# tf.contrib.distributions.bijectors.Affine

## Class Affine

Inherits From: Bijector

See the guide: Random variable transformations (contrib) > Bijectors

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

Here scale = c * I + diag(D1) + tril(L) + V @ diag(D2) @ V.T.

In TF parlance, the scale term is logically equivalent to:

scale = (
scale_identity_multiplier * tf.diag(tf.ones(d)) +
tf.diag(scale_diag) +
scale_tril +
scale_perturb_factor @ diag(scale_perturb_diag) @
tf.transpose([scale_perturb_factor])
)


The scale term is applied without necessarily materializing constituent matrices, i.e., the matmul is matrix-free when possible.

#### Examples

# Y = X
b = Affine()

# Y = X + shift
b = Affine(shift=[1., 2, 3])

# Y = 2 * I @ X.T + shift
b = Affine(shift=[1., 2, 3],
scale_identity_multiplier=2.)

# Y = tf.diag(d1) @ X.T + shift
b = Affine(shift=[1., 2, 3],
scale_diag=[-1., 2, 1])         # Implicitly 3x3.

# Y = (I + v * v.T) @ X.T + shift
b = Affine(shift=[1., 2, 3],
scale_perturb_factor=[[1., 0],
[0, 1],
[1, 1]])

# Y = (diag(d1) + v * diag(d2) * v.T) @ X.T + shift
b = Affine(shift=[1., 2, 3],
scale_diag=[1., 3, 3],          # Implicitly 3x3.
scale_perturb_diag=[2., 1],     # Implicitly 2x2.
scale_perturb_factor=[[1., 0],
[0, 1],
[1, 1]])



## Properties

### dtype

dtype of Tensors transformable by this distribution.

### event_ndims

Returns then number of event dimensions this bijector operates on.

### graph_parents

Returns this Bijector's graph_parents as a Python list.

### is_constant_jacobian

Returns true iff the Jacobian 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_identity_multiplier=None,
scale_diag=None,
scale_tril=None,
scale_perturb_factor=None,
scale_perturb_diag=None,
validate_args=False,
name='affine'
)


Instantiates the Affine bijector.

This Bijector is initialized with shift Tensor and scale arguments, giving the forward operation:

Y = g(X) = scale @ X + shift


where the scale term is logically equivalent to:

scale = (
scale_identity_multiplier * tf.diag(tf.ones(d)) +
tf.diag(scale_diag) +
scale_tril +
scale_perturb_factor @ diag(scale_perturb_diag) @
tf.transpose([scale_perturb_factor])
)


If none of scale_identity_multiplier, scale_diag, or scale_tril are specified then scale += IdentityMatrix. Otherwise specifying a scale argument has the semantics of scale += Expand(arg), i.e., scale_diag != None means scale += tf.diag(scale_diag).

#### Args:

• shift: Floating-point Tensor. If this is set to None, no shift is applied.
• scale_identity_multiplier: floating point rank 0 Tensor representing a scaling done to the identity matrix. When scale_identity_multiplier = scale_diag = scale_tril = None then scale += IdentityMatrix. Otherwise no scaled-identity-matrix is added to scale.
• scale_diag: Floating-point Tensor representing the diagonal matrix. scale_diag has shape [N1, N2, ... k], which represents a k x k diagonal matrix. When None no diagonal term is added to scale.
• scale_tril: Floating-point Tensor representing the diagonal matrix. scale_diag has shape [N1, N2, ... k, k], which represents a k x k lower triangular matrix. When None no scale_tril term is added to scale. The upper triangular elements above the diagonal are ignored.
• scale_perturb_factor: Floating-point Tensor representing factor matrix with last two dimensions of shape (k, r). When None, no rank-r update is added to scale.
• scale_perturb_diag: Floating-point Tensor representing the diagonal matrix. scale_perturb_diag has shape [N1, N2, ... r], which represents an r x r diagonal matrix. When None low rank updates will take the form scale_perturb_factor * scale_perturb_factor.T.
• validate_args: Python bool indicating whether arguments should be checked for correctness.
• name: Python str name given to ops managed by this object.

#### Raises:

• ValueError: if perturb_diag is specified but not perturb_factor.
• TypeError: if shift has different dtype from scale arguments.

### 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,
name='forward_log_det_jacobian'
)


Returns both the forward_log_det_jacobian.

#### Args:

• x: Tensor. The input to the "forward" Jacobian evaluation.
• 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,
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 evaluation.
• 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.