xlog1py

→Tensor

xlog1py(x: Tensor, y: Tensor)

source

Safe product $x \log(1 + y)$ with limit-convention zero handling.

Computes $x \log(1 + y)$ element-wise but enforces the convention $0 \cdot \log(1 + 0) = 0$ , and more generally propagates the zero whenever $x = 0$ regardless of y. Mirrors lucid.xlogy but uses $\log(1 + y)$ instead of $\log y$ , which is the right primitive for log-densities of distributions expressed in terms of small offsets (Negative Binomial log-likelihood, Beta survival functions, etc.).

Parameters

xTensor

Multiplier tensor.

yTensor

Argument of log1p; broadcast-compatible with x.

Returns

Tensor

$x \log(1 + y)$ element-wise, broadcast to the common shape of x and y.

Notes

Mathematical definition with the limit convention:

\text{xlog1py}(x, y) = \begin{cases} 0, & x = 0 \\[2pt] x \log(1 + y), & \text{otherwise}. \end{cases}

Using $\log(1 + y)$ avoids precision loss for small y where 1 + y would round to 1.0.

Examples

>>> import lucid
>>> from lucid.special import xlog1py
>>> x = lucid.tensor([0.0, 1.0, 2.0])
>>> y = lucid.tensor([0.0, 1.0, 3.0])
>>> xlog1py(x, y)
Tensor([0.0000, 0.6931, 2.7726])