scipy.misc.derivative for multiple argument function

Question

It is straightforward to compute the partial derivatives of a function at a point with respect to the first argument using the SciPy function scipy.misc.derivative

Answer 1

Here is an answer for numerical differentiation using numdifftools.

import numpy as np
import numdifftools as nd

def partial_function(f___,input,pos,value):
    tmp  = input[pos]
    input[pos] = value
    ret = f___(*input)
    input[pos] = tmp
    return ret

def partial_derivative(f,input):
    ret = np.empty(len(input))
    for i in range(len(input)):
        fg = lambda x:partial_function(f,input,i,x)
        ret[i] = nd.Derivative(fg)(input[i])
    return ret

Then:

print (partial_derivative(lambda x,y: x*x*x+y*y,np.array([1.0,1.0])))

Gives:

[ 3.  2.]