Solves automatic numerical differentiation problems in one or more variables.

## Project description

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:* Compute the derivatives of order 1 through 4 on any scalar function.

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

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

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

*Hessdiag:* Compute only the diagonal elements of the Hessian matrix

All of these methods also produce error estimates on the result. The documentation for these tools are given at http://numdifftools.readthedocs.org.

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

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