papyri
{ } Raw JSON

bundles / scipy latest / scipy / optimize / _optimize / approx_fprime

function

scipy.optimize._optimize:approx_fprime

source: /scipy/optimize/_optimize.py :970

Signature

def   approx_fprime ( xk ,  f ,  epsilon = 1.4901161193847656e-08 ,  * args )

Summary

Finite difference approximation of the derivatives of a scalar or vector-valued function.

Extended Summary

If a function maps from to , its derivatives form an m-by-n matrix called the Jacobian, where an element is a partial derivative of f[i] with respect to xk[j].

Parameters

xk : array_like

The coordinate vector at which to determine the gradient of f.

f : callable

Function of which to estimate the derivatives of. Has the signature f(xk, *args) where xk is the argument in the form of a 1-D array and args is a tuple of any additional fixed parameters needed to completely specify the function. The argument xk passed to this function is an ndarray of shape (n,) (never a scalar even if n=1). It must return a 1-D array_like of shape (m,) or a scalar.

Suppose the callable has signature f0(x, *my_args, **my_kwargs), where my_args and my_kwargs are required positional and keyword arguments. Rather than passing f0 as the callable, wrap it to accept only x; e.g., pass fun=lambda x: f0(x, *my_args, **my_kwargs) as the callable, where my_args (tuple) and my_kwargs (dict) have been gathered before invoking this function.

epsilon : {float, array_like}, optional

Increment to xk to use for determining the function gradient. If a scalar, uses the same finite difference delta for all partial derivatives. If an array, should contain one value per element of xk. Defaults to sqrt(np.finfo(float).eps), which is approximately 1.49e-08.

\*args : args, optional

Any other arguments that are to be passed to f.

Returns

jac : ndarray

The partial derivatives of f to xk.

Notes

The function gradient is determined by the forward finite difference formula 

         f(xk[i] + epsilon[i]) - f(xk[i])
f'[i] = ---------------------------------
                    epsilon[i]

Examples

import numpy as np
from scipy import optimize
def func(x, c0, c1):
    "Coordinate vector `x` should be an array of size two."
    return c0 * x[0]**2 + c1*x[1]**2
✓
x = np.ones(2)
c0, c1 = (1, 200)
eps = np.sqrt(np.finfo(float).eps)
✓
optimize.approx_fprime(x, func, [eps, np.sqrt(200) * eps], c0, c1)
✗

See also

check_grad

Check correctness of gradient function against approx_fprime.

Aliases

  • scipy.optimize.approx_fprime

Referenced by

This package