def _MakeTransformTestRotationMatrices(self, batch_size):
# Make a batch of 4x4 transformation matrices that only has rotation around
# the z-axis (world rotation).
rot_matrices = []
for _ in range(batch_size):
rot_matrix = geometry._MakeRotationMatrix(tf.random_uniform([]), 0., 0.)
# Embed rotation matrix into a 4 x 4 matrix
rot_matrix = tf.pad(rot_matrix, [[0, 1], [0, 1]]) + tf.diag([0, 0, 0, 1.])
rot_matrices.append(rot_matrix)
transforms = tf.stack(rot_matrices, axis=0)
return transforms
def _MakeTransformTestTranslationMatrices(self, batch_size):
# Make a batch of 4x4 transformation matrices that translate in all
# directions.
translation_matrices = []
for _ in range(batch_size):
translation_matrix = tf.random_uniform([3, 1])
translation_matrix = tf.pad(translation_matrix, [[0, 1], [3, 0]])
translation_matrix += tf.diag([1., 1., 1., 1.])
translation_matrices.append(translation_matrix)
transforms = tf.stack(translation_matrices, axis=0)
return transforms
def inverse_pth_root(self, input_t, exponent, epsilon=1e-12):
input_t_f64 = tf.cast(input_t, tf.float64)
s, u, v = tf.svd(
input_t_f64 +
tf.eye(tf.shape(input_t_f64)[0], dtype=tf.float64) * epsilon,
full_matrices=True)
val = tf.matmul(
tf.matmul(
u,
tf.diag(
tf.pow(tf.maximum(s, epsilon),
tf.cast(exponent, tf.float64)))), tf.transpose(v))
return tf.cast(val, tf.float32), tf.reduce_max(tf.abs(u - v))