class

PowerTransform

extendsTransform

PowerTransform(exponent: Tensor | float)

source

Element-wise power bijection $y = x^{\mathrm{exponent}}$ .

Bijection on $(0, \infty) \to (0, \infty)$ (the input must be positive; the implementation does not check this). Useful for Box–Cox-style reparameterisations and for mapping between Gamma families with different shape parameters.

Parameters

exponentTensor or float

Power

p

applied element-wise. Sign-aware: negative exponents are admissible but flip orientation, and zero exponents are not invertible (excluded).

Notes

Forward: $y = x^{p}$ .

Inverse: $x = y^{1/p}$ .

Log Jacobian determinant:

\log\!\left|\frac{\partial y}{\partial x}\right| = \log|p| + (p - 1)\log x

Special cases:

$p = 1$ → identity.
$p = -1$ → reciprocal $y = 1/x$ .
$p = 2$ → squaring on the positive half-line.

Examples

>>> import lucid
>>> from lucid.distributions.transforms import PowerTransform
>>> T = PowerTransform(exponent=2.0)
>>> T(lucid.tensor(3.0))  # 3² = 9
Tensor(9.0)

Methods (2)

dunder

init

→None

__init__(exponent: Tensor | float)

source

Store the (element-wise) power exponent.

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source

$\log|\partial y/\partial x| = \log|\text{exponent}| + (\text{exponent} - 1)\log x$ .