Positive definite check for matrices over RDF/CDF

[rbeezer]

Having a Cholesky decomposition is equivalent to being positive definite. With #13035 this is a cheap feature and a cheap computation, and will maintain feature sets with the exact case.

Depends: #13035

Apply:

1. attachment: trac_13052-is-positive-definite-RDF-v2.patch

Depends on #13035

CC: @dandrake

Component: linear algebra

Keywords: sd40.5

Author: Rob Beezer

Reviewer: Dan Drake, Andrey Novoseltsev

Merged: sage-5.2.beta0

Issue created by migration from https://trac.sagemath.org/ticket/13052

[rbeezer]

Changed keywords from none to sd40.5

[rbeezer]

Author: Rob Beezer

[rbeezer]

Dependencies: #13035

[novoselt]

comment:2

One too many squares in "A square matrix A is positive definite if it is square,"

[novoselt]

comment:3

And I am having the same problem as the patchbot applying it - something is wrong with dependencies?

[dandrake]

comment:4

Replying to @novoselt:

And I am having the same problem as the patchbot applying it - something is wrong with dependencies?

No, there really is a conflict with William's referee patch at #13035. Shouldn't be too hard to fix up.

[dandrake]

comment:5

Without the referee patch from #13035 (which does not affect functionality), I get some numerical noise on 64-bit Ubuntu 10.04:

sage -t  devel/sage/sage/matrix/matrix_double_dense.pyx
**********************************************************************
File "/home/drake/s/sage-5.1.beta0/devel/sage-main/sage/matrix/matrix_double_dense.pyx", line 3537:
    sage: [M[:i,:i].determinant() for i in range(1, M.nrows()+1)]
Expected:
    [1.0, 4.0, 460.0, 27936.0, 82944.0]
Got:
    [1.0, 4.0, 460.0, 27936.0, 82943.9999998]
**********************************************************************

That's from an integer matrix, so putting a round() in there will not harm anything.

[rbeezer]

comment:6

Attachment: trac_13052-is-positive-definite-RDF-v2.patch.gz

Thanks, Dan and Andrey. v2 patch is standalone patch.

• Rebased with missed reviewer patch from other ticket.
• Double "square" is gone.
• round() on all integer determinants and output reformatted

Thanks for all your work on the Cholesky stack!

Rob

[rbeezer]

Reviewer: Dan Drake, Andrey Novoselt

[novoselt]

Changed reviewer from Dan Drake, Andrey Novoselt to Dan Drake, Andrey Novoseltsev

[dandrake]

comment:8

Patchbot, only apply trac_13052-is-positive-definite-RDF-v2.patch.

[jdemeyer]

Merged: sage-5.2.beta0