def test_rotate_zonal_harmonics_random(self):
"""Tests the outputs of test_rotate_zonal_harmonics."""
dtype = tf.float64
max_band = 2
zonal_coeffs = tf.constant(np.random.uniform(-1.0, 1.0, size=[3]),
dtype=dtype)
tensor_size = np.random.randint(3)
tensor_shape = np.random.randint(1, 10, size=(tensor_size)).tolist()
theta = tf.constant(np.random.uniform(0.0,
np.pi,
size=tensor_shape + [1]),
dtype=dtype)
phi = tf.constant(np.random.uniform(0.0,
2.0 * np.pi,
size=tensor_shape + [1]),
dtype=dtype)
rotated_zonal_coeffs = spherical_harmonics.rotate_zonal_harmonics(
zonal_coeffs, theta, phi)
zonal_coeffs = spherical_harmonics.tile_zonal_coefficients(
zonal_coeffs)
l, m = spherical_harmonics.generate_l_m_permutations(max_band)
l = tf.broadcast_to(l, tensor_shape + l.shape.as_list())
m = tf.broadcast_to(m, tensor_shape + m.shape.as_list())
theta_zero = tf.constant(0.0, shape=tensor_shape + [1], dtype=dtype)
phi_zero = tf.constant(0.0, shape=tensor_shape + [1], dtype=dtype)
gt = zonal_coeffs * spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta_zero, phi_zero)
gt = tf.reduce_sum(input_tensor=gt, axis=-1)
pred = rotated_zonal_coeffs * spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta + theta_zero, phi + phi_zero)
pred = tf.reduce_sum(input_tensor=pred, axis=-1)
self.assertAllClose(gt, pred)
def test_evaluate_spherical_harmonics_exception_m_raised(self):
"""Tests that an exception is raised when m is not in the expected range."""
l = np.random.randint(1, 4, size=(1, ))
m = np.random.randint(5, 10, size=(1, ))
theta = np.random.uniform(0.0, np.pi, size=(1, ))
phi = np.random.uniform(0.0, 2.0 * np.pi, size=(1, ))
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(
spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi))
m = np.random.randint(-10, -5, size=(1, ))
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(
spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi))
def test_evaluate_spherical_harmonics_exception_phi_raised(self):
"""Tests exceptions on the values of phi."""
l = np.random.randint(1, 4, size=(1, ))
m = np.random.randint(5, 10, size=(1, ))
theta = np.random.uniform(0.0, np.pi, size=(1, ))
phi = np.random.uniform(2.0 * np.pi + sys.float_info.epsilon,
4.0 * np.pi,
size=(1, ))
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(
spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi))
phi = np.random.uniform(-2.0 * np.pi,
0.0 - sys.float_info.epsilon,
size=(1, ))
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(
spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi))
def test_evaluate_spherical_harmonics_jacobian_random(self):
"""Test the Jacobian of the evaluate_spherical_harmonics function."""
tensor_size = np.random.randint(3)
tensor_shape = np.random.randint(1, 5, size=(tensor_size)).tolist()
l_init = np.random.randint(5, 10, size=tensor_shape)
l_init = np.expand_dims(l_init, axis=-1)
m_init = np.random.randint(0, 4, size=tensor_shape)
m_init = np.expand_dims(m_init, axis=-1)
theta_init = np.random.uniform(0.0, np.pi, size=tensor_shape)
theta_init = np.expand_dims(theta_init, axis=-1)
phi_init = np.random.uniform(0.0, 2.0 * np.pi, size=tensor_shape)
phi_init = np.expand_dims(phi_init, axis=-1)
theta = tf.convert_to_tensor(value=theta_init)
phi = tf.convert_to_tensor(value=phi_init)
y = spherical_harmonics.evaluate_spherical_harmonics(
l_init, m_init, theta, phi)
self.assert_jacobian_is_correct(theta, theta_init, y)
self.assert_jacobian_is_correct(phi, phi_init, y)
def test_evaluate_spherical_harmonics_jacobian_random(self):
"""Test the Jacobian of the evaluate_spherical_harmonics function."""
