class

AffineTransform

extendsTransform

AffineTransform(loc: Tensor | float, scale: Tensor | float)

source

Element-wise affine bijection $y = \mathrm{loc} + \mathrm{scale}\cdot x$ .

The fundamental location-scale transform. Composing with a standard Normal yields $\mathcal{N}(\mathrm{loc}, \mathrm{scale}^2)$ ; it underpins virtually every reparameterised sampler in the codebase. Bijective with sign matching sign(scale); the implementation fixes self.sign = +1, so the caller is responsible for ensuring scale > 0.

Parameters

locTensor or float

Additive offset

b

scaleTensor or float

Multiplicative slope

a

(assumed positive).

Notes

Forward: $y = b + a\,x$ .

Inverse: $x = (y - b) / a$ .

Log Jacobian determinant (broadcast to x.shape):

\log\!\left|\frac{\partial y}{\partial x}\right| = \log|a|

For element-wise application (event_dim = 0) this is summed by IndependentTransform if the caller reinterprets trailing dims as event dims.

Examples

>>> import lucid
>>> from lucid.distributions.transforms import AffineTransform
>>> T = AffineTransform(loc=1.0, scale=2.0)
>>> T(lucid.tensor(3.0))
Tensor(7.0)

Methods (2)

dunder

init

→None

__init__(loc: Tensor | float, scale: Tensor | float)

source

Store the affine offset loc and multiplier scale.

The caller is responsible for ensuring scale > 0; sign is fixed at +1 here so the transform is treated as increasing.

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source

Constant log-Jacobian $\log|\text{scale}|$ , broadcast to x's shape.