def _test_cross_arbitrary_basis(testj=4, nterms=10, npix=500):
"""Verify the functions are orthogonal, by taking the
integrals of a given mode times N other ones.
This is a helper function for test_cross_arbitrary_basis.
Parameters :
--------------
testj : int
Index of the Zernike-like polynomial to test against the others
nterms : int
Test that polynomial against those from 1 to this N
npix : int
Size of array to use for this test
"""
# choose a square aperture for the test
square_aperture = optics.SquareAperture(size=1.).sample(npix=npix,grid_size=1.1)
square_basis = zernike.arbitrary_basis(square_aperture,nterms=nterms)
test_mode = square_basis[testj - 1]
assert np.sum(np.isfinite(test_mode)) > 0, "Basis function calculation failure; all NaNs."
for idx, array in enumerate(square_basis):
j = idx + 1
if j == testj or j == 1:
continue # discard piston term and self
prod = array * test_mode
wg = np.where(np.isfinite(prod))
cross_sum = np.abs(prod[wg].sum())
# Threshold was originally 1e-9, but we ended up getting 1.19e-9 on some machines (not always)
# this seems acceptable, so relaxing criteria slightly
assert cross_sum < 2e-9, (
"orthogonality failure, Sum[Mode(j={}) * Mode(j={})] = {} (> 2e-9)".format(
j, testj, cross_sum)
)
def test_arbitrary_basis_rms(nterms=10, size=500):
"""Verify RMS(Zernike[n,m]) == 1."""
# choose a square aperture for the test
square_aperture = optics.SquareAperture(size=1.).sample(npix=size,grid_size=1.1)
square_basis = zernike.arbitrary_basis(square_aperture,nterms=nterms)
assert np.nanstd(square_basis[0]) == 0.0, "Mode(j=0) has nonzero RMS"
for j in range(1, nterms):
rms = np.nanstd(square_basis[j]) # exclude masked pixels
assert abs(1.0 - rms) < 0.001, "Mode(j={}) has RMS value of {}".format(j, rms)
