def test_evaluate_legendre_polynomial_preset(self):
"""Tests that evaluate_legendre_polynomial generates expected results."""
tensor_size = np.random.randint(1, 3)
tensor_shape = np.random.randint(1, 10, size=(tensor_size)).tolist()
x = np.random.uniform(size=tensor_shape)
with self.subTest(name="l_0_m_0"):
l = tf.constant(0, shape=tensor_shape)
m = tf.constant(0, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = np.ones_like(x)
self.assertAllClose(pred, gt)
with self.subTest(name="l_1_m_0"):
l = tf.constant(1, shape=tensor_shape)
m = tf.constant(0, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = x
self.assertAllClose(pred, gt)
with self.subTest(name="l_1_m_1"):
l = tf.constant(1, shape=tensor_shape)
m = tf.constant(1, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = -tf.sqrt(1.0 - x * x)
self.assertAllClose(pred, gt)
with self.subTest(name="l_2_m_0"):
l = tf.constant(2, shape=tensor_shape)
m = tf.constant(0, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = 0.5 * (3.0 * x * x - 1.0)
self.assertAllClose(pred, gt)
with self.subTest(name="l_2_m_1"):
l = tf.constant(2, shape=tensor_shape)
m = tf.constant(1, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = -3.0 * x * tf.sqrt(1.0 - x * x)
self.assertAllClose(pred, gt)
with self.subTest(name="l_2_m_2"):
l = tf.constant(2, shape=tensor_shape)
m = tf.constant(2, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = 3.0 * (1.0 - x * x)
self.assertAllClose(pred, gt)
with self.subTest(name="l_3_m_0"):
l = tf.constant(3, shape=tensor_shape)
m = tf.constant(0, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = 0.5 * x * (5.0 * x * x - 3.0)
self.assertAllClose(pred, gt)
with self.subTest(name="l_3_m_1"):
l = tf.constant(3, shape=tensor_shape)
m = tf.constant(1, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = 1.5 * (1.0 - 5.0 * x * x) * tf.sqrt(1.0 - x * x)
self.assertAllClose(pred, gt)
with self.subTest(name="l_3_m_2"):
l = tf.constant(3, shape=tensor_shape)
m = tf.constant(2, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = 15.0 * x * (1.0 - x * x)
self.assertAllClose(pred, gt)
with self.subTest(name="l_3_m_3"):
l = tf.constant(3, shape=tensor_shape)
m = tf.constant(3, shape=tensor_shape)
pred = spherical_harmonics.evaluate_legendre_polynomial(l, m, x)
gt = -15.0 * tf.pow(1.0 - x * x, 1.5)
self.assertAllClose(pred, gt)
def evaluate_legendre_polynomial_fn(x):
return spherical_harmonics.evaluate_legendre_polynomial(
l_init, m_init, x)