Left eigenvectors for CBF

[a67c9e2f-a36c-4a8e-80bb-0c82631d944f]

For matrices over ComplexBallField, one can get right eigenvectors but asking for left eigenvectors triggers a not-implemented error.

sage: M = random_matrix(CBF, 2, 2)
sage: right = M.eigenvectors_right()
sage: left = M.eigenvectors_left()
NotImplementedError: eigenspaces cannot be computed reliably for inexact rings such as Complex ball field with 256 bits of precision,
consult numerical or symbolic matrix classes for other options

Here we make eigenvectors_left return the right eigenvectors of the transpose.

CC: @videlec @mezzarobba @seblabbe

Component: linear algebra

Keywords: ComplexBallField, thursdaysbdx

Author: Vincent Delecroix

Branch/Commit: c02327f

Reviewer: Marc Mezzarobba

Issue created by migration from https://trac.sagemath.org/ticket/33652

[videlec]

comment:2

The problem is that in the generic code (matrix2.pyx) it is implemented the other way around : there is a default implementation for eigenvectors_left and eigenvectors_right calls eigenvectors_left with the transposed matrix.

[videlec]

New commits:

c637231

33652: transpose and left eigenvectors for acb_mat

[videlec]

Author: Vincent Delecroix

[videlec]

Changed keywords from ComplexBallField to ComplexBallField, thursdaysbdx

[videlec]

Branch: u/vdelecroix/33652

[videlec]

Commit: c637231

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from c637231 to bac4ef1

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

bac4ef1

33652: transpose and left eigenvectors for acb_mat

[mezzarobba]

comment:5

Lgtm except for one occurrence of eigenvectors_right_approx that should be `eigenvectors_left_approxin the doc ofeigenvectors_left``.

[mezzarobba]

Reviewer: Marc Mezzarobba

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from bac4ef1 to 4012cd2

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

46ee558	33625: _new_matrix -> _new
4012cd2	33625: fix in the doc `_right_` -> _left_

[videlec]

comment:7

Thanks for having a look. Indeed I was not very careful when copying the doc.

[seblabbe]

comment:8

Patchbot says:

========== blocks ==========
git checkout patchbot/ticket_merged
inside file:  b/src/sage/matrix/matrix_complex_ball_dense.pyx
@@ -551,6 +551,26 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
+        Returns the transpose of ``self``.
wrong syntax for blocks (INPUT, OUTPUT, EXAMPLES, NOTE, etc) inserted on 1 non-empty lines
blocks -- 0 seconds
========== end blocks ==========

It should be Return with no s.

[seblabbe]

comment:10

Other issues on the patchbot seems unrelated to this branch. Only the issue with blocks remain.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 4012cd2 to c02327f

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

c02327f

33652: returns -> return

[slel]

Description changed:

--- 
+++ 
@@ -1,13 +1,14 @@
-When computing left eigenvectors for ComplexBallField matrices, sage raises a not implemented error, whereas right eigenvectors are working.
-
-Example :
+For matrices over `ComplexBallField`, one can get
+right eigenvectors but asking for left eigenvectors
+triggers a not-implemented error.

-M = random_matrix(CBF,2,2) -print(M.eigenvectors_right()) -print(M.eigenvectors_left())

+sage: M = random_matrix(CBF, 2, 2) +sage: right = M.eigenvectors_right() +sage: left = M.eigenvectors_left() NotImplementedError: eigenspaces cannot be computed reliably for inexact rings such as Complex ball field with 256 bits of precision, consult numerical or symbolic matrix classes for other options

+Here we make `eigenvectors_left` return
+the right eigenvectors of the transpose.

[vbraun]

Changed branch from u/vdelecroix/33652 to c02327f