#10795: Fix and upgrade double dense matrix QR decomposition
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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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Description changed by rbeezer:
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.patch]
> 1. [attachment:trac_10795-QR-decomposition-numerical.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]
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10795#comment:20>
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