numdifftools 0.7.3

Solves automatic numerical differentiation problems in one or more variables.

Suite of tools written in Python to solve automatic numerical differentiation problems in one or more variables. Finite differences are used in an adaptive manner, coupled with a Romberg extrapolation methodology to provide a maximally accurate result. The user can configure many options like; changing the order of the method or the extrapolation, even allowing the user to specify whether central, forward or backward differences are used. The methods provided are:

Derivative: Computate derivatives of order 1 through 4 on any scalar function.

Gradient: Computes the gradient vector of a scalar function of one or more variables.

Jacobian: Computes the Jacobian matrix of a vector valued function of one or more variables.

Hessian: Computes the Hessian matrix of all 2nd partial derivatives of a scalar function of one or more variables.

Hessdiag: Computes only the diagonal elements of the Hessian matrix

All of these methods also produce error estimates on the result. A pdf file is also provided to explain the theory behind these tools.

To test if the toolbox is working paste the following in an interactive python session:

import numdifftools as nd
nd.test(coverage=True, doctests=True)

Examples

Compute 1’st and 2’nd derivative of exp(x), at x == 1:

>>> import numpy as np
>>> import numdifftools as nd
>>> fd = nd.Derivative(np.exp)              # 1'st derivative
>>> fdd = nd.Derivative(np.exp, n=2)  # 2'nd derivative
>>> fd(1)
array([ 2.71828183])

Nonlinear least squares:

>>> xdata = np.reshape(np.arange(0,1,0.1),(-1,1))
>>> ydata = 1+2*np.exp(0.75*xdata)
>>> fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2
>>> Jfun = nd.Jacobian(fun)
>>> np.abs(Jfun([1,2,0.75])) < 1e-14 # should be numerically zero
array([[ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True]], dtype=bool)

Compute gradient of sum(x**2):

>>> fun = lambda x: np.sum(x**2)
>>> dfun = nd.Gradient(fun)
>>> dfun([1,2,3])
array([ 2.,  4.,  6.])

See also

scipy.misc.derivative