Class MatrixInverseTriL
Inherits From: Bijector
Defined in tensorflow/contrib/distributions/python/ops/bijectors/matrix_inverse_tril.py
.
Computes g(L) = inv(L)
, where L
is a lower-triangular matrix.
L
must be nonsingular; equivalently, all diagonal entries of L
must be
nonzero.
The input must have rank >= 2
. The input is treated as a batch of matrices
with batch shape input.shape[:-2]
, where each matrix has dimensions
input.shape[-2]
by input.shape[-1]
(hence input.shape[-2]
must equal
input.shape[-1]
).
Examples
tfd.bijectors.MatrixInverseTriL().forward(x=[[1., 0], [2, 1]])
# Result: [[1., 0], [-2, 1]], i.e., inv(x)
tfd.bijectors.MatrixInverseTriL().inverse(y=[[1., 0], [-2, 1]])
# Result: [[1., 0], [2, 1]], i.e., inv(y).
__init__
__init__(
validate_args=False,
name='matrix_inverse_tril'
)
Instantiates the MatrixInverseTriL
bijector. (deprecated)
Args:
validate_args
: Pythonbool
indicating whether arguments should be checked for correctness.name
: Pythonstr
name given to ops managed by this object.
Properties
dtype
dtype of Tensor
s transformable by this distribution.
forward_min_event_ndims
Returns the minimal number of dimensions bijector.forward operates on.
graph_parents
Returns this Bijector
's graph_parents as a Python list.
inverse_min_event_ndims
Returns the minimal number of dimensions bijector.inverse operates on.
is_constant_jacobian
Returns true iff the Jacobian matrix is not a function of x.
Returns:
is_constant_jacobian
: Pythonbool
.
name
Returns the string name of this Bijector
.
validate_args
Returns True if Tensor arguments will be validated.
Methods
tf.contrib.distributions.bijectors.MatrixInverseTriL.forward
forward(
x,
name='forward'
)
Returns the forward Bijector
evaluation, i.e., X = g(Y).
Args:
x
:Tensor
. The input to the "forward" evaluation.name
: The name to give this op.
Returns:
Tensor
.
Raises:
TypeError
: ifself.dtype
is specified andx.dtype
is notself.dtype
.NotImplementedError
: if_forward
is not implemented.
tf.contrib.distributions.bijectors.MatrixInverseTriL.forward_event_shape
forward_event_shape(input_shape)
Shape of a single sample from a single batch as a TensorShape
.
Same meaning as forward_event_shape_tensor
. May be only partially defined.
Args:
input_shape
:TensorShape
indicating event-portion shape passed intoforward
function.
Returns:
forward_event_shape_tensor
:TensorShape
indicating event-portion shape after applyingforward
. Possibly unknown.
tf.contrib.distributions.bijectors.MatrixInverseTriL.forward_event_shape_tensor
forward_event_shape_tensor(
input_shape,
name='forward_event_shape_tensor'
)
Shape of a single sample from a single batch as an int32
1D Tensor
.
Args:
input_shape
:Tensor
,int32
vector indicating event-portion shape passed intoforward
function.name
: name to give to the op
Returns:
forward_event_shape_tensor
:Tensor
,int32
vector indicating event-portion shape after applyingforward
.
tf.contrib.distributions.bijectors.MatrixInverseTriL.forward_log_det_jacobian
forward_log_det_jacobian(
x,
event_ndims,
name='forward_log_det_jacobian'
)
Returns both the forward_log_det_jacobian.
Args:
x
:Tensor
. The input to the "forward" Jacobian determinant evaluation.event_ndims
: Number of dimensions in the probabilistic events being transformed. Must be greater than or equal toself.forward_min_event_ndims
. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shapex.shape.ndims - event_ndims
dimensions.name
: The name to give this op.
Returns:
Tensor
, if this bijector is injective.
If not injective this is not implemented.
Raises:
TypeError
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if neither_forward_log_det_jacobian
nor {_inverse
,_inverse_log_det_jacobian
} are implemented, or this is a non-injective bijector.
tf.contrib.distributions.bijectors.MatrixInverseTriL.inverse
inverse(
y,
name='inverse'
)
Returns the inverse Bijector
evaluation, i.e., X = g^{-1}(Y).
Args:
y
:Tensor
. The input to the "inverse" evaluation.name
: The name to give this op.
Returns:
Tensor
, if this bijector is injective.
If not injective, returns the k-tuple containing the unique
k
points (x1, ..., xk)
such that g(xi) = y
.
Raises:
TypeError
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if_inverse
is not implemented.
tf.contrib.distributions.bijectors.MatrixInverseTriL.inverse_event_shape
inverse_event_shape(output_shape)
Shape of a single sample from a single batch as a TensorShape
.
Same meaning as inverse_event_shape_tensor
. May be only partially defined.
Args:
output_shape
:TensorShape
indicating event-portion shape passed intoinverse
function.
Returns:
inverse_event_shape_tensor
:TensorShape
indicating event-portion shape after applyinginverse
. Possibly unknown.
tf.contrib.distributions.bijectors.MatrixInverseTriL.inverse_event_shape_tensor
inverse_event_shape_tensor(
output_shape,
name='inverse_event_shape_tensor'
)
Shape of a single sample from a single batch as an int32
1D Tensor
.
Args:
output_shape
:Tensor
,int32
vector indicating event-portion shape passed intoinverse
function.name
: name to give to the op
Returns:
inverse_event_shape_tensor
:Tensor
,int32
vector indicating event-portion shape after applyinginverse
.
tf.contrib.distributions.bijectors.MatrixInverseTriL.inverse_log_det_jacobian
inverse_log_det_jacobian(
y,
event_ndims,
name='inverse_log_det_jacobian'
)
Returns the (log o det o Jacobian o inverse)(y).
Mathematically, returns: log(det(dX/dY))(Y)
. (Recall that: X=g^{-1}(Y)
.)
Note that forward_log_det_jacobian
is the negative of this function,
evaluated at g^{-1}(y)
.
Args:
y
:Tensor
. The input to the "inverse" Jacobian determinant evaluation.event_ndims
: Number of dimensions in the probabilistic events being transformed. Must be greater than or equal toself.inverse_min_event_ndims
. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shapey.shape.ndims - event_ndims
dimensions.name
: The name to give this op.
Returns:
Tensor
, if this bijector is injective.
If not injective, returns the tuple of local log det
Jacobians, log(det(Dg_i^{-1}(y)))
, where g_i
is the restriction
of g
to the ith
partition Di
.
Raises:
TypeError
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if_inverse_log_det_jacobian
is not implemented.