tensor_size = np.random.randint(3)
tensor_shape = np.random.randint(1, 5, size=(tensor_size)).tolist()
l_init = np.random.randint(5, 10, size=tensor_shape)
l_init = np.expand_dims(l_init, axis=-1)
m_init = np.random.randint(0, 4, size=tensor_shape)
m_init = np.expand_dims(m_init, axis=-1)
theta_init = np.random.uniform(0.0, np.pi, size=tensor_shape)
theta_init = np.expand_dims(theta_init, axis=-1)
phi_init = np.random.uniform(0.0, 2.0 * np.pi, size=tensor_shape)
phi_init = np.expand_dims(phi_init, axis=-1)
# Wrap these in identities because some assert_* ops look at the constant
# tensor value and mark it as unfeedable.
theta = tf.identity(tf.convert_to_tensor(value=theta_init))
phi = tf.identity(tf.convert_to_tensor(value=phi_init))
y = spherical_harmonics.evaluate_spherical_harmonics(
l_init, m_init, theta, phi)
self.assert_jacobian_is_correct(theta, theta_init, y)
self.assert_jacobian_is_correct(phi, phi_init, y)
def test_evaluate_spherical_harmonics_preset(self):
tensor_size = np.random.randint(3)
tensor_shape = np.random.randint(1, 10, size=(tensor_size)).tolist()
pt_3d = tf.convert_to_tensor(value=np.random.uniform(
size=tensor_shape + [3]))
pt_3d = tf.math.l2_normalize(pt_3d, axis=-1)
x, y, z = tf.unstack(pt_3d, axis=-1)
x = tf.expand_dims(x, axis=-1)
y = tf.expand_dims(y, axis=-1)
z = tf.expand_dims(z, axis=-1)
pt_spherical = math_helpers.cartesian_to_spherical_coordinates(pt_3d)
_, theta, phi = tf.unstack(pt_spherical, axis=-1)
theta = tf.expand_dims(theta, axis=-1)
phi = tf.expand_dims(phi, axis=-1)
ones = tf.ones_like(z)
with self.subTest(name="l_0_m_0"):
l = tf.zeros_like(theta, dtype=tf.int32)
m = tf.zeros_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = ones / (2.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_1_m_-1"):
l = tf.ones_like(theta, dtype=tf.int32)
m = -tf.ones_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = -tf.sqrt(3.0 * ones) * y / (2.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_1_m_0"):
l = tf.ones_like(theta, dtype=tf.int32)
m = tf.zeros_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = (tf.sqrt(3.0 * ones) * z) / (2.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_1_m_1"):
l = tf.ones_like(theta, dtype=tf.int32)
m = tf.ones_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = -tf.sqrt(3.0 * ones) * x / (2.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_2_m-2"):
l = 2 * tf.ones_like(theta, dtype=tf.int32)
m = -2 * tf.ones_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = tf.sqrt(15.0 * ones) * y * x / (2.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_2_m_-1"):
l = 2 * tf.ones_like(theta, dtype=tf.int32)
m = -tf.ones_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = -tf.sqrt(15.0 * ones) * y * z / (2.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_2_m_0"):
l = 2 * tf.ones_like(theta, dtype=tf.int32)
m = tf.zeros_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = tf.sqrt(5.0 * ones) * (3.0 * z * z -
ones) / (4.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_2_m_1"):
l = 2 * tf.ones_like(theta, dtype=tf.int32)
m = tf.ones_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = -tf.sqrt(15.0 * ones) * x * z / (2.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
with self.subTest(name="l_2_m_2"):
l = 2 * tf.ones_like(theta, dtype=tf.int32)
m = 2 * tf.ones_like(theta, dtype=tf.int32)
val = spherical_harmonics.evaluate_spherical_harmonics(
l, m, theta, phi)
gt = tf.sqrt(
15.0 * ones) * (x * x - y * y) / (4.0 * tf.sqrt(ones * np.pi))
self.assertAllClose(val, gt)
def evaluate_spherical_harmonics_fn(theta, phi):
return spherical_harmonics.evaluate_spherical_harmonics(
l_init, m_init, theta, phi)
