def _tril_spherical_uniform(dimension, batch_shape, dtype, seed):
"""Returns a `Tensor` of samples of lower triangular matrices.
Each row of the lower triangular part follows a spherical uniform
distribution.
Args:
dimension: Scalar `int` `Tensor`, representing the dimensionality of the
output matrices.
batch_shape: Vector-shaped, `int` `Tensor` representing batch shape of
output. The output will have shape `batch_shape + [dimension, dimension]`.
dtype: TF `dtype` representing `dtype` of output.
seed: PRNG seed; see `tfp.random.sanitize_seed` for details.
Returns:
tril_spherical_uniform: `Tensor` with specified `batch_shape` and `dtype`
consisting of real values drawn row-wise from a spherical uniform
distribution.
"""
# Essentially, we will draw lower triangular samples where each lower
# triangular entry follows a normal distribution, then apply `x / norm(x)`
# for each row of the samples.
# To avoid possible NaNs, we will use spherical_uniform directly for
# the first two rows.
assert dimension > 0, '`dimension` needs to be positive.'
num_seeds = min(dimension, 3)
seeds = list(samplers.split_seed(seed, n=num_seeds, salt='sample_lkj'))
rows = []
paddings_prepend = [[0, 0]] * len(batch_shape)
for n in range(1, min(dimension, 2) + 1):
rows.append(
tf.pad(random_ops.spherical_uniform(shape=batch_shape,
dimension=n,
dtype=dtype,
seed=seeds.pop()),
paddings_prepend + [[0, dimension - n]],
constant_values=0.))
samples = tf.stack(rows, axis=-2)
if dimension > 2:
normal_shape = ps.concat(
[batch_shape, [dimension * (dimension + 1) // 2 - 3]], axis=0)
normal_samples = samplers.normal(shape=normal_shape,
dtype=dtype,
seed=seeds.pop())
# We fill the first two rows of the triangular matrix with ones.
# Note that fill_triangular fills elements in a clockwise spiral.
normal_samples = tf.concat([
normal_samples[..., :dimension],
tf.ones(ps.concat([batch_shape, [1]], axis=0), dtype=dtype),
normal_samples[..., dimension:(2 * dimension - 1)],
tf.ones(ps.concat([batch_shape, [2]], axis=0), dtype=dtype),
normal_samples[..., (2 * dimension - 1):],
],
axis=-1)
normal_samples = linalg.fill_triangular(normal_samples,
upper=False)[..., 2:, :]
remaining_rows = normal_samples / tf.norm(
normal_samples, ord=2, axis=-1, keepdims=True)
samples = tf.concat([samples, remaining_rows], axis=-2)
return samples
def _uniform_correlation_like_matrix(num_rows, batch_shape, dtype, seed):
"""Returns a uniformly random `Tensor` of "correlation-like" matrices.
A "correlation-like" matrix is a symmetric square matrix with all entries
between -1 and 1 (inclusive) and 1s on the main diagonal. Of these,
the ones that are positive semi-definite are exactly the correlation
matrices.
Args:
num_rows: Python `int` dimension of the correlation-like matrices.
batch_shape: `Tensor` or Python `tuple` of `int` shape of the
batch to return.
dtype: `dtype` of the `Tensor` to return.
seed: PRNG seed; see `tfp.random.sanitize_seed` for details.
Returns:
matrices: A `Tensor` of shape `batch_shape + [num_rows, num_rows]`
and dtype `dtype`. Each entry is in [-1, 1], and each matrix
along the bottom two dimensions is symmetric and has 1s on the
main diagonal.
"""
num_entries = num_rows * (num_rows + 1) // 2
ones = tf.ones(shape=[num_entries], dtype=dtype)
# It seems wasteful to generate random values for the diagonal since
# I am going to throw them away, but `fill_triangular` fills the
# diagonal, so I probably need them.
# It's not impossible that it would be more efficient to just fill
# the whole matrix with random values instead of messing with
# `fill_triangular`. Then would need to filter almost half out with
# `matrix_band_part`.
unifs = uniform.Uniform(-ones, ones).sample(batch_shape, seed=seed)
tril = fill_triangular(unifs)
symmetric = tril + tf.linalg.matrix_transpose(tril)
diagonal_ones = tf.ones(prefer_static.pad(batch_shape,
paddings=[[0, 1]],
constant_values=num_rows),
dtype=dtype)
return tf.linalg.set_diag(symmetric, diagonal_ones)
def _forward(self, x): return fill_triangular(x, upper=self._upper)
