def test_convert_variables_to_tensors(self):
tril = variables_module.Variable([[1., 0.], [0., 1.]])
operator = linalg_lib.LinearOperatorLowerTriangular(
tril, is_non_singular=True)
with self.cached_session() as sess:
sess.run([tril.initializer])
self.check_convert_variables_to_tensors(operator)
def testTriL(self):
with self.cached_session():
shift = np.array([-1, 0, 1], dtype=np.float32)
tril = np.array([[[3, 0, 0], [2, -1, 0], [3, 2, 1]],
[[2, 0, 0], [3, -2, 0], [4, 3, 2]]],
dtype=np.float32)
scale = linalg.LinearOperatorLowerTriangular(tril,
is_non_singular=True)
affine = AffineLinearOperator(shift=shift,
scale=scale,
validate_args=True)
x = np.array([[[1, 0, -1], [2, 3, 4]], [[4, 1, -7], [6, 9, 8]]],
dtype=np.float32)
# If we made the bijector do x*A+b then this would be simplified to:
# y = np.matmul(x, tril) + shift.
y = np.squeeze(np.matmul(tril, np.expand_dims(x, -1)), -1) + shift
ildj = -np.sum(
np.log(np.abs(np.diagonal(tril, axis1=-2, axis2=-1))))
self.assertEqual(affine.name, "affine_linear_operator")
self.assertAllClose(y, affine.forward(x).eval())
self.assertAllClose(x, affine.inverse(y).eval())
self.assertAllClose(
ildj,
affine.inverse_log_det_jacobian(y, event_ndims=2).eval())
self.assertAllClose(
-affine.inverse_log_det_jacobian(y, event_ndims=2).eval(),
affine.forward_log_det_jacobian(x, event_ndims=2).eval())
def __init__(self,
df,
scale,
cholesky_input_output_matrices=False,
validate_args=False,
allow_nan_stats=True,
name="WishartCholesky"):
"""Construct Wishart distributions.
Args:
df: `float` or `double` `Tensor`. Degrees of freedom, must be greater than
or equal to dimension of the scale matrix.
scale: `float` or `double` `Tensor`. The Cholesky factorization of
the symmetric positive definite scale matrix of the distribution.
cholesky_input_output_matrices: Python `bool`. Any function which whose
input or output is a matrix assumes the input is Cholesky and returns a
Cholesky factored matrix. Example `log_prob` input takes a Cholesky and
`sample_n` returns a Cholesky when
`cholesky_input_output_matrices=True`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
result is undefined. When `False`, an exception is raised if one or
more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
"""
parameters = dict(locals())
with ops.name_scope(name, values=[scale]) as name:
with ops.name_scope("init", values=[scale]):
scale = ops.convert_to_tensor(scale)
if validate_args:
scale = control_flow_ops.with_dependencies([
check_ops.assert_positive(
array_ops.matrix_diag_part(scale),
message="scale must be positive definite"),
check_ops.assert_equal(
array_ops.shape(scale)[-1],
array_ops.shape(scale)[-2],
message="scale must be square")
] if validate_args else [], scale)
super(WishartCholesky, self).__init__(
df=df,
scale_operator=linalg.LinearOperatorLowerTriangular(
tril=scale,
is_non_singular=True,
is_positive_definite=True,
is_square=True),
cholesky_input_output_matrices=cholesky_input_output_matrices,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
def test_triangular_diag_matmul(self):
operator1 = linalg_lib.LinearOperatorLowerTriangular([[1., 0., 0.],
[2., 1., 0.],
[2., 3., 3.]])
operator2 = linalg_lib.LinearOperatorDiag([2., 2., 3.])
operator_matmul = operator1.matmul(operator2)
self.assertTrue(
isinstance(operator_matmul,
linalg_lib.LinearOperatorLowerTriangular))
self.assertAllClose(
math_ops.matmul(operator1.to_dense(), operator2.to_dense()),
self.evaluate(operator_matmul.to_dense()))
operator_matmul = operator2.matmul(operator1)
self.assertTrue(
isinstance(operator_matmul,
linalg_lib.LinearOperatorLowerTriangular))
self.assertAllClose(
math_ops.matmul(operator2.to_dense(), operator1.to_dense()),
self.evaluate(operator_matmul.to_dense()))
def test_tape_safe(self):
tril = variables_module.Variable([[1., 0.], [0., 1.]])
operator = linalg_lib.LinearOperatorLowerTriangular(
tril, is_non_singular=True)
self.check_tape_safe(operator)
def make_tril_scale(loc=None,
scale_tril=None,
scale_diag=None,
scale_identity_multiplier=None,
shape_hint=None,
validate_args=False,
assert_positive=False,
name=None):
"""Creates a LinOp representing a lower triangular matrix.
Args:
loc: Floating-point `Tensor`. This is used for inferring shape in the case
where only `scale_identity_multiplier` is set.
scale_tril: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ... k, k], which represents a k x k
lower triangular matrix.
