Upgrade unitary check for RDF/CDF matrices

[rbeezer]

This is an upgrade of the is_unitary() method, based on experience building is_normal(), is_hermitian(). (#10848, #11104)

One test is discovering a bug elsewhere (#11248), so needs to be adjusted slightly to preserve that discovery, though at this writing, the test is disabled (#11277).

(a) Adds a "orthonormal" variant, which is now the default, based on the Schur decomposition, an idea used in the other two methods, but not considered here previously.

(b) Makes the existing naive algorithm a bit more efficent by using the break command twice.

(c) Fixes an ommission in the naive algorithm where the loop on i previously did not start at zero.

(d) Upgraded error-checking on tolerance parameter.

(e) Docstring upgraded to reflect changes above.

Depends on:

1. Schur matrix decomposition over RDF/CDF #11027
2. Checks for Hermitian matrices #10848
3. Temporarily disable failing SVD doctest #11277

Apply:

1. attachment: trac_11306-upgrade-unitary-matrix-check.patch
2. attachment: trac_11306-docfix.patch

Depends on #11027
Depends on #10848
Depends on #11277

CC: @jasongrout

Component: linear algebra

Keywords: days30

Author: Rob Beezer

Reviewer: David Loeffler

Merged: sage-5.0.beta9

Issue created by migration from https://trac.sagemath.org/ticket/11306

[rbeezer]

comment:1

Attachment: trac_11306-upgrade-unitary-matrix-check.patch.gz

For the patchbot:

Depends on 11027, 10848, 11277

[rbeezer]

Author: Rob Beezer

[rbeezer]

Dependencies: 11027, 10848, 11277

[saliola]

Changed keywords from none to days30

[fchapoton]

Changed dependencies from 11027, 10848, 11277 to #11027, #10848, #11277

[loefflerd]

comment:5

Looks good and passes doctests

[loefflerd]

Reviewer: David Loeffler

[jdemeyer]

comment:6

There is some misformatting of the documentation (check http://sagemath.org/doc/developer/conventions.html#documentation-strings for a template):

dochtml.log:docstring of sage.matrix.matrix_double_dense.Matrix_double_dense.is_normal:29: WARNING: Literal block expected; none found.
dochtml.log:docstring of sage.matrix.matrix_double_dense.Matrix_double_dense.is_normal:46: WARNING: Literal block expected; none found.
dochtml.log:docstring of sage.matrix.matrix_double_dense.Matrix_double_dense.is_unitary:32: WARNING: Literal block expected; none found.

[loefflerd]

comment:7

Attachment: trac_11306-docfix.patch.gz

Two of these aren't related to this ticket (I guess you were testing this and #11104 at the same time). The other one is fixed by the single-character patch above.

[rbeezer]

comment:8

Dear David,

Gotta love those one-character patches. I'll get this reviewed as well.

Thanks for plowing though the "needs_rewview" backlog.

Rob

[rbeezer]

comment:10

Positive review. I'm inclined to just leave the author/reviewer fields as-is, but if David wants to double them up, that's fine too.

Thanks for the review, David.

[jdemeyer]

Merged: sage-5.0.beta9