def test_zernike_edges(num):
"""Make sure same result is obtained at 0 and 0.0 and 1 and 1.0"""
n, m = choose_random_nm()
theta = np.random.rand() * 2 * np.pi - np.pi
assert zernike(float(num), theta, n,
m) == zernike(int(num), theta, n,
m), f"theta, n, m = {theta}, {n}, {m}"
def test_norm_sum():
"""Test RMS of sum of zernikes is the square root of the sum of the coefficients."""
# set up coordinates
x = np.linspace(-1, 1, 2048)
xx, yy = np.meshgrid(x, x) # xy indexing is default
r, theta = cart2pol(yy, xx)
# make coefs
np.random.seed(12345)
c0, c1 = np.random.randn(2)
astig_zern = c0 * zernike(r, theta, 2, -2, norm=True)
spherical_zern = c1 * zernike(r, theta, 3, -3, norm=True)
np.testing.assert_allclose(abs(c0),
np.sqrt((astig_zern[r <= 1]**2).mean()),
atol=1e-3,
rtol=1e-3)
np.testing.assert_allclose(abs(c1),
np.sqrt((spherical_zern[r <= 1]**2).mean()),
atol=1e-3,
rtol=1e-3)
np.testing.assert_allclose(
np.sqrt(c0**2 + c1**2),
np.sqrt(((astig_zern + spherical_zern)[r <= 1]**2).mean()),
atol=1e-3,
rtol=1e-3,
)
def test_zernike_return_shape():
"""Make sure that the return shape matches input shape"""
x = np.linspace(-1, 1, 512)
xx, yy = np.meshgrid(x, x)
r, theta = cart2pol(yy, xx)
zern = zernike(r, theta, 10)
assert zern.shape == r.shape
def test_zernike_zero():
"""Make sure same result is obtained for integer and float"""
n, m = choose_random_nm()
r = 0.5
theta = np.random.rand() * 2 * np.pi - np.pi
assert np.isfinite(zernike(
r, theta, n, m)).all(), f"r, theta, n, m = {r}, {theta}, {n}, {m}"
def test_odd_nm():
"""Make sure that n and m seperated by odd numbers gives zeros"""
n, m = choose_random_nm(True)
theta = np.random.rand(100) * 2 * np.pi - np.pi
# we'll check outside the normal range too, when r
r = np.random.rand(100) * 2
assert (zernike(r, theta, n,
m) == 0).all(), f"theta, n, m = {theta}, {n}, {m}"
def test_norm():
"""Test that normalization works."""
# set up coordinates
x = np.linspace(-1, 1, 2048)
xx, yy = np.meshgrid(x, x) # xy indexing is default
r, theta = cart2pol(yy, xx)
# fill out plot
for (n, m), v in sorted(degrees2name.items())[0:]:
zern = zernike(r, theta, n, m, norm=True)
tol = 10.0**(n - 6)
np.testing.assert_allclose(1.0,
np.sqrt((zern[r <= 1]**2).mean()),
err_msg=f"{v} failed!",
atol=tol,
rtol=tol)
def test_r_theta_dims():
"""Make sure that a ValueError is raised if the dims are greater than 2"""
r = np.ones((3, 3, 3))
with pytest.raises(ValueError):
zernike(r, r, 10)
def test_n_lt_m():
"""n must always be greater than or equal to m"""
with pytest.raises(ValueError):
zernike(0.5, 0.0, 4, 5)
def test_zernike_errors(test_input):
"""Make sure zernike doesn't accept bad input."""
with pytest.raises(ValueError):
zernike(*test_input)