numdifftools

https://pypip.in/d/numdifftools/badge.png

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.])

Release files for numdifftools 0.7.7

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Source distribution (sdist)

Source distribution for numdifftools 0.7.7
File	Size	Uploaded
numdifftools-0.7.7.zip	181.5 kB	Dec 17, 2014	Details

Built distribution (wheel)

Table of built distributions (wheels) for numdifftools 0.7.7
File	Interpreter	ABI	Platform	Reset
numdifftools-0.7.7.win32.exe 223.1 kB Dec 17, 2014				Details

Total release size: 404.6 kB

Release files / numdifftools-0.7.7.zip

Download URL	numdifftools-0.7.7.zip
Size	181.5 kB
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SHA-256 checksum How to use checksums	`c5a309a7a0b58f6177dc7e3d55c2830c07ca2715c9c706644d500fc4eca97c4d`
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Release files / numdifftools-0.7.7.win32.exe

Download URL	numdifftools-0.7.7.win32.exe
Size	223.1 kB
Tags	Source
SHA-256 checksum How to use checksums	`2a9fa00e33a3d5ff8576f017c5e7abafdc51278ad88861e1b9640c7ccf5e1d99`
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Upload date	Dec 17, 2014
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