[with patch] 2.8.13.alpha1: modular/modform/numerical.py with new numpy/scipy from #1198

[mabshoff]

With

 http://sage.math.washington.edu/home/jkantor/spkgs/scipy-20071020-0.6.spkg  http://sage.math.washington.edu/home/jkantor/spkgs/numpy-20071020-1.0.3.1.spkg

I get the following failures:

mabshoff@sage:/tmp/Work-mabshoff/release-cycles/sage-2.8.13.alpha0$ ./sage -t  devel/sage-main/sage/modular/modform/numerical.py
sage -t  devel/sage-main/sage/modular/modform/numerical.py  **********************************************************************
File "numerical.py", line 53:
    sage: n.ap(2)
Expected:
    [3.0, 0.61803398875, -1.61803398875]
Got:
    [0.326481263444, -0.241771189268, 0.632965191003]
**********************************************************************
File "numerical.py", line 55:
    sage: n.systems_of_eigenvalues(7)
Expected:
    [
    [-1.61803398875, 2.2360679775, -3.2360679775],
    [0.61803398875, -2.2360679775, 1.2360679775],
    [3.0, 4.0, 6.0]
    ]
Got:
    [
    [-0.241771189268, -0.516457621465, -0.483542378535],
    [0.326481263444, -1.65296252689, 0.652962526888],
    [0.632965191003, -2.26593038201, 1.26593038201]
    ]
**********************************************************************
File "numerical.py", line 67:
    sage: n.eigenvalues([2,3,5])
Expected:
    [[3.0, 0.61803398875, -1.61803398875],
     [4.0, -2.2360679775, 2.2360679775],
     [6.0, 1.2360679775, -3.2360679775]]
Got:
    [[0.326481263444, -0.241771189268, 0.632965191003], [-1.65296252689, -0.516457621465, -2.26593038201], [0.652962526888, -0.483542378535, 1.26593038201]]
**********************************************************************
1 items had failures:
   3 of   5 in __main__.example_1
***Test Failed*** 3 failures.
For whitespace errors, see the file .doctest_numerical.py
         [1.9 s]
exit code: 256

----------------------------------------------------------------------

Cheers,

Michael

[jkantor]

Something happened and the issue is eigen_left is supposed to compute left eigen_vectors (v*m=\lambda*v), but is computing right eigen_vectors. There are some other issues so I'm going to add methods right_eigenvectors and left_eigenvectors to make this clearer. I have already done this and with the new methods the above tests pass. I am going to run test all to make sure my change didn't break something else, I will post a patch in a few hours.

[jkantor]

The other issues being that the meaning of eigen_left is not consistent between real and complex double matrices.

[jkantor]

I have a patch that fixes the eigenvector issue with real and complex double matrices. All doc tests (including the above) pass with this patch and the new numpy/scipy

 http://sage.math.washington.edu/home/jkantor/spkgs/double_matrices.hg

The function eigen_left and eigen_right are replaced by left_eigenvectors and right_eigenvectors. Hopefully this makes it more clear that for example left_eigenvectors are eigenvectors so that v*m=\lambda*v

(I have to admit I'm still not terribly satisfied with the name)

One line in graph.py as well as numerical.py needed to be changed to reflect this.

[mabshoff]

Merged in 2.8.13.alpha1.