5.1.8.2. numdifftools.nd_statsmodels.Jacobian¶

class Jacobian(fun, step=None, method='central', order=None)[source]¶

Calculate Jacobian with finite difference approximation

Parameters

funfunction: function of one array fun(x, *args, **kwds)
stepfloat, 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

#(nonlinear least squares)

>>> xdata = np.arange(0,1,0.1)
>>> ydata = 1+2*np.exp(0.75*xdata)
>>> fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2
>>> np.allclose(fun([1, 2, 0.75]).shape, (10,))
True
>>> dfun = nd.Jacobian(fun)
>>> np.allclose(dfun([1, 2, 0.75]), np.zeros((10,3)))
True

>>> fun2 = lambda x : x[0]*x[1]*x[2]**2
>>> dfun2 = nd.Jacobian(fun2)
>>> np.allclose(dfun2([1.,2.,3.]), [[18., 9., 12.]])
True

>>> fun3 = lambda x : np.vstack((x[0]*x[1]*x[2]**2, x[0]*x[1]*x[2]))
>>> np.allclose(nd.Jacobian(fun3)([1., 2., 3.]), [[[18.], [9.], [12.]], [[6.], [3.], [2.]]])
True
>>> np.allclose(nd.Jacobian(fun3)([4., 5., 6.]),
...            [[[180.], [144.], [240.]], [[30.], [24.], [20.]]])
True

>>> np.allclose(nd.Jacobian(fun3)(np.array([[1.,2.,3.], [4., 5., 6.]]).T),
...            [[[  18.,  180.],
...              [   9.,  144.],
...              [  12.,  240.]],
...             [[   6.,   30.],
...              [   3.,   24.],
...              [   2.,   20.]]])
True

__init__(fun, step=None, method='central', order=None)¶

Methods

__init__(fun[, step, method, order])

Attributes

`method`
`n`
`order`