# tf.contrib.distributions.bijectors.AffineLinearOperator

## Class AffineLinearOperator

Inherits From: Bijector

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

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 the scalar product.

1. If there are no sample dims, we call X = tf.expand_dims(X, 0), i.e., new_sample_shape = [1]. Otherwise do nothing.
2. The sample shape is flattened to have one dimension, i.e., new_sample_shape = [n] where n = tf.reduce_prod(old_sample_shape).
3. The sample dim is cyclically rotated left by 1, i.e., new_shape = [B1,...,Bb, k, n] where n is as above, k is the event_shape, and B1,...,Bb are the batch shapes for each of b batch dimensions.

(For more details see shape.make_batch_of_event_sample_matrices.)

The result of the above transformation is that X can be regarded as a batch of matrices where each column is a draw from the distribution. After premultiplying by scale, we take the inverse of this procedure. The input Y also undergoes the same transformation before/after premultiplying by inv(scale).

Example Use:

linalg = tf.linalg

x = [1., 2, 3]

shift = [-1., 0., 1]
diag = [1., 2, 3]
scale = 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 = 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]


## Properties

### 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.

#### Returns:

• is_constant_jacobian: Python bool.

### name

Returns the string name of this Bijector.

### scale

The scale LinearOperator in Y = scale @ X + shift.

### shift

The shift Tensor in Y = scale @ X + shift.

### validate_args

Returns True if Tensor arguments will be validated.

## Methods

### __init__

__init__(
shift=None,
scale=None,
validate_args=False,
name='affine_linear_operator'
)


Instantiates the AffineLinearOperator bijector. (deprecated)

THIS FUNCTION IS DEPRECATED. It will be removed after 2018-10-01. Instructions for updating: The TensorFlow Distributions library has moved to TensorFlow Probability (https://github.com/tensorflow/probability). You should update all references to use tfp.distributions instead of tf.contrib.distributions.

#### Args:

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

#### Raises:

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

### 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: if self.dtype is specified and x.dtype is not self.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 into forward function.

#### Returns:

• forward_event_shape_tensor: TensorShape 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 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

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 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 x.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: 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

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: if self.dtype is specified and y.dtype is not self.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 into inverse function.

#### Returns:

• inverse_event_shape_tensor: TensorShape 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 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

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