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.
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}
Further reading¶
https://njet.readthedocs.io/en/latest/index.html
License¶
njet: Automatic Differentiation Library
Copyright (C) 2021, 2022, 2023 by Malte Titze
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/.