Softmax in Python

softmax.py

#! /usr/bin/env python
"""
Author: Jeremy M. Stober
Program: SOFTMAX.PY
Date: Wednesday, February 29 2012
Description: Simple softmax function.
"""

import numpy as np
npa = np.array

def softmax(w, t = 1.0):
    e = np.exp(npa(w) / t)
    dist = e / np.sum(e)
    return dist

if __name__ == '__main__':

    w = np.array([0.1,0.2])
    print softmax(w)

    w = np.array([-0.1,0.2])
    print softmax(w)

    w = np.array([0.9,-10])
    print softmax(w)

alex2awesome,

%timeit softmax(w)
The slowest run took 4.66 times longer than the fastest. This could mean that an intermediate result is being cached.
100000 loops, best of 3: 9.41 µs per loop

%timeit softmax_2(w)
The slowest run took 6.51 times longer than the fastest. This could mean that an intermediate result is being cached.
100000 loops, best of 3: 10.9 µs per loop

But it can for some be better, because in some cases "softmax" breaks because of too high values when "softmax_2" lives on.

import numpy as np
space = np.linspace(-0, 300000000000, n)
softmax_2(space)

will survive while softmax will be dead even after

import numpy as np
space = np.linspace(-0, 3000, 10)
softmax(space)

So I would indeed highly recommend to use your softmax_2 function instead.

Adapting for 2-d array input x

def softmax(x):
    if x.ndim == 1:
        x = x.reshape([1, x.size])
    softmaxInvx = x -  np.max(x, 1).reshape([x.shape[0],1]);
    matExp = np.exp(softmaxInvx)
return `matExp/np.sum(matExp,axis=1).reshape([matExp.shape[0],1]);

Vote for @piyushbhardwaj

A clearer version with doctest:

def softmax(x):
    '''
    >>> res = softmax(np.array([0, 200, 10]))
    >>> np.sum(res)
    1.0
    >>> np.all(np.abs(res - np.array([0, 1, 0])) < 0.0001)
    True
    >>> res = softmax(np.array([[0, 200, 10], [0, 10, 200], [200, 0, 10]]))
    >>> np.sum(res, axis=1)
    array([ 1.,  1.,  1.])
    >>> res = softmax(np.array([[0, 200, 10], [0, 10, 200]]))
    >>> np.sum(res, axis=1)
    array([ 1.,  1.])
    '''
    if x.ndim == 1:
        x = x.reshape((1, -1))
    max_x = np.max(x, axis=1).reshape((-1, 1))
    exp_x = np.exp(x - max_x)
    return exp_x / np.sum(exp_x, axis=1).reshape((-1, 1))

labels = [0, 0, 0, 0, 0.68, 0.32, 0, 0, 0, 0]

%timeit softmax = np.exp([element for element in labels]) / np.sum(np.exp([element for element in labels]))
The slowest run took 5.03 times longer than the fastest. This could mean that an intermediate result is being cached.
100000 loops, best of 3: 12.2 µs per loop

It can be simple one liner.

def softmax(x):
return np.exp(x)/np.sum(np.exp(x),axis=0)