skip to navigation
skip to content

Not Logged In

Numdifftools 0.5.0

Solves automatic numerical differentiation problems in one or more variables.

Latest Version: 0.6.0

Suite of tools to solve automatic numerical differentiation problems in one or more variables. 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)

Derivative:

A flexible tool for the computation of derivatives of order 1 through 4 on any scalar function. 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 of the options, changing the order of the method or the extrapolation, even allowing the user to specify whether central, forward or backward differences are used.

Gradient

Computes the gradient vector of a scalar function of one or more variables at any location.

Jacobian

Computes the Jacobian matrix of a vector (or array) 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

The diagonal elements of the Hessian matrix are the pure second order partial derivatives.

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

 
File Type Py Version Uploaded on Size
Numdifftools-0.5.0.win32.exe (md5) MS Windows installer any 2014-01-10 226KB
Numdifftools-0.5.0.zip (md5) Source 2014-01-10 181KB
  • Downloads (All Versions):
  • 28 downloads in the last day
  • 335 downloads in the last week
  • 2114 downloads in the last month