pbrod/numdifftools

Indicates that a set of similar lines has been detected among multiple file. This usually means that the code should be refactored to avoid this duplication. ==numdifftools.ndscipy:[86:143] ==numdifftools.ndstatsmodels:[298:355] class Gradient(Jacobian): ``` Calculate Gradient with finite difference approximation

Parameters

fun : function function of one array fun(x, *args, **kwds) step : float, optional Stepsize, if None, optimal stepsize is used, i.e., x * _EPS for method==complex x * _EPS(1/2) for method==forward x * _EPS(1/3) for method==central. method : {'central', 'complex', 'forward', 'backward'} defines the method used in the approximation.

Examples

import numpy as np import numdifftools.nd_statsmodels as nd fun = lambda x: np.sum(x**2) dfun = nd.Gradient(fun) np.allclose(dfun([1,2,3]), [ 2., 4., 6.]) True

# At [x,y] = [1,1], compute the numerical gradient # of the function sin(x-y) + y*exp(x)

sin = np.sin; exp = np.exp z = lambda xy: sin(xy[0]-xy[1]) + xy[1]*exp(xy[0]) dz = nd.Gradient(z) grad2 = dz([1, 1]) np.allclose(grad2, [ 3.71828183, 1.71828183]) True

# At the global minimizer (1,1) of the Rosenbrock function, # compute the gradient. It should be essentially zero.

rosen = lambda x : (1-x[0])2 + 105.*(x[1]-x[0]2)**2 rd = nd.Gradient(rosen) grad3 = rd([1,1]) np.allclose(grad3,[0, 0]) True

See also

Hessian, Jacobian ```

def call(self, x, args, *kwds): return super(Gradient, self).call(np.atleast_1d(x).ravel(), args, *kwds).squeeze()

if name == 'main': from numdifftools.testing import testdocstrings testdocstrings(file)

Indicates that a set of similar lines has been detected among multiple file. This usually means that the code should be refactored to avoid this duplication. ==numdifftools.finitedifference:[562:582] ==numdifftools.limits:[210:219] originalshape = np.shape(sequence[0]) fdel = np.vstack([np.ravel(r) for r in sequence]) one = np.ones(originalshape) h = np.vstack([np.ravel(one * step) for step in steps]) assert(fdel.size == h.size, 'fun did not return data of correct ' 'size (it must be vectorized)') return fdel, h, originalshape

def apply(self, sequence, steps, step_ratio=2.0): ``` Apply finite difference rule along the first axis.

Return derivative estimates of fun at x0 for a sequence of stepsizes h

Parameters

sequence: finite differences steps: steps

It is better to specify an encoding when opening documents. Using the system default implicitly can create problems on other operating systems. See https://peps.python.org/pep-0597/

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