class

ExpTransform

extendsTransform

ExpTransform()

source

Element-wise exponential bijection $y = e^x$ .

Maps $\mathbb{R} \to (0, \infty)$ element-wise; composed with a Normal base distribution it yields a LogNormal. Monotone increasing, bijective, event_dim = 0.

Notes

Forward: $y = e^x$ .

Inverse: $x = \log y$ (defined for $y > 0$ ).

Log Jacobian determinant (element-wise):

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

since $|dy/dx| = e^x$ .

Examples

>>> import lucid
>>> from lucid.distributions.transforms import ExpTransform
>>> T = ExpTransform()
>>> x = lucid.tensor(0.0)
>>> y = T(x)
>>> T.log_abs_det_jacobian(x, y)
Tensor(0.0)

Methods (1)

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source

$\log|\partial y/\partial x| = x$ since $|dy/dx| = e^x$ .