def _test_cross_zernikes(testj=4, nterms=10, npix=500):
"""Verify the functions are orthogonal, by taking the
integrals of a given Zernike times N other ones.
Parameters :
--------------
testj : int
Index of the Zernike 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
"""
zj = zernike.zernike1(testj, npix=npix)
assert np.sum(
np.isfinite(zj)) > 0, "Zernike calculation failure; all NaNs."
zbasis = zernike.zernike_basis(nterms=nterms, npix=npix)
for idx, z in enumerate(zbasis):
j = idx + 1
if j == testj or j == 1:
continue # discard piston term and self
prod = z * zj
wg = np.where(np.isfinite(prod))
cross_sum = np.abs(prod[wg].sum())
assert cross_sum < 1e-9, (
"orthogonality failure, Sum[Zernike(j={}) * Zernike(j={})] = {} (> 1e-9)"
.format(j, testj, cross_sum))
def test_zernike_basis_faster():
bf = zernike.zernike_basis_faster(12, outside=0)
bs = zernike.zernike_basis(12, outside=0)
assert np.allclose(
bf, bs
), "Fast zernike basis calculation doesn't match the slow calculation"
def _test_cross_zernikes(testj=4, nterms=10, npix=500):
"""Verify the functions are orthogonal, by taking the
integrals of a given Zernike times N other ones.
Parameters :
--------------
testj : int
Index of the Zernike 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
"""
Zj = zernike.zernike1(testj, npix=npix)
Zbasis = zernike.zernike_basis(nterms=nterms, npix=npix)
for idx, Z in enumerate(Zbasis):
j = idx + 1
if j == testj or j == 1:
continue # discard piston term and self
prod = Z * Zj
wg = np.where(np.isfinite(prod))
cross_sum = np.abs(prod[wg].sum())
assert cross_sum < 1e-9, (
"orthogonality failure, Sum[Zernike(j={}) * Zernike(j={})] = {} (> 1e-9)".format(
j, testj, cross_sum)
)
def test_opd_expand(npix=512, input_coefficients=(0.1, 0.2, 0.3, 0.4, 0.5)):
basis = zernike.zernike_basis(nterms=len(input_coefficients), npix=npix)
for idx, coeff in enumerate(input_coefficients):
basis[idx] *= coeff
opd = basis.sum(axis=0)
recovered_coeffs = zernike.opd_expand(opd, nterms=len(input_coefficients))
max_diff = np.max(np.abs(np.asarray(input_coefficients) - np.asarray(recovered_coeffs)))
assert max_diff < 1e-3, "recovered coefficients from wf_expand more than 0.1% off"
# Test the nonorthonormal version too
# At a minimum, fitting with this variant version shouldn't be
# worse than the regular one on a clear circular aperture.
# We do the test in this same function for efficiency
recovered_coeffs_v2 = zernike.opd_expand_nonorthonormal(opd, nterms=len(input_coefficients))
max_diff_v2 = np.max(np.abs(np.asarray(input_coefficients) - np.asarray(recovered_coeffs_v2)))
assert max_diff_v2 < 1e-3, "recovered coefficients from wf_expand more than 0.1% off"
def test_opd_expand(npix=512, input_coefficients=(0.1, 0.2, 0.3, 0.4, 0.5)):
basis = zernike.zernike_basis(nterms=len(input_coefficients), npix=npix)
for idx, coeff in enumerate(input_coefficients):
basis[idx] *= coeff
opd = basis.sum(axis=0)
recovered_coeffs = zernike.opd_expand(opd, nterms=len(input_coefficients))
max_diff = np.max(np.abs(np.asarray(input_coefficients) - np.asarray(recovered_coeffs)))
assert max_diff < 1e-3, "recovered coefficients from wf_expand more than 0.1% off"
# Test the nonorthonormal version too
# At a minimum, fitting with this variant version shouldn't be
# worse than the regular one on a clear circular aperture.
# We do the test in this same function for efficiency
recovered_coeffs_v2 = zernike.opd_expand_nonorthonormal(opd, nterms=len(input_coefficients))
max_diff_v2 = np.max(np.abs(np.asarray(input_coefficients) - np.asarray(recovered_coeffs_v2)))
assert max_diff_v2 < 1e-3, "recovered coefficients from wf_expand more than 0.1% off"
def test_zernike_basis_faster():
bf = zernike.zernike_basis_faster(12, outside=0)
bs = zernike.zernike_basis(12, outside=0)
assert np.allclose(bf,bs), "Fast zernike basis calculation doesn't match the slow calculation"
