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 = "0.7"

Example

Python

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

from num_dual import second_derivative
import numpy as np

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

f, df, d2f = second_derivative(f, 1.5)

print(f'f(x)    = {f}')
print(f'df/dx   = {df}')
print(f'd2f/dx2 = {d2f}')

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 using dual numbers
    let x_dual = Dual64::from(x).derivative();
    let y_dual = Dual64::from(y);
    println!("{}", f(x_dual, y_dual)); // 2000 + [1200]ε

    // or use the provided function instead
    let (_, df) = first_derivative(|x| f(x, y.into()), x);
    println!("{df}"); // 1200

    // Calculate a gradient
    let (value, grad) = gradient(|v| f(v[0], v[1]), SMatrix::from([x, y]));
    println!("{value} {grad}"); // 2000 [1200, 1000]

    // Calculate a Hessian
    let (_, _, hess) = hessian(|v| f(v[0], v[1]), SMatrix::from([x, y]));
    println!("{hess}"); // [[480, 600], [600, 250]]

    // for x=cos(t) and y=sin(t) calculate the third derivative w.r.t. t
    let (_, _, _, d3f) = third_derivative(|t| f(t.cos(), t.sin()), 1.0);
    println!("{d3f}"); // 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}
}

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distributions

No source distribution files available for this release.See tutorial on generating distribution archives.

Built Distributions

If you're not sure about the file name format, learn more about wheel file names.

The dropdown lists show the available interpreters, ABIs, and platforms. Enable javascript to be able to filter the list of wheel files.

num_dual-0.7.1-cp37-abi3-win_amd64.whl (2.8 MB view details)

Uploaded May 31, 2023 CPython 3.7+Windows x86-64

num_dual-0.7.1-cp37-abi3-win32.whl (2.7 MB view details)

Uploaded May 31, 2023 CPython 3.7+Windows x86

num_dual-0.7.1-cp37-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (3.1 MB view details)

Uploaded May 31, 2023 CPython 3.7+manylinux: glibc 2.17+ x86-64

num_dual-0.7.1-cp37-abi3-macosx_10_9_x86_64.macosx_11_0_arm64.macosx_10_9_universal2.whl (5.3 MB view details)

Uploaded May 31, 2023 CPython 3.7+macOS 10.9+ universal2 (ARM64, x86-64)macOS 10.9+ x86-64macOS 11.0+ ARM64

num_dual-0.7.1-cp37-abi3-macosx_10_7_x86_64.whl (2.8 MB view details)

Uploaded May 31, 2023 CPython 3.7+macOS 10.7+ x86-64

File details

Details for the file num_dual-0.7.1-cp37-abi3-win_amd64.whl.

File metadata

Download URL: num_dual-0.7.1-cp37-abi3-win_amd64.whl
Upload date: May 31, 2023
Size: 2.8 MB
Tags: CPython 3.7+, Windows x86-64
Uploaded using Trusted Publishing? No
Uploaded via: twine/4.0.2 CPython/3.9.16

File hashes

Hashes for num_dual-0.7.1-cp37-abi3-win_amd64.whl
Algorithm	Hash digest
SHA256	`b336b8175cd035392d1ab7673cf00b6ce624c8074a007a35e6ec3a470f122c81`
MD5	`97d9260f35cdf8870986a19954185fa7`
BLAKE2b-256	`577214eaa07a5e2b242ebafb7666d9ffd954c9fe30ff04bcb303645cc9269f28`

See more details on using hashes here.

File details

Details for the file num_dual-0.7.1-cp37-abi3-win32.whl.

File metadata

Download URL: num_dual-0.7.1-cp37-abi3-win32.whl
Upload date: May 31, 2023
Size: 2.7 MB
Tags: CPython 3.7+, Windows x86
Uploaded using Trusted Publishing? No
Uploaded via: twine/4.0.2 CPython/3.9.16

File hashes

Hashes for num_dual-0.7.1-cp37-abi3-win32.whl
Algorithm	Hash digest
SHA256	`a9ac5bb3d2608a7d1a9ecc7daa2660da9f3ef39f4e5f75161b0e19b40841a662`
MD5	`a57c395a0ebeceb6881e358c41fb84d8`
BLAKE2b-256	`5995c973dd31c3065d3a6156eedbcd52f9b983aade4e2b59e765b13968415b24`

See more details on using hashes here.

File details

Details for the file num_dual-0.7.1-cp37-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.

File metadata

Download URL: num_dual-0.7.1-cp37-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
Upload date: May 31, 2023
Size: 3.1 MB
Tags: CPython 3.7+, manylinux: glibc 2.17+ x86-64
Uploaded using Trusted Publishing? No
Uploaded via: twine/4.0.2 CPython/3.9.16

File hashes

Hashes for num_dual-0.7.1-cp37-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
Algorithm	Hash digest
SHA256	`493df16ae149e25b2e3b05967225bc76b8441c960665c0249b386400989b42a1`
MD5	`09a321396ae15dd7218903bd4b184983`
BLAKE2b-256	`e7f8853e14dd96b743b76afff6aa5c917f18eb7de2c82cae25986096ff911b72`

See more details on using hashes here.

File details

Details for the file num_dual-0.7.1-cp37-abi3-macosx_10_9_x86_64.macosx_11_0_arm64.macosx_10_9_universal2.whl.

File metadata

Download URL: num_dual-0.7.1-cp37-abi3-macosx_10_9_x86_64.macosx_11_0_arm64.macosx_10_9_universal2.whl
Upload date: May 31, 2023
Size: 5.3 MB
Tags: CPython 3.7+, macOS 10.9+ universal2 (ARM64, x86-64), macOS 10.9+ x86-64, macOS 11.0+ ARM64
Uploaded using Trusted Publishing? No
Uploaded via: twine/4.0.2 CPython/3.9.16

File hashes

Hashes for num_dual-0.7.1-cp37-abi3-macosx_10_9_x86_64.macosx_11_0_arm64.macosx_10_9_universal2.whl
Algorithm	Hash digest
SHA256	`c349bab5997931eecc37254ee70ae60dcea8124661687feb6fcdd27709eafbb1`
MD5	`2d86994f19b5199116880b83108c6400`
BLAKE2b-256	`3e202cfbb3fb91623099400a1d4f253acbc8f64f1ae926c327773cdb4c1fddfe`

See more details on using hashes here.

File details

Details for the file num_dual-0.7.1-cp37-abi3-macosx_10_7_x86_64.whl.

File metadata

Download URL: num_dual-0.7.1-cp37-abi3-macosx_10_7_x86_64.whl
Upload date: May 31, 2023
Size: 2.8 MB
Tags: CPython 3.7+, macOS 10.7+ x86-64
Uploaded using Trusted Publishing? No
Uploaded via: twine/4.0.2 CPython/3.9.16

File hashes

Hashes for num_dual-0.7.1-cp37-abi3-macosx_10_7_x86_64.whl
Algorithm	Hash digest
SHA256	`526415d01042a1cf7d314f2f8a0e0e38aae197e2738d06a361d81b49fe161ad1`
MD5	`c4a99c24af14cb4253d1a5676ff9ecbd`
BLAKE2b-256	`b2e883aa8cfe1c171267296fffaab8c7979672fc5a285c4a874344aaa84fbf89`