Implement more algorithms for computing eigenvalues #39804

user202729 · 2025-03-27T16:49:39Z

Now eigenvalues() and eigenvectors_left() takes algorithm parameter.

Partially handles #39762

Also changes the default algorithm of eigenvalues() to pari_charpoly when the base field is RR or CC.

Additional changes required:

implement conversion from mpmath object to RR or CC
implement shifting elements of RR by a negative value
detect error of conversion to mpmath object
change a hard error to a warning

📝 Checklist

The title is concise and informative.
The description explains in detail what this PR is about.
I have linked a relevant issue or discussion.
I have created tests covering the changes.
I have updated the documentation and checked the documentation preview.

⌛ Dependencies

github-actions · 2025-03-27T19:08:38Z

Documentation preview for this PR (built with commit 74f8760; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

user202729 · 2025-03-28T04:30:30Z

src/doc/en/prep/Quickstarts/Linear-Algebra.rst

-    [0 0 0 0 0]
-    [0 0 0 0 0]
+    sage: P*D-H*P == matrix.zero(5)
+    True


This is necessary because now check=False is passed, so exactify is no longer called, so it shows some 0.000000?e-16 thing instead.

tscrim

LGTM modulo some details.

src/sage/libs/mpmath/ext_main.pyx

src/sage/matrix/matrix2.pyx

Co-authored-by: Travis Scrimshaw <[email protected]>

user202729 · 2025-03-28T15:18:19Z

I decide to make eigenvalues() and eigenvectors_left() with the default algorithm never raise experimental warning.

The reason being the functionality and interface never need to change, even if flint decide to remove algorithm=None, we can just automatically switch to something else (pari is the next fastest, but sage wins in case only eigenvalues are needed because pari need to compute eigenvectors also, though we can compute charpoly → polroots in pari)

user202729 · 2025-03-28T16:24:20Z

Thought: is .eigenvalues(algorithm="pari") a good idea? Later on pari may implement a function that computes the eigenvalues only and is faster, then what are we going to call it, .eigenvalues(algorithm="pari_faster")?

The situation is somewhat analogous to https://github.com/sagemath/sage/pull/39243/files where small_roots_algorithm is added…

user202729 · 2025-03-31T06:10:52Z

By benchmarking result it appears that pari_charpoly is faster than flint for computing eigenvalues of random matrix over RR, so I use that.

tscrim

I think that is good for the algorithm to not issue a warning.

I don't have an answer with regards to PARI. It's based on a potential future case, and we can worry about it later if that does happen.

Just one last little doc tweak, then a positive review.

src/sage/matrix/matrix2.pyx

Co-authored-by: Travis Scrimshaw <[email protected]>

user202729 · 2025-04-02T12:36:43Z

Test failure looks like #22482 and unrelated to this one.

(Still waiting for documentation to build to check it)

Edit: the links work https://doc-pr-39804--sagemath.netlify.app/html/en/reference/matrices/sage/matrix/matrix2#hunk5

tscrim · 2025-04-03T06:03:55Z

Thank you. Sorry, I thought that short version would work based on what is important at startup. Positive review.

sagemathgh-39804: Implement more algorithms for computing eigenvalues Now `eigenvalues()` and `eigenvectors_left()` takes `algorithm` parameter. Partially handles sagemath#39762 Also changes the default algorithm of `eigenvalues()` to `pari_charpoly` when the base field is `RR` or `CC`. Additional changes required: * implement conversion from mpmath object to RR or CC * implement shifting elements of RR by a negative value * detect error of conversion to mpmath object * change a hard error to a warning ### 📝 Checklist  - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies    URL: sagemath#39804 Reported by: user202729 Reviewer(s): Travis Scrimshaw, user202729

vbraun · 2025-04-06T11:40:07Z

On 32-bit:

