Eigenvalue solver gives inconsistent results

[rabernat]

The test in https://github.com/rabernat/oceanmodes/blob/master/oceanmodes/test/test_modes.py#L248 is currently failing because scipy.sparse.linalg.eig does not return the eigenvalues we expect.

@roxyboy, can you post the image of the plot you made showing the expected vs. actual results?

[rabernat]

This is what the expected vs. actual results are.

[roxyboy]

Setting k=2 (parameter for the number of eigenvalues) in the function scipy.sparse.linalg.eigs() gives smooth results for the growth rate, although slightly biased to larger wavenumbers than the analytical solution

[roxyboy]

The syntax I used for the above results were:
val, func = eigs( csc_matrix(inv(csc_matrix(G)).dot(csc_matrix(L))), k=2, which='LI', ncv=20 )

[rabernat]

Cool! This is very promising.

Can you improve the agreement with the analytical solution by adjusting the tolerance of the solver?

Sent from my iPhone

On Feb 16, 2016, at 10:57 PM, Takaya Uchida notifications@github.com wrote:

The syntax I used for the above results were:
val, func = eigs( csc_matrix(inv(csc_matrix(G)).dot(csc_matrix(L))),
k=2, which='LI', ncv=20 )

—
Reply to this email directly or view it on GitHub.

[rabernat]

After looking at this closer, it looks like there could be some small problem with the definition of k. If we rescale k a bit, everything would line up perfectly.

[rabernat]

Maybe l != 0?

[rabernat]

I played with this a lot today. I think the issue might have to do with the details of the vertical discretization.

[roxyboy]

I can't find any problems with the vertical discretization. Could you tell a little more about the issues you found?

[rabernat]

Maybe @anirban89 can help with this.