[SciPy-dev] Comments on API for Matlab's eigs equivalent (computing a few eigenvalues only)

[Dag Sverre Seljebotn]

David Cournapeau wrote:
> Charles R Harris wrote:
>>
>> On Wed, Feb 3, 2010 at 11:27 PM, David Cournapeau <david at silveregg.co.jp 
>> <mailto:david at silveregg.co.jp>> wrote:
>>
>>     Hi,
>>
>>     I have played a bit with adding support for computing a few eigenvalues
>>     of full symmetric matrices. I would like some comments on the
>>     current API:
>>
>>     import numpy as np
>>     from scipy.linalg import eigs
>>     x = np.random.randn(10, 10)
>>     x = np.dot(x.T, x)
>>     # Retrieve the 3 biggest eigenvalues
>>     eigs(x, 3)[0]
>>     # Retrieve the 3 smallest eigenvalues
>>     eigs(x, -3)[0]
>>     # Retrieve the 3 biggest eigenvalues
>>     eigs(x, [0, 3], mode="index")[0]
>>     # Retrieve the 2nd and 3rd biggest
>>     eigs(x, [1, 3], mode="index")[0]
>>     # Retrieve all the eigenvalues in the range [1.5, 3.5[
>>     eigs(x, [1.5, 3.5], mode="range")[0]
>>
>>     One thing which does not feel right is that that the range in the
>>     "index" mode is exactly inverted compared to the output (i.e. if you ask
>>
>>
>> Why not use separate keywords for index and range.
> 
> Then I am not sure how to handle the "give me the k biggest/smallest" 
> case, which is the most common I think (that's the only one I care 
> personally :) ).
> 
> Maybe this just warrants several functions ? But then there is the issue 
> of naming (supporting non-symmetric matrices would be nice, but requires 
> a totally different implementation, as LAPACK does not support it AFAIK 
> - the easiest way would be to use ARPACK ATM).
> 
>> Changing the meaning 
>> of an argument using another keyword is just weird. 
> 
> Agreed - this is just the best I could came up with one function to 
> support all cases while keeping the common case simple. But I feel a bit 
> like I outsmarted myself here.
> 
>> Why the index on the end? Is the return a list?
> 
> Yes, it also returns eigenvectors
> 
>>     for the range [0, 3], you get the last three items from what you would
>>     get if you asked for the full range [0, 10]), but this is because I kept
>>     compatibility with Octave (always showing from biggest to smallest). It
>>
>>
>> Why follow Octave, isn't Octave like Matlab? Matlab functions are a mess.
> 
> Actually, there is another reason I forgot to mention: that's how eigen 
> in scipy.sparse does as well (in decreasing order). I think that the 
> ARPACK wrappers are not that well thought out, though.

I feel there's also a certain convention of listing the largest 
eigenvalues first; "let \lambda_i be the eigenvalues...assume \lambda_2 
< \lambda_1 ...".


I know I'd assume that the largest eigenvalue came out first, and I've 
barely used either MATLAB or Octave.

(Also with SVD one would typically put the largest singular values 
first, and so on.)

Just a data-point, I don't really care either way...

-- 
Dag Sverre