tfp.substrates.jax.bijectors.FillTriangular

Note: This API is new and only available in tfp-nightly.

Transforms vectors to triangular.

Inherits From: Bijector

View aliases

Main aliases

tfp.experimental.substrates.jax.bijectors.FillTriangular

tfp.substrates.jax.bijectors.FillTriangular(
    upper=False, validate_args=False, name='fill_triangular'
)

Triangular matrix elements are filled in a clockwise spiral.

Given input with shape batch_shape + [d], produces output with shape batch_shape + [n, n], where n = (-1 + sqrt(1 + 8 * d))/2. This follows by solving the quadratic equation d = 1 + 2 + ... + n = n * (n + 1)/2.

Example

b = tfb.FillTriangular(upper=False)
b.forward([1, 2, 3, 4, 5, 6])
# ==> [[4, 0, 0],
#      [6, 5, 0],
#      [3, 2, 1]]

b = tfb.FillTriangular(upper=True)
b.forward([1, 2, 3, 4, 5, 6])
# ==> [[1, 2, 3],
#      [0, 5, 6],
#      [0, 0, 4]]

Args
upper	Python bool representing whether output matrix should be upper triangular (True) or lower triangular (False, default).
validate_args	Python bool indicating whether arguments should be checked for correctness.
name	Python str name given to ops managed by this object.

Attributes
dtype
forward_min_event_ndims	Returns the minimal number of dimensions bijector.forward operates on. Multipart bijectors return structured ndims, which indicates the expected structure of their inputs. Some multipart bijectors, notably Composites, may return structures of None.
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. Multipart bijectors return structured event_ndims, which indicates the expected structure of their outputs. Some multipart bijectors, notably Composites, may return structures of None.
is_constant_jacobian	Returns true iff the Jacobian matrix is not a function of x. Note: Jacobian matrix is either constant for both forward and inverse or neither.
name	Returns the string name of this Bijector.
parameters	Dictionary of parameters used to instantiate this Bijector.
trainable_variables
validate_args	Returns True if Tensor arguments will be validated.
variables

Methods

forward

View source

forward(
    x, name='forward', **kwargs
)

Returns the forward Bijector evaluation, i.e., X = g(Y).

Args
x	Tensor (structure). The input to the 'forward' evaluation.
name	The name to give this op.
**kwargs	Named arguments forwarded to subclass implementation.

Returns
Tensor (structure).

Raises
TypeError	if self.dtype is specified and x.dtype is not self.dtype.
NotImplementedError	if _forward is not implemented.

forward_dtype

View source

forward_dtype(
    dtype=UNSPECIFIED, name='forward_dtype', **kwargs
)

Returns the dtype returned by forward for the provided input.

forward_event_ndims

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forward_event_ndims(
    event_ndims, **kwargs
)

Returns the number of event dimensions produced by forward.

forward_event_shape

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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 (structure) indicating event-portion shape passed into forward function.

Returns
forward_event_shape_tensor	TensorShape (structure) indicating event-portion shape after applying forward. Possibly unknown.

forward_event_shape_tensor

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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 (structure) indicating event-portion shape passed into forward function.
name	name to give to the op

Returns
forward_event_shape_tensor	Tensor, int32 vector (structure) indicating event-portion shape after applying forward.

forward_log_det_jacobian

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forward_log_det_jacobian(
    x, event_ndims, name='forward_log_det_jacobian', **kwargs
)

Returns both the forward_log_det_jacobian.

Args
x	Tensor (structure). 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 to self.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 shape rank(x) - event_ndims dimensions. Multipart bijectors require structured event_ndims, such that rank(y[i]) - rank(event_ndims[i]) is the same for all elements i of the structured input. Furthermore, the first event_ndims[i] of each x[i].shape must be the same for all i (broadcasting is not allowed).
name	The name to give this op.
**kwargs	Named arguments forwarded to subclass implementation.

Returns
Tensor (structure), if this bijector is injective. If not injective this is not implemented.

