Adding Karhunen-Loeve

[GillesOrban]

Python implementation of KL basis based on Cannon 1996 and resp. IDL and Yorick (YAO) codes.

[codecov]

Codecov Report

Merging #41 into master will decrease coverage by 0.26%.
The diff coverage is 92.57%.

@@            Coverage Diff             @@
##           master      #41      +/-   ##
==========================================
- Coverage   94.06%   93.79%   -0.27%     
==========================================
  Files          24       25       +1     
  Lines        1011     1241     +230     
==========================================
+ Hits          951     1164     +213     
- Misses         60       77      +17

Impacted Files	Coverage Δ
aotools/functions/__init__.py	100% <ø> (ø)	⬆️
aotools/functions/karhunenLoeve.py	92.57% <92.57%> (ø)

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[andrewpaulreeves]

Looks great! This would be really useful to have.

There seems to be a problem with Python 2 however and it would be nice to fix this before merging. This is the output from Travis:

======================================================================
ERROR: test_KL.test_make
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/travis/miniconda3/lib/python2.7/site-packages/nose/case.py", line 197, in runTest
    self.test(*self.arg)
  File "/home/travis/build/AOtools/aotools/test/test_KL.py", line 5, in test_make
    kl, _, _, _ = KL.make_kl(150, 128, ri=0.2, stf='kolmogorov')
  File "/home/travis/build/AOtools/aotools/aotools/functions/karhunenLoeve.py", line 635, in make_kl
    stf=stf, outerscale=outerscale)
  File "/home/travis/build/AOtools/aotools/aotools/functions/karhunenLoeve.py", line 374, in gkl_basis
    evals, nord, npo, oord, rabas = gkl_fcom(ri, kers, nfunc)
  File "/home/travis/build/AOtools/aotools/aotools/functions/karhunenLoeve.py", line 252, in gkl_fcom
    newev, vs = np.linalg.eigh(fktom * kers[:, :, nxt])
IndexError: index 200 is out of bounds for axis 2 with size 200
-------------------- >> begin captured stdout << ---------------------
('note, for this size basis, radial discretization on ', 40)
points is finer than necessary - it should work, but you 
could take a smaller 'nr' without loss of accuracy
--------------------- >> end captured stdout << ----------------------

I've had a quick look at the code and can't see anything obvious that will break it, the main difference that I can think would have caused this is a difference in float division - in Python 2 a/b = Integer division and in Python 3 it is Floating point division. This could maybe cause an index to be rounded up at some point to a value that is too large? Thats the first thing that springs to mind anyway. Do you have a convenient setup to do some python 2 debugging?

[GillesOrban]

Hi! I ve seen it but didn't have time to fix it yet. Indeed, not obvious at first sight (agree with you, probably some integer division issue).
As soon as I have time to setup a python 2 env and debug, I ll do.
Regarding tests, this might be more tedious. I don't guarantee immediate improvement...

[matthewtownson]

This is hugely useful, thanks! Will merge it in now.