def test_sph_harm_isft():
""" Tests the SFT by doing ISFT -> SFT -> ISFT. """
for n in [8, 16]:
# sft for real signals: c_{-m} = (-1)^m Re(c_m) + (-1)^{m+1} Im(c_m)
coeffs = [np.zeros(2 * l + 1, dtype=np.complex) for l in range(n // 2)]
coeffs[0][0], coeffs[1][1], coeffs[2][2] = [
np.random.rand() for _ in range(3)
]
c = np.random.rand() + 1j * np.random.rand()
coeffs[1][0] = c
coeffs[1][2] = -np.real(c) + 1j * np.imag(c)
c = np.random.rand() + 1j * np.random.rand()
coeffs[2][0] = c
coeffs[2][4] = np.real(c) - 1j * np.imag(c)
c = np.random.rand() + 1j * np.random.rand()
coeffs[2][1] = c
coeffs[2][3] = -np.real(c) + 1j * np.imag(c)
f = spherical.sph_harm_inverse(coeffs)
coeffs_ = spherical.sph_harm_transform(f)
f_ = spherical.sph_harm_inverse(coeffs_)
for c1, c2 in zip(coeffs, coeffs_):
assert np.allclose(c1, c2)
assert np.allclose(f, f_)
def test_sph_harm_sft():
""" Tests the SFT by doing SFT -> ISFT -> SFT -> ISFT """
f = np.random.rand(16, 16)
coeffs = spherical.sph_harm_transform(f)
# we are constraining the bandwidth to n/2 here, so f1 != f
f1 = spherical.sph_harm_inverse(coeffs)
coeffs1 = spherical.sph_harm_transform(f1)
f2 = spherical.sph_harm_inverse(coeffs1)
# now both f1 and f2 have constrained bandwidths, so they must be equal
assert np.allclose(f1, f2)
def test_sph_conv():
""" Test spherical convolution and rotation commutativity.
sph_conv and sphrot_shtools are exercised here.
"""
if 'pyshtools' not in sys.modules:
warnings.warn('pyshtools not available; skipping test_sph_conv')
return
n = 32
f = np.random.rand(n, n)
# lowpass
f = spherical.sph_harm_inverse(spherical.sph_harm_transform(f))
g = np.zeros_like(f)
g[:, :5] = np.random.rand(5)
g /= g.sum()
ang = np.random.rand(3) * 2 * np.pi
# check if (pi f * g) == pi(f * g)
rot_conv = util.sphrot_shtools(spherical.sph_conv(f, g), ang)
conv_rot = spherical.sph_conv(util.sphrot_shtools(f, ang), g)
assert not np.allclose(rot_conv, f)
assert not np.allclose(rot_conv, g)
assert np.allclose(rot_conv, conv_rot)
def test_sph_harm_tf():
""" Test spherical harmonics expansion/inversion with tensorflow Tensors. """
n = 32
f = np.random.rand(n, n)
ref = spherical.sph_harm_inverse(spherical.sph_harm_transform(f))
inp = tf.placeholder('complex128', shape=[n, n])
coeffs = spherical.sph_harm_transform(inp)
recons = spherical.sph_harm_inverse(coeffs)
with tf.Session(config=tf_config()).as_default() as sess:
c, r = sess.run([coeffs, recons], feed_dict={inp: f})
assert np.allclose(r, ref)
for x1, x2 in zip(c, spherical.sph_harm_transform(f)):
assert np.allclose(x1, x2)
def test_sph_harm_tf_harmonics_input():
""" Test spherical harmonics inputs as tensorflow Variables. """
n = 32
f = np.random.rand(n, n)
for real in [False, True]:
dtype = tf.complex64
harmonics = [[tf.Variable(hh.astype('complex64')) for hh in h]
for h in spherical.sph_harm_all(n, real=real)]
inp = tf.placeholder(dtype, shape=[n, n])
c1 = spherical.sph_harm_transform(inp, harmonics=harmonics)
r1 = spherical.sph_harm_inverse(c1, harmonics=harmonics)
c2 = spherical.sph_harm_transform(inp, harmonics=harmonics)
r2 = spherical.sph_harm_inverse(c2, harmonics=harmonics)
with tf.Session(config=tf_config()).as_default() as sess:
sess.run(tf.global_variables_initializer())
c1v, c2v, r1v, r2v = sess.run([c1, c2, r1, r2], feed_dict={inp: f})
for x1, x2 in zip(c1v, c2v):
assert np.allclose(x1, x2)
for x1, x2 in zip(r1v, r2v):
assert np.allclose(x1, x2)
def test_sph_harm_shtools():
""" Compare our sph harmonics expansion with pyshtools. """
if 'pyshtools' not in sys.modules:
warnings.warn(
'pyshtools not available; skipping test_sph_harm_shtools')
return
n = 32
f = np.random.rand(n, n)
# lowpass
f = spherical.sph_harm_inverse(spherical.sph_harm_transform(f))
c_mine = spherical.sph_harm_transform(f)
c_pysh = pyshtools.SHGrid.from_array(f.T).expand(csphase=-1,
normalization='ortho')
c1 = spherical.sph_harm_to_shtools(c_mine)
c2 = c_pysh.coeffs
# there seems to be a bug on the coefficient of highes degree l, order -l in pyshtools
# we don't test that value
c1[1][(n // 2) - 1][-1] = c2[1][(n // 2) - 1][-1] = 0
assert np.allclose(c1, c2)