changes (by rbeezer):
* keywords: beginner =>
* status: needs_work => needs_review
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.
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.patch]
1. [attachment:trac_10795-QR-decomposition-numerical.patch]
--
Comment:
"numerical" patch applies accumulated techniques for these numerical
computations and should address the doctest failures.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10795#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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