expm1

→Tensor

expm1(input: Tensor)

source edit

Element-wise $e^{x} - 1$ .

Computes the exponential-minus-one function to full relative precision, including for $|x| \ll 1$ , where exp(x) - 1 cancels: in float32 that naive form returned 1.19e-7 for x = 1e-7 (19% off) and 0 below it.

Parameters

inputTensor

Input tensor. Any floating-point dtype.

Returns

Tensor

Element-wise $e^{x} - 1$ .

Notes

Mathematical definition:

\text{out}_i = e^{x_i} - 1.

The function is useful in probability and finance where $x$ is a small log-difference, since log(1 + y) = expm1⁻¹(y) and the pair avoids subtractive cancellation when chained.

Examples

>>> import lucid
>>> x = lucid.tensor([0.0, 1.0, 2.0])
>>> lucid.expm1(x)
tensor([0., 1.718, 6.389])

expm1

→Tensor

expm1(input: Tensor)

source edit

Element-wise $e^{x} - 1$ .

Parameters

inputTensor

Input tensor. Any floating-point dtype.

Returns

Tensor

Element-wise $e^{x} - 1$ .

Notes

Mathematical definition:

\text{out}_i = e^{x_i} - 1.

The function is useful in probability and finance where $x$ is a small log-difference, since log(1 + y) = expm1⁻¹(y) and the pair avoids subtractive cancellation when chained.

Examples

>>> import lucid
>>> x = lucid.tensor([0.0, 1.0, 2.0])
>>> lucid.expm1(x)
tensor([0., 1.718, 6.389])