class

AbsTransform

extendsTransform

AbsTransform()

source

Element-wise absolute value $y = |x|$ (folded, not bijective).

Maps $\mathbb{R} \to [0, \infty)$ element-wise by folding the sign. Useful when composing with symmetric base distributions (e.g. a Normal) to produce a half-Normal or folded-Normal pushforward. bijective = False and sign = +1.

Because both $x$ and $-x$ map to the same $y$ , the transform is non-invertible. The pseudo-inverse used here is the identity, under the convention that the preimage is assumed to lie on the non-negative half-line.

Notes

Forward: $y = |x|$ .

Pseudo-inverse: $x = y$ (assumes $x \geq 0$ ).

Log Jacobian determinant:

\log\!\left|\frac{\partial y}{\partial x}\right| = 0

everywhere off the measure-zero set $\{x = 0\}$ where the map is non-differentiable.

Folding the sign halves the density: composing with a Normal(0,1) base gives the half-Normal density $p(y) = 2 \phi(y)$ for $y \geq 0$ , which requires special handling outside the standard change-of-variable formula. Lucid's TransformedDistribution does not currently correct for this folding factor — apply the $+\log 2$ constant manually when needed.

Examples

>>> import lucid
>>> from lucid.distributions.transforms import AbsTransform
>>> T = AbsTransform()
>>> T(lucid.tensor(-3.0))
Tensor(3.0)

Methods (1)

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source

Zero everywhere — $|dy/dx| = 1$ outside the kink at zero.