Raises
TypeError	if y's dtype is incompatible with the expected output dtype.
NotImplementedError	if neither _forward_log_det_jacobian nor {_inverse, _inverse_log_det_jacobian} are implemented, or this is a non-injective bijector.

inverse

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inverse(
    y, name='inverse', **kwargs
)

Returns the inverse Bijector evaluation, i.e., X = g^{-1}(Y).

Args
y	Tensor (structure). The input to the 'inverse' evaluation.
name	The name to give this op.
**kwargs	Named arguments forwarded to subclass implementation.

Returns
Tensor (structure), 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	if y's structured dtype is incompatible with the expected output dtype.
NotImplementedError	if _inverse is not implemented.

inverse_dtype

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inverse_dtype(
    dtype=UNSPECIFIED, name='inverse_dtype', **kwargs
)

Returns the dtype returned by forward for the provided input.

inverse_event_ndims

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inverse_event_ndims(
    event_ndims, **kwargs
)

Returns the number of event dimensions produced by inverse.

inverse_event_shape

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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 (structure) indicating event-portion shape passed into inverse function.

Returns
inverse_event_shape_tensor	TensorShape (structure) indicating event-portion shape after applying inverse. Possibly unknown.

inverse_event_shape_tensor

View source

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 (structure) indicating event-portion shape passed into inverse function.
name	name to give to the op

Returns
inverse_event_shape_tensor	Tensor, int32 vector (structure) indicating event-portion shape after applying inverse.

inverse_log_det_jacobian

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inverse_log_det_jacobian(
    y, event_ndims, name='inverse_log_det_jacobian', **kwargs
)

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 (structure). 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 to self.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 shape rank(y) - event_ndims dimensions. Multipart bijectors require structured event_ndims, such that rank(y[i]) - rank(event_ndims[i]) is the same for all elements i of the structured input. Furthermore, the first event_ndims[i] of each x[i].shape must be the same for all i (broadcasting is not allowed).
name	The name to give this op.
**kwargs	Named arguments forwarded to subclass implementation.

Returns
ildj	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	if x's dtype is incompatible with the expected inverse-dtype.
NotImplementedError	if _inverse_log_det_jacobian is not implemented.

__call__

View source

__call__(
    value, name=None, **kwargs
)

Applies or composes the Bijector, depending on input type.

This is a convenience function which applies the Bijector instance in three different ways, depending on the input:

1. If the input is a tfd.Distribution instance, return tfd.TransformedDistribution(distribution=input, bijector=self).
2. If the input is a tfb.Bijector instance, return tfb.Chain([self, input]).
3. Otherwise, return self.forward(input)

Args
value	A tfd.Distribution, tfb.Bijector, or a (structure of) Tensor.
name	Python str name given to ops created by this function.
**kwargs	Additional keyword arguments passed into the created tfd.TransformedDistribution, tfb.Bijector, or self.forward.

Returns
composition	A tfd.TransformedDistribution if the input was a tfd.Distribution, a tfb.Chain if the input was a tfb.Bijector, or a (structure of) Tensor computed by self.forward.

Examples

sigmoid = tfb.Reciprocal()(
    tfb.AffineScalar(shift=1.)(
      tfb.Exp()(
        tfb.AffineScalar(scale=-1.))))
# ==> `tfb.Chain([
#         tfb.Reciprocal(),
#         tfb.AffineScalar(shift=1.),
#         tfb.Exp(),
#         tfb.AffineScalar(scale=-1.),
#      ])`  # ie, `tfb.Sigmoid()`

log_normal = tfb.Exp()(tfd.Normal(0, 1))
# ==> `tfd.TransformedDistribution(tfd.Normal(0, 1), tfb.Exp())`

tfb.Exp()([-1., 0., 1.])
# ==> tf.exp([-1., 0., 1.])

__eq__

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__eq__(
    other
)

Return self==value.

__ne__

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__ne__(
    other
)

Return self!=value.