https://github.com/itt-ustutt/num-dual
Generalized (hyper-) dual numbers in rust
https://github.com/itt-ustutt/num-dual
automatic-differentiation numerical-methods python rust
Last synced: 4 months ago
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Generalized (hyper-) dual numbers in rust
- Host: GitHub
- URL: https://github.com/itt-ustutt/num-dual
- Owner: itt-ustutt
- License: apache-2.0
- Created: 2020-08-24T10:46:26.000Z (almost 6 years ago)
- Default Branch: master
- Last Pushed: 2026-01-13T14:53:06.000Z (5 months ago)
- Last Synced: 2026-01-14T00:59:05.873Z (5 months ago)
- Topics: automatic-differentiation, numerical-methods, python, rust
- Language: Rust
- Homepage:
- Size: 6.82 MB
- Stars: 81
- Watchers: 4
- Forks: 10
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: license-apache
Awesome Lists containing this project
README
# num-dual
[](https://crates.io/crates/num-dual)
[](https://docs.rs/num-dual)
[](https://rust-lang.github.io/rfcs/2495-min-rust-version.html)
[](https://itt-ustutt.github.io/num-dual/)
[](https://badge.fury.io/py/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
```
[//]: # "or from source (you need a rust compiler for that):"
[//]: # "```"
[//]: # "pip install git+https://github.com/itt-ustutt/num-dual"
[//]: # "```"
### Rust
Add this to your `Cargo.toml`:
```toml
[dependencies]
num-dual = "0.13"
```
## Example
### Python
Compute the first and second derivative of a scalar-valued function.
```python
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.
```rust
use num_dual::*;
use nalgebra::SMatrix;
fn f>(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 + 1200ε
// 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](https://docs.rs/num-dual/).
- The documentation of the python package can be found [here](https://itt-ustutt.github.io/num-dual/).
### 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.
## Further reading
If you want to learn more about the topic of dual numbers and automatic differentiation, we have listed some useful resources for you here:
- Initial paper about hyper-dual numbers: [Fike, J. and Alonso, J., 2011](https://arc.aiaa.org/doi/abs/10.2514/6.2011-886)
- Website about all topics regarding automatic differentiation: [autodiff.org](http://www.autodiff.org/)
- Our paper about dual numbers in equation of state modeling: [Rehner, P. and Bauer, G., 2021](https://www.frontiersin.org/article/10.3389/fceng.2021.758090)
## Cite us
If you find `num-dual` useful for your own scientific studies, consider [citing our publication](https://www.frontiersin.org/article/10.3389/fceng.2021.758090) 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}
}
```