def _inverse_event_shape(self, input_shape):
if not input_shape.rank:
return input_shape
n = input_shape[-1]
if n is not None:
n -= 1
y_shape = input_shape[:-2].concatenate([n, n])
return fill_triangular.FillTriangular().inverse_event_shape(y_shape)
def _forward_event_shape(self, input_shape):
if tensorshape_util.rank(input_shape) is None:
return input_shape
tril_shape = fill_triangular.FillTriangular().forward_event_shape(
input_shape)
n = tril_shape[-1]
if n is not None:
n += 1
return tril_shape[:-2].concatenate([n, n])
def __init__(self,
diag_bijector=None,
diag_shift=1e-5,
validate_args=False,
name='fill_scale_tril'):
"""Instantiates the `FillScaleTriL` bijector.
Args:
diag_bijector: `Bijector` instance, used to transform the output diagonal
to be positive. Must be an instance of `tf.__internal__.CompositeTensor`
(including `tfb.AutoCompositeTensorBijector`).
Default value: `None` (i.e., `tfb.Softplus()`).
diag_shift: Float value broadcastable and added to all diagonal entries
after applying the `diag_bijector`. Setting a positive
value forces the output diagonal entries to be positive, but
prevents inverting the transformation for matrices with
diagonal entries less than this value.
Default value: `1e-5`.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
Default value: `False` (i.e., arguments are not validated).
name: Python `str` name given to ops managed by this object.
Default value: `fill_scale_tril`.
Raises:
TypeError, if `diag_bijector` is not an instance of
`tf.__internal__.CompositeTensor`.
"""
parameters = dict(locals())
with tf.name_scope(name) as name:
if diag_bijector is None:
diag_bijector = softplus.Softplus(validate_args=validate_args)
if not isinstance(diag_bijector, tf.__internal__.CompositeTensor):
raise TypeError('`diag_bijector` must be an instance of '
'`tf.__internal__.CompositeTensor`.')
if diag_shift is not None:
dtype = dtype_util.common_dtype([diag_bijector, diag_shift],
tf.float32)
diag_shift = tensor_util.convert_nonref_to_tensor(
diag_shift, name='diag_shift', dtype=dtype)
diag_bijector = chain.Chain(
[shift.Shift(shift=diag_shift), diag_bijector])
super(FillScaleTriL, self).__init__([
transform_diagonal.TransformDiagonal(
diag_bijector=diag_bijector),
fill_triangular.FillTriangular()
],
validate_args=validate_args,
validate_event_size=False,
parameters=parameters,
name=name)
def _inverse(self, y):
n = ps.shape(y)[-1]
batch_shape = ps.shape(y)[:-2]
# Extract the reciprocal of the row norms from the diagonal.
diag = tf.linalg.diag_part(y)[..., tf.newaxis]
# Set the diagonal to 0s.
y = tf.linalg.set_diag(
y, tf.zeros(ps.concat([batch_shape, [n]], axis=-1), dtype=y.dtype))
# Multiply with the norm (or divide by its reciprocal) to recover the
# unconstrained reals in the (strictly) lower triangular part.
x = y / diag
# Remove the first row and last column before inverting the FillTriangular
# transformation.
return fill_triangular.FillTriangular().inverse(x[..., 1:, :-1])
def __init__(self,
diag_bijector=None,
diag_shift=1e-5,
validate_args=False,
name="scale_tril"):
"""Instantiates the `ScaleTriL` bijector.
Args:
diag_bijector: `Bijector` instance, used to transform the output diagonal
to be positive.
Default value: `None` (i.e., `tfb.Softplus()`).
diag_shift: Float value broadcastable and added to all diagonal entries
after applying the `diag_bijector`. Setting a positive
value forces the output diagonal entries to be positive, but
prevents inverting the transformation for matrices with
diagonal entries less than this value.
Default value: `1e-5`.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
Default value: `False` (i.e., arguments are not validated).
name: Python `str` name given to ops managed by this object.
Default value: `scale_tril`.
"""
with tf.compat.v1.name_scope(name, values=[diag_shift]) as name:
if diag_bijector is None:
diag_bijector = softplus.Softplus(validate_args=validate_args)
if diag_shift is not None:
diag_shift = tf.convert_to_tensor(value=diag_shift,
dtype=diag_bijector.dtype,
name="diag_shift")
diag_bijector = chain.Chain([
affine_scalar.AffineScalar(shift=diag_shift), diag_bijector
])
super(ScaleTriL, self).__init__([
transform_diagonal.TransformDiagonal(
diag_bijector=diag_bijector),
fill_triangular.FillTriangular()
],
validate_args=validate_args,
name=name)
self._use_tf_function = False # So input bijectors cache EagerTensors.
def _forward(self, x):
x = tf.convert_to_tensor(x, name='x')
batch_shape = ps.shape(x)[:-1]
# Pad zeros on the top row and right column.
y = fill_triangular.FillTriangular().forward(x)
rank = ps.rank(y)
paddings = ps.concat(
[ps.zeros([rank - 2, 2], dtype=tf.int32), [[1, 0], [0, 1]]],
axis=0)
y = tf.pad(y, paddings)
# Set diagonal to 1s.
n = ps.shape(y)[-1]
diag = tf.ones(ps.concat([batch_shape, [n]], axis=-1), dtype=x.dtype)
y = tf.linalg.set_diag(y, diag)
# Normalize each row to have Euclidean (L2) norm 1.
y /= tf.norm(y, axis=-1)[..., tf.newaxis]
return y
def _inverse_event_shape_tensor(self, input_shape):
n = input_shape[-1] - 1
y_shape = tf.concat([input_shape[:-2], [n, n]], axis=-1)
return fill_triangular.FillTriangular().inverse_event_shape_tensor(
y_shape)
def _forward_event_shape_tensor(self, input_shape):
tril_shape = fill_triangular.FillTriangular(
).forward_event_shape_tensor(input_shape)
n = tril_shape[-1] + 1
return tf.concat([tril_shape[:-2], [n, n]], axis=-1)
