class

CatTransform

extendsTransform

CatTransform(transforms: list[Transform], dim: int = 0, lengths: list[int] | None = None)

source edit

Apply different transforms to contiguous partitions along an axis.

Splits the input along dim into contiguous chunks of size lengths[i] (one element each if lengths is None), applies the $i$ -th transform to the $i$ -th chunk, and concatenates the results back along the same axis. Differs from StackTransform in that each partition can have a different length, not just a single index.

Parameters

transformslist[Transform]

One transform per partition.

dimint= 0

Concatenation dimension. Default 0.

lengthslist[int]= None

Length of each partition. Default None: one per transform, so dim holds len(transforms) elements. dim must hold sum(lengths) of them, as the reference requires.

Raises

ValueError

If transforms is empty, or lengths is not one per transform.

lucid._C.engine.InvalidArgument

When applied, if dim does not hold sum(lengths) elements.

Notes

Forward (with $\mathbf{x}_i$ the $i$ -th partition):

\mathbf{y} = \mathrm{cat}\bigl([T_i(\mathbf{x}_i)]_{i=1}^{n}, \;\mathrm{dim}\bigr)

Inverse: split, invert, re-concatenate.

Log Jacobian determinant: per-partition Jacobians concatenated back along dim:

\log|\det J| = \mathrm{cat}\bigl( [\log|\det J_{T_i}|(\mathbf{x}_i, \mathbf{y}_i)]_{i=1}^{n}, \;\mathrm{dim}\bigr)

Examples

>>> import lucid
>>> from lucid.distributions.transforms import ExpTransform, AffineTransform, CatTransform
>>> T = CatTransform([ExpTransform(), AffineTransform(0.0, 2.0)],
...                  dim=0, lengths=[2, 3])
>>> T(lucid.tensor([0.0, 0.0, 1.0, 2.0, 3.0])).shape
(5,)

Used by 1

lucid.distributions

Constructors

dunder

init

→None

__init__(transforms: list[Transform], dim: int = 0, lengths: list[int] | None = None)

source edit

Store the per-partition transforms, concat axis, and partition lengths.

Raises

ValueError

If transforms is empty, or lengths is not one per transform.

Properties

prop

codomain

→Constraint

codomain: Constraint

source edit

Concatenated codomain constraint across all partition transforms.

prop

domain

→Constraint

domain: Constraint

source edit

Concatenated domain constraint across all partition transforms.

Instance methods

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source edit

Per-partition Jacobians concatenated back along dim.

>>> import lucid >>> from lucid.distributions.transforms import ExpTransform, AffineTransform, CatTransform >>> T = CatTransform([ExpTransform(), AffineTransform(0.0, 2.0)], ... dim=0, lengths=[2, 3]) >>> T(lucid.tensor([0.0, 0.0, 1.0, 2.0, 3.0])).shape (5,)