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Class FillTriangular
Transforms vectors to triangular.
Inherits From: Bijector
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]]
__init__
__init__(
upper=False,
validate_args=False,
name='fill_triangular'
)
Instantiates the FillTriangular
bijector.
Args:
upper
: Pythonbool
representing whether output matrix should be upper triangular (True
) or lower triangular (False
, default).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
.
name_scope
Returns a tf.name_scope
instance for this class.
submodules
Sequence of all sub-modules.
Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).
a = tf.Module()
b = tf.Module()
c = tf.Module()
a.b = b
b.c = c
assert list(a.submodules) == [b, c]
assert list(b.submodules) == [c]
assert list(c.submodules) == []
Returns:
A sequence of all submodules.
trainable_variables
Sequence of variables owned by this module and it's submodules.
Returns:
A sequence of variables for the current module (sorted by attribute name) followed by variables from all submodules recursively (breadth first).
validate_args
Returns True if Tensor arguments will be validated.
variables
Sequence of variables owned by this module and it's submodules.
Returns:
A sequence of variables for the current module (sorted by attribute name) followed by variables from all submodules recursively (breadth first).
Methods
__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
: Atfd.Distribution
,tfb.Bijector
, or aTensor
.name
: Pythonstr
name given to ops created by this function.**kwargs
: Additional keyword arguments passed into the createdtfd.TransformedDistribution
,tfb.Bijector
, orself.forward
.
Returns:
composition
: Atfd.TransformedDistribution
if the input was atfd.Distribution
, atfb.Chain
if the input was atfb.Bijector
, or aTensor
computed byself.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.])
forward
forward(
x,
name='forward',
**kwargs
)
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.**kwargs
: Named arguments forwarded to subclass implementation.
Returns:
Tensor
.
Raises:
TypeError
: ifself.dtype
is specified andx.dtype
is notself.dtype
.NotImplementedError
: if_forward
is not implemented.
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.
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
.
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
. 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 shaperank(x) - event_ndims
dimensions.name
: The name to give this op.**kwargs
: Named arguments forwarded to subclass implementation.
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.
inverse
inverse(
y,
name='inverse',
**kwargs
)
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.**kwargs
: Named arguments forwarded to subclass implementation.
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.
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.
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
.
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
. 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 shaperank(y) - event_ndims
dimensions.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)))
, whereg_i
is the restriction ofg
to theith
partitionDi
.
Raises:
TypeError
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if_inverse_log_det_jacobian
is not implemented.
with_name_scope
with_name_scope(
cls,
method
)
Decorator to automatically enter the module name scope.
class MyModule(tf.Module):
@tf.Module.with_name_scope
def __call__(self, x):
if not hasattr(self, 'w'):
self.w = tf.Variable(tf.random.normal([x.shape[1], 64]))
return tf.matmul(x, self.w)
Using the above module would produce tf.Variable
s and tf.Tensor
s whose
names included the module name:
mod = MyModule()
mod(tf.ones([8, 32]))
# ==> <tf.Tensor: ...>
mod.w
# ==> <tf.Variable ...'my_module/w:0'>
Args:
method
: The method to wrap.
Returns:
The original method wrapped such that it enters the module's name scope.