**********************************************************************
File "src/sage/matrix/matrix2.pyx", line 7321, in sage.matrix.matrix2.Matrix.list
Failed example:
    l = m.eigenvectors_left(algorithm="pari"); l
Expected:
    [(-1.4142135623730950487637880730318329370*I,
      [(0.707106781186547524*I, 1.00000000000000000)],
      1),
     (1.4142135623730950487637880730318329370*I,
      [(-0.707106781186547524*I, 1.00000000000000000)],
      1)]
Got:
    [(-1.41421356237309505*I,
      [(0.7071067811865475243818940365*I, 1.000000000000000000000000000)],
      1),
     (1.41421356237309505*I,
      [(-0.7071067811865475243818940365*I, 1.000000000000000000000000000)],
      1)]
**********************************************************************
File "src/sage/matrix/matrix2.pyx", line 7328, in sage.matrix.matrix2.Matrix.list
Failed example:
    m._fix_eigenvectors_extend(l, extend=True)
Expected:
    [(-1.4142135623730950487637880730318329370*I,
      [(0.707106781186547524*I, 1.00000000000000000)],
      1),
     (1.4142135623730950487637880730318329370*I,
      [(-0.707106781186547524*I, 1.00000000000000000)],
      1)]
Got:
    [(-1.41421356237309505*I,
      [(0.7071067811865475243818940365*I, 1.000000000000000000000000000)],
      1),
     (1.41421356237309505*I,
      [(-0.7071067811865475243818940365*I, 1.000000000000000000000000000)],
      1)]
**********************************************************************
File "src/sage/matrix/matrix2.pyx", line 7422, in sage.matrix.matrix2.Matrix.list
Failed example:
    m.eigenvectors_left(algorithm="pari")
Expected:
    [(-1.4142135623730950487637880730318329370*I,
      [(0.707106781186547524*I, 1.00000000000000000)],
      1),
     (1.4142135623730950487637880730318329370*I,
      [(-0.707106781186547524*I, 1.00000000000000000)],
      1)]
Got:
    [(-1.41421356237309505*I,
      [(0.7071067811865475243818940365*I, 1.000000000000000000000000000)],
      1),
     (1.41421356237309505*I,
      [(-0.7071067811865475243818940365*I, 1.000000000000000000000000000)],
      1)]
**********************************************************************

user202729 · 2025-04-06T13:56:31Z

Are they all the failures? (I haven't figured how to install pari 32-bit on my machine)

vbraun · 2025-04-06T22:31:06Z

Yes, those were the only ones

sagemathgh-39804: Implement more algorithms for computing eigenvalues Now `eigenvalues()` and `eigenvectors_left()` takes `algorithm` parameter. Partially handles sagemath#39762 Also changes the default algorithm of `eigenvalues()` to `pari_charpoly` when the base field is `RR` or `CC`. Additional changes required: * implement conversion from mpmath object to RR or CC * implement shifting elements of RR by a negative value * detect error of conversion to mpmath object * change a hard error to a warning ### 📝 Checklist  - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies    URL: sagemath#39804 Reported by: user202729 Reviewer(s): Travis Scrimshaw, user202729

github-actions bot added the s: needs review label Mar 27, 2025

user202729 force-pushed the matrix-eigenvalue branch from 785d796 to 6a308d0 Compare March 27, 2025 16:54

user202729 added 2 commits March 28, 2025 11:11

Implement more algorithms for computing eigenvalues

df8ea61

Fix a test

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user202729 force-pushed the matrix-eigenvalue branch from 6a308d0 to 1724f23 Compare March 28, 2025 04:29

user202729 commented Mar 28, 2025

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user202729 mentioned this pull request Mar 28, 2025

experimental warning messages are only raised once, ignoring warnings.simplefilter() #39811

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user202729 force-pushed the matrix-eigenvalue branch from d9076dc to da1845a Compare March 28, 2025 13:15

Add tests for eigenvalues, rename result argument

5a30e3c

user202729 force-pushed the matrix-eigenvalue branch from da1845a to 5a30e3c Compare March 28, 2025 13:16

Suppress warnings when algorithm=None

fa9134a

Implement pari_charpoly algorithm for eigenvalues

b955ffd

user202729 mentioned this pull request Mar 31, 2025

Matrix singular values #39831

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5 tasks

Make sure eigenvalues() return Sequence

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vbraun force-pushed the develop branch from 8a8453f to b8f98e7 Compare March 31, 2025 22:55

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user202729 and others added 2 commits April 2, 2025 18:03

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Co-authored-by: Travis Scrimshaw <[email protected]>

Fix documentation rendering

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Actually fix documentation rendering

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tscrim added s: positive review c: linear algebra and removed s: needs review labels Apr 3, 2025

vbraun added the s: needs work label Apr 6, 2025

Add tolerance in doctest

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github-actions bot added s: needs review and removed s: positive review s: needs work labels Apr 6, 2025

vbraun added the s: positive review label Apr 6, 2025

vbraun merged commit 3229ce4 into sagemath:develop Apr 18, 2025
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