[Octave-bug-tracker] [bug #58926] Octave gives wrong results with intel-mkl when diagonalizing large matrices

[Archisman Panigrahi]

Follow-up Comment #5, bug #58926 (project octave):

[comment #3 comment #3:]
> Can you test it using a different linear algebra library like openblas,
atlas, or even the reference blas? If it works with that and not on MKL then
we localize one end of the problem.
> 
I have tested it with openblas (which is installed as a dependency with
default installation of Octave in Ubuntu), and there is no error (ans =
16.915).

> Can you compute the same thing using MKL and a front end other than Octave
like Python / Anaconda or even just C++ or Fortran? If that works / doesn't
work we'll know whether the problem is in Octave or in MKL.

I initially posted this in AskUbuntu and someone confirmed the bug (last
comment of https://askubuntu.com/a/1265802/124466). He also mentioned that the
same code produces correct results with Scilab (mentioned in the comment). He
made a gist (https://gist.github.com/N0rbert/cfda101b8f0aa326df1edb6beee0076d)
containing Octave and Scilab codes.

I don't have much experience with doing linear algebra in C or Fortran (I can
produce the matrix, but I don't know how to use the Eigen library to
diagonalize it). I am trying to write a Python program with Numpy. Meanwhile,
if someone can post a Python code based on the following algorithm, I will be
happy to test it.

Algorithm: Create a 500x500 matrix A with
 A(i,j) = sin(i + j*j)

Diagonalize A, and find the maximum among the real parts of all eigenvalues of
A.

The correct answer is approximately 16.915

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