https://github.com/igorjakus/nomad
Numerical Optimization, Mathematics and Automatic Differentiation library in OCaml!🐫
https://github.com/igorjakus/nomad
automatic-differentiation gradient-descent mathematical-expressions mathematics numerical-methods numerical-optimization ocaml
Last synced: 9 months ago
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Numerical Optimization, Mathematics and Automatic Differentiation library in OCaml!🐫
- Host: GitHub
- URL: https://github.com/igorjakus/nomad
- Owner: igorjakus
- License: mit
- Created: 2024-12-14T11:58:01.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2025-01-29T23:14:27.000Z (about 1 year ago)
- Last Synced: 2025-07-06T14:42:38.439Z (10 months ago)
- Topics: automatic-differentiation, gradient-descent, mathematical-expressions, mathematics, numerical-methods, numerical-optimization, ocaml
- Language: OCaml
- Homepage:
- Size: 656 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Nomad
**N**umerical **O**ptimization, **