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: Random seed.
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 = util.fill_triangular(unifs)
symmetric = tril + tf.linalg.transpose(tril)
diagonal_ones = tf.ones(shape=util.pad(batch_shape,
axis=0,
back=True,
value=num_rows),
dtype=dtype)
return tf.linalg.set_diag(symmetric, diagonal_ones)
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: Random seed.
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 = util.fill_triangular(unifs)
symmetric = tril + tf.matrix_transpose(tril)
diagonal_ones = tf.ones(
shape=util.pad(batch_shape, axis=0, back=True, value=num_rows),
dtype=dtype)
return tf.matrix_set_diag(symmetric, diagonal_ones)
def _forward(self, x): return distribution_util.fill_triangular(x, upper=self._upper)
def _random_scale_tril(self, event_size): n = np.int32(event_size * (event_size + 1) // 2) p = 2. * self._rng.random_sample(n).astype(np.float32) - 1. return distribution_util.fill_triangular(0.25 * p)
def _forward(self, x): return distribution_util.fill_triangular(x, upper=self._upper)
def _random_scale_tril(self, event_size):
n = np.int32(event_size * (event_size + 1) // 2)
p = 2. * self._rng.random_sample(n).astype(np.float32) - 1.
return distribution_util.fill_triangular(0.25 * p)