When `None` no `scale_tril` term is added to the LinOp.
The upper triangular elements above the diagonal are ignored.
scale_diag: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ... k], which represents a k x k
diagonal matrix.
When `None` no diagonal term is added to the LinOp.
scale_identity_multiplier: floating point rank 0 `Tensor` representing a
scaling done to the identity matrix.
When `scale_identity_multiplier = scale_diag = scale_tril = None` then
`scale += IdentityMatrix`. Otherwise no scaled-identity-matrix is added
to `scale`.
shape_hint: scalar integer `Tensor` representing a hint at the dimension of
the identity matrix when only `scale_identity_multiplier` is set.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
assert_positive: Python `bool` indicating whether LinOp should be checked
for being positive definite.
name: Python `str` name given to ops managed by this object.
Returns:
`LinearOperator` representing a lower triangular matrix.
Raises:
ValueError: If only `scale_identity_multiplier` is set and `loc` and
`shape_hint` are both None.
"""
def _maybe_attach_assertion(x):
if not validate_args:
return x
if assert_positive:
return control_flow_ops.with_dependencies([
check_ops.assert_positive(
array_ops.matrix_diag_part(x),
message="diagonal part must be positive"),
], x)
return control_flow_ops.with_dependencies([
check_ops.assert_none_equal(
array_ops.matrix_diag_part(x),
array_ops.zeros([], x.dtype),
message="diagonal part must be non-zero"),
], x)
with ops.name_scope(name,
"make_tril_scale",
values=[loc, scale_diag, scale_identity_multiplier]):
loc = _convert_to_tensor(loc, name="loc")
scale_tril = _convert_to_tensor(scale_tril, name="scale_tril")
scale_diag = _convert_to_tensor(scale_diag, name="scale_diag")
scale_identity_multiplier = _convert_to_tensor(
scale_identity_multiplier, name="scale_identity_multiplier")
if scale_tril is not None:
scale_tril = array_ops.matrix_band_part(scale_tril, -1,
0) # Zero out TriU.
tril_diag = array_ops.matrix_diag_part(scale_tril)
if scale_diag is not None:
tril_diag += scale_diag
if scale_identity_multiplier is not None:
tril_diag += scale_identity_multiplier[..., array_ops.newaxis]
scale_tril = array_ops.matrix_set_diag(scale_tril, tril_diag)
return linalg.LinearOperatorLowerTriangular(
tril=_maybe_attach_assertion(scale_tril),
is_non_singular=True,
is_self_adjoint=False,
is_positive_definite=assert_positive)
return make_diag_scale(loc=loc,
scale_diag=scale_diag,
scale_identity_multiplier=scale_identity_multiplier,
shape_hint=shape_hint,
validate_args=validate_args,
assert_positive=assert_positive,
name=name)
def __init__(self,
loc=None,
scale_tril=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalTriL"):
"""Construct Multivariate Normal distribution on `R^k`.
The `batch_shape` is the broadcast shape between `loc` and `scale`
arguments.
The `event_shape` is given by last dimension of the matrix implied by
`scale`. The last dimension of `loc` (if provided) must broadcast with this.
Recall that `covariance = scale @ scale.T`. A (non-batch) `scale` matrix is:
```none
scale = scale_tril
```
where `scale_tril` is lower-triangular `k x k` matrix with non-zero
diagonal, i.e., `tf.linalg.tensor_diag_part(scale_tril) != 0`.
Additional leading dimensions (if any) will index batches.
Args:
loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
`b >= 0` and `k` is the event size.
scale_tril: Floating-point, lower-triangular `Tensor` with non-zero
diagonal elements. `scale_tril` has shape `[B1, ..., Bb, k, k]` where `b
>= 0` and `k` is the event size.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
result is undefined. When `False`, an exception is raised if one or more
of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: if neither `loc` nor `scale_tril` are specified.
"""
parameters = dict(locals())
def _convert_to_tensor(x, name):
return None if x is None else ops.convert_to_tensor(x, name=name)
if loc is None and scale_tril is None:
raise ValueError(
"Must specify one or both of `loc`, `scale_tril`.")
with ops.name_scope(name) as name:
with ops.name_scope("init", values=[loc, scale_tril]):
loc = _convert_to_tensor(loc, name="loc")
scale_tril = _convert_to_tensor(scale_tril, name="scale_tril")
if scale_tril is None:
scale = linalg.LinearOperatorIdentity(
num_rows=distribution_util.dimension_size(loc, -1),
dtype=loc.dtype,
is_self_adjoint=True,
is_positive_definite=True,
assert_proper_shapes=validate_args)
else:
# No need to validate that scale_tril is non-singular.
# LinearOperatorLowerTriangular has an assert_non_singular
# method that is called by the Bijector.
scale = linalg.LinearOperatorLowerTriangular(
scale_tril,
is_non_singular=True,
is_self_adjoint=False,
is_positive_definite=False)
super(MultivariateNormalTriL,
self).__init__(loc=loc,
scale=scale,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
