# tfp.experimental.substrates.jax.bijectors.AffineLinearOperator

Compute Y = g(X; shift, scale) = scale @ X + shift.

Inherits From: Bijector

shift is a numeric Tensor and scale is a LinearOperator.

If X is a scalar then the forward transformation is: scale * X + shift where * denotes broadcasted elementwise product.

#### Example Use:

linalg = tf.linalg

x = [1., 2, 3]

shift = [-1., 0., 1]
diag = [1., 2, 3]
scale = tf.linalg.LinearOperatorDiag(diag)
affine = AffineLinearOperator(shift, scale)
# In this case, `forward` is equivalent to:
# y = scale @ x + shift
y = affine.forward(x)  # [0., 4, 10]

shift = [2., 3, 1]
tril = [[1., 0, 0],
[2, 1, 0],
[3, 2, 1]]
scale = tf.linalg.LinearOperatorLowerTriangular(tril)
affine = AffineLinearOperator(shift, scale)
# In this case, `forward` is equivalent to:
# np.squeeze(np.matmul(tril, np.expand_dims(x, -1)), -1) + shift
y = affine.forward(x)  # [3., 7, 11]

shift Floating-point Tensor.
scale Subclass of LinearOperator. Represents the (batch) positive definite matrix M in R^{k x k}.
adjoint Python bool indicating whether to use the scale matrix as specified or its adjoint. Default value: False.
validate_args Python bool indicating whether arguments should be checked for correctness.
name Python str name given to ops managed by this object.

TypeError if scale is not a LinearOperator.
TypeError if shift.dtype does not match scale.dtype.
ValueError if not scale.is_non_singular.

adjoint bool indicating scale should be used as conjugate transpose.
dtype dtype of Tensors 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.

name Returns the string name of this Bijector.
parameters Dictionary of parameters used to instantiate this Bijector.
scale The scale LinearOperator in Y = scale @ X + shift.
shift The shift Tensor in Y = scale @ X + shift.
trainable_variables

validate_args Returns True if Tensor arguments will be validated.
variables

## Methods

### forward

View source

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

### forward_dtype

View source

Returns the dtype of the output of the forward transformation.

Args
dtype tf.dtype, or nested structure of tf.dtypes, of the input to forward.
name The name to give this op.
**kwargs Named arguments forwarded to subclass implementation.

Returns
tf.dtype or nested structure of tf.dtypes of the output of forward.

### forward_event_shape

View source

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 into forward function.

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

### forward_event_shape_tensor

View source

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 into forward function.
name name to give to the op

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

### forward_log_det_jacobian

View source

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 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.
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 if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError if neither _forward_log_det_jacobian nor {_inverse, _inverse_log_det_jacobian} are implemented, or this is a non-injective bijector.

### inverse

View source

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 if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError if _inverse is not implemented.

### inverse_dtype

View source

Returns the dtype of the output of the inverse transformation.

Args
dtype tf.dtype, or nested structure of tf.dtypes, of the input to inverse.
name The name to give this op.
**kwargs Named arguments forwarded to subclass implementation.

Returns
tf.dtype or nested structure of tf.dtypes of the output of inverse.

### inverse_event_shape

View source

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 into inverse function.

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

### inverse_event_shape_tensor

View source

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 into inverse function.
name name to give to the op

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

### inverse_log_det_jacobian

View source

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 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.
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 self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError if _inverse_log_det_jacobian is not implemented.

### __call__

View source

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 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 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.])