scipy.special.

softplus

scipy.special.softplus(x, **kwargs)

Compute the softplus function element-wise.

The softplus function is defined as: softplus(x) = log(1 + exp(x)). It is a smooth approximation of the rectifier function (ReLU).

Parameters:

xarray_like

Input value.

**kwargs

For other keyword-only arguments, see the ufunc docs.

Returns:

softplusndarray

Logarithm of exp(0) + exp(x).

Notes

Array API Standard Support

softplus has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	✅	✅
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

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>>> from scipy import special

>>> special.softplus(0)
0.6931471805599453

>>> special.softplus([-1, 0, 1])
array([0.31326169, 0.69314718, 1.31326169])

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