njet: Lightweight automatic differentiation

A lightweight AD package, using forward-mode automatic differentiation, in order to determine the higher-order derivatives of a given function in several variables.

Features

Higher-order (forward-mode) automatic differentiation in several variables.
Support for NumPy, SymPy and mpmath.
Differentiation of expressions containing nested higher-order derivatives.
Complex differentiation (Wirtinger calculus) possible.
Faa di Bruno's formula for vector-valued functions implemented.
Lightweight and easy to use.

Installation

Install this module with pip

pip install njet

Quickstart

An example function we want to differentiate

from njet.functions import exp
f = lambda x, y, z: exp(-0.23*x**2 - 0.33*x*y - 0.11*z**2)

Generate a class to handle the derivatives of the given function (in this example up to order 3)

from njet import derive
df = derive(f, order=3)

Evaluate the derivatives at a specific point

df(0.4, 2.1, 1.73)

{(0, 0, 0): 0.5255977986928584,
 (0, 0, 1): -0.2000425221825019,
 (1, 0, 0): -0.46094926945363685,
 (0, 1, 0): -0.06937890942745731,
 (0, 0, 2): -0.03949533176976862,
 (0, 2, 0): 0.009158016044424365,
 (1, 0, 1): 0.1754372919540542,
 (0, 1, 1): 0.026405612928090252,
 (2, 0, 0): 0.1624775219121247,
 (1, 1, 0): -0.11260197000076322,
 (2, 1, 0): 0.2827794849469999,
 (1, 1, 1): 0.04285630978229049,
 (0, 1, 2): 0.005213383793609458,
 (0, 2, 1): -0.0034855409065079135,
 (0, 3, 0): -0.0012088581178640162,
 (3, 0, 0): 0.2815805411804125,
 (2, 0, 1): -0.061838944839754675,
 (0, 0, 3): 0.10305063303187477,
 (1, 2, 0): 0.03775850015116166,
 (1, 0, 2): 0.034637405962087094}

The indices here correspond to the powers of the variables x, y, z in the multivariate Taylor expansion. They can be translated to the tensor indices of the corresponding multilinear map using a built-in routine. Example:

Obtain the gradient and the Hessian

df.grad()

{(2,): -0.2000425221825019,
 (0,): -0.46094926945363685,
 (1,): -0.06937890942745731}

df.hess()

{(2, 2): -0.03949533176976862,
 (1, 1): 0.009158016044424365,
 (0, 2): 0.1754372919540542,
 (1, 2): 0.026405612928090252,
 (0, 0): 0.1624775219121247,
 (0, 1): -0.11260197000076322}

License

njet: Automatic Differentiation Library

njet is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

njet is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with njet. If not, see https://www.gnu.org/licenses/.

Metadata

Release files for njet 0.5.2

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

Source distribution (sdist)

Source distribution for njet 0.5.2
File	Size	Uploaded
njet-0.5.2.tar.gz	90.0 kB	May 2, 2023	Details

Built distribution (wheel)

Table of built distributions (wheels) for njet 0.5.2
File	Interpreter	ABI	Platform	Reset
njet-0.5.2-py3-none-any.whl 63.0 kB May 2, 2023	Python 3	none	any	Details

Total release size: 153.0 kB

Release files / njet-0.5.2.tar.gz

Download URL	njet-0.5.2.tar.gz
Size	90.0 kB
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SHA-256 checksum How to use checksums	`57f8678e6b4ee272dc88edf416a6975c5122a10a6f77fc06d6530e8cd647ea80`
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Uploaded via	`twine/3.1.1 pkginfo/1.4.2 requests/2.22.0 setuptools/45.2.0 requests-toolbelt/0.8.0 tqdm/4.30.0 CPython/3.8.10`

Release files / njet-0.5.2-py3-none-any.whl

Download URL	njet-0.5.2-py3-none-any.whl
Size	63.0 kB
Tags	Python 3
SHA-256 checksum How to use checksums	`ddd0223942113c27f2047a4cd0a61eae321ce5d8288cc1289fdf51c20ee048fb`
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Upload date	May 2, 2023
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Uploaded via	`twine/3.1.1 pkginfo/1.4.2 requests/2.22.0 setuptools/45.2.0 requests-toolbelt/0.8.0 tqdm/4.30.0 CPython/3.8.10`