num-dual

Generalized, recursive, scalar and vector (hyper) dual numbers for the automatic and exact calculation of (partial) derivatives. Including bindings for python.

Installation and Usage

Python

The python package can be installed directly from PyPI:

pip install num_dual

Rust

Add this to your Cargo.toml:

[dependencies]
num-dual = "0.5"

Example

Python

Compute the first and second derivative of a scalar-valued function.

from num_dual import derive2
import numpy as np

def f(x):
    return np.exp(x) / np.sqrt(np.sin(x)**3 + np.cos(x)**3)

x = derive2(1.5)
result = f(x)
print('f(x)    = {}'.format(result.value))
print('df/dx   = {}'.format(result.first_derivative))
print('d2f/dx2 = {}'.format(result.second_derivative))

Rust

This example defines a generic function that can be called using any (hyper) dual number and automatically calculates derivatives.

use num_dual::*;
fn f<D: DualNum<f64>>(x: D, y: D) -> D {
    x.powi(3) * y.powi(2)
}
fn main() {
    let (x, y) = (5.0, 4.0);
    // Calculate a simple derivative
    let x_dual = Dual64::from(x).derive();
    let y_dual = Dual64::from(y);
    println!("{}", f(x_dual, y_dual));                      // 2000 + [1200]ε
    // Calculate a gradient
    let xy_dual_vec = StaticVec::new_vec([x,y]).map(DualVec64::<2>::from).derive();
    println!("{}", f(xy_dual_vec[0], xy_dual_vec[1]).eps);  // [1200, 1000]
    // Calculate a Hessian
    let xy_dual2 = StaticVec::new_vec([x,y]).map(Dual2Vec64::<2>::from).derive();
    println!("{}", f(xy_dual2[0], xy_dual2[1]).v2);         // [[480, 600], [600, 250]]
    // for x=cos(t) and y=sin(t) calculate the third derivative w.r.t. t
    let t = Dual3_64::from(1.0).derive();
    println!("{}", f(t.cos(), t.sin()).v3);                 // 7.358639755305733
}

Documentation

You can find the documentation of the rust crate here.
The documentation of the python package can be found here.

Python

For the following commands to work you have to have the package installed (see: installing from source).

cd docs
make html

Open _build/html/index.html in your browser.

Cite us

If you find num-dual useful for your own scientific studies, consider citing our publication accompanying this library.

@ARTICLE{rehner2021,
    AUTHOR={Rehner, Philipp and Bauer, Gernot},
    TITLE={Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling},
    JOURNAL={Frontiers in Chemical Engineering},
    VOLUME={3},
    YEAR={2021},
    URL={https://www.frontiersin.org/article/10.3389/fceng.2021.758090},
    DOI={10.3389/fceng.2021.758090},
    ISSN={2673-2718}
}

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