Python routine on matrix diagonalization

Question

Good morning: I have a doubt about the python routine at: https://www.google.com/url?sa=t&source=web&rct=j&url=https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.sparse.linalg.eigsh.html&ved=2ahUKEwjJxrid8ezoAhXj6eAKHQbzBCwQFjAAegQIARAB&usg=AOvVaw29YNiM2xotOUio89RVOe_x&cshid=1587038068544

It says that it computers k eigenvectors and eigenvalues, with k smaller than matrix dimension, but is it possible to use it to get the lowest k eigenvalues or are those eigenvalues randomly ordered in the spectrum?

Answer 1

As the documentation you linked states, the keywords which and mode affects which eigenvalues are selected:

*which* : str ['LM' | 'SM' | 'LA' | 'SA' | 'BE']

Which k eigenvectors and eigenvalues to find:
'LM' : Largest (in magnitude) eigenvalues 
'SM' : Smallest (in magnitude) eigenvalues
...

and

*mode* : string ['normal' | 'buckling' | 'cayley']

...
The choice of mode will affect which eigenvalues are selected by the keyword 'which'.

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The default of which is 'LM' (largest eigenvalues) so you might want to pass 'SM' to retrieve the lowest.