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. Here is an example:

def foo(x, y):
  return(x**2 + y**3)

from scipy.misc import derivative
derivative(foo, 1, dx = 1e-6, args = (3, ))

But how would I go about taking the derivative of the function foo with respect to the second argument? One way I can think of is to generate a lambda function that rejigs the arguments around, but that can quickly get cumbersome.

Also, is there a way to generate an array of partial derivatives with respect to some or all of the arguments of a function?

what is the role of the args in the derivative() function? – laszlopanaflex Aug 30 '18 at 00:47 — laszlopanaflex, Aug 30 '18 at 00:47

score 22 · Accepted Answer · answered Dec 20 '13 at 17:05

22

I would write a simple wrapper, something along the lines of

def partial_derivative(func, var=0, point=[]):
    args = point[:]
    def wraps(x):
        args[var] = x
        return func(*args)
    return derivative(wraps, point[var], dx = 1e-6)

Demo:

>>> partial_derivative(foo, 0, [3,1])
6.0000000008386678
>>> partial_derivative(foo, 1, [3,1])
2.9999999995311555

answered Dec 20 '13 at 17:05

alko

46,136
12
94
102

1

That's nice, and I can put them together as a vector of partial derivatives, but would have thought that between SciPy and SymPy, one of them would implement this. What I was looking for is the functionality provided by the R `deriv` function. – tchakravarty Dec 20 '13 at 21:37
@fgnu not well acquinted with R, can you link to docs for `deriv` – alko Dec 20 '13 at 21:38
[Here you go](http://stat.ethz.ch/R-manual/R-patched/library/stats/html/deriv.html). To quote the manual "It returns a call for computing the expr _and its (partial) derivatives, simultaneously._" – tchakravarty Dec 20 '13 at 21:39

score 2 · Answer 2 · answered Apr 07 '14 at 01:14

2

Yes, it is implemented in sympy. Demo:

>>> from sympy import symbols, diff
>>> x, y = symbols('x y', real=True)
>>> diff( x**2 + y**3, y)
3*y**2
>>> diff( x**2 + y**3, y).subs({x:3, y:1})
3

answered Apr 07 '14 at 01:14

eseprimo

49
2

score 0 · Answer 3 · answered Aug 04 '15 at 15:55

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.]

scipy.misc.derivative for multiple argument function

3 Answers3

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