`scipy.special._logsumexp:log_softmax`

source: /scipy/special/_logsumexp.py :350

Signature

def log_softmax ( x , axis = None )

Summary

Compute the logarithm of the softmax function.

Extended Summary

In principle

log_softmax(x) = log(softmax(x))

but using a more accurate implementation.

Parameters

x : array_like: Input array.
axis : int or tuple of ints, optional: Axis to compute values along. Default is None and softmax will be computed over the entire array x.

Returns

s : ndarray or scalar: An array with the same shape as x. Exponential of the result will sum to 1 along the specified axis. If x is a scalar, a scalar is returned.

Notes

log_softmax is more accurate than np.log(softmax(x)) with inputs that make softmax saturate (see examples below).

Array API Standard Support

log_softmax has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. 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 dev-arrayapi for more information.

Examples

import numpy as np
from scipy.special import log_softmax
from scipy.special import softmax
np.set_printoptions(precision=5)

✓

x = np.array([1000.0, 1.0])

✓

y = log_softmax(x)
y

✓

with np.errstate(divide='ignore'):
  y = np.log(softmax(x))
y