Singular matrix in PixelGrid.reflux

[rmjarvis]

Sometimes the PixelGrid matrix solution will involve a singular matrix according to numpy.linalg:

Building SimplePSF
Iteration 1: Fitting 367 stars
             Total chisq = 341418.36 / 89248 dof
Iteration 2: Fitting 367 stars
             Removed 3 outliers
             Total chisq = 42972.41 / 88515 dof
Iteration 3: Fitting 364 stars
             Removed 3 outliers
             Total chisq = 27166.78 / 87793 dof
Iteration 4: Fitting 361 stars
             Removed 3 outliers
             Total chisq = 23088.40 / 87059 dof
Iteration 5: Fitting 358 stars
             Removed 3 outliers
             Total chisq = 21235.73 / 86318 dof
Iteration 6: Fitting 355 stars
             Removed 2 outliers
             Total chisq = 20214.33 / 85828 dof
Iteration 7: Fitting 353 stars
ERROR: LinAlgError: Singular matrix [numpy.linalg.linalg]
Traceback (most recent call last):
  File "/astro/u/mjarvis/bin/piffify", line 5, in <module>
    pkg_resources.run_script('Piff==0.1', 'piffify')
  File "/opt/astro/SL64/anaconda/lib/python2.7/site-packages/pkg_resources.py", line 505, in run_script
    self.require(requires)[0].run_script(script_name, ns)
  File "/opt/astro/SL64/anaconda/lib/python2.7/site-packages/pkg_resources.py", line 1245, in run_script
    execfile(script_filename, namespace, namespace)
  File "/direct/astro+u/mjarvis/lib/python2.7/site-packages/Piff-0.1-py2.7.egg/EGG-INFO/scripts/piffify", line 93, in <module>
    main()
  File "/direct/astro+u/mjarvis/lib/python2.7/site-packages/Piff-0.1-py2.7.egg/EGG-INFO/scripts/piffify", line 90, in main
    piff.piffify(config, logger)
  File "/astro/u/mjarvis/lib/python2.7/site-packages/Piff-0.1-py2.7.egg/piff/config.py", line 130, in piffify
    psf.fit(stars, wcs, pointing, logger=logger)
  File "/astro/u/mjarvis/lib/python2.7/site-packages/Piff-0.1-py2.7.egg/piff/simplepsf.py", line 151, in fit
    for s in self.stars]
  File "/astro/u/mjarvis/lib/python2.7/site-packages/Piff-0.1-py2.7.egg/piff/pixelgrid.py", line 633, in reflux
    df = np.linalg.solve(alpha, beta)
  File "/astro/u/mjarvis/.local/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 384, in solve
    r = gufunc(a, b, signature=signature, extobj=extobj)
  File "/astro/u/mjarvis/.local/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 90, in _raise_linalgerror_singular
    raise LinAlgError("Singular matrix")
numpy.linalg.linalg.LinAlgError: Singular matrix

We should at least guard against this kind of thing and exclude the star that had the problem. (I'll go ahead and do that directly on master.) But probably the better solution would be to figure out why this happens and find a real workaround. Possibly using svd for the solution rather than the normal lud.

[rmjarvis]

This is already being caught and handled properly. And I'm pretty sure the changes in #88 make this significantly less common.