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Transforms vectors to triangular.
Inherits From: Bijector
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 |
graph_parents
|
Returns this Bijector 's graph_parents as a Python list.
|
has_static_min_event_ndims
|
Returns True if the bijector has statically-known min_event_ndims .
|
inverse_min_event_ndims
|
Returns the minimal number of dimensions bijector.inverse operates on.
Multipart bijectors return structured |
is_constant_jacobian
|
Returns true iff the Jacobian matrix is not a function of x. |
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
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
forward_dtype(
dtype=UNSPECIFIED, name='forward_dtype', **kwargs
)
Returns the dtype returned by forward
for the provided input.
forward_event_ndims
forward_event_ndims(
event_ndims, **kwargs
)
Returns the number of event dimensions produced by forward
.
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 (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
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
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
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
inverse_dtype(
dtype=UNSPECIFIED, name='inverse_dtype', **kwargs
)
Returns the dtype returned by inverse
for the provided input.
inverse_event_ndims
inverse_event_ndims(
event_ndims, **kwargs
)
Returns the number of event dimensions produced by inverse
.
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 (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
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
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__
__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:
- If the input is a
tfd.Distribution
instance, returntfd.TransformedDistribution(distribution=input, bijector=self)
. - If the input is a
tfb.Bijector
instance, returntfb.Chain([self, input])
. - 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.Shift(shift=1.)(
tfb.Exp()(
tfb.Scale(scale=-1.))))
# ==> `tfb.Chain([
# tfb.Reciprocal(),
# tfb.Shift(shift=1.),
# tfb.Exp(),
# tfb.Scale(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__
__eq__(
other
)
Return self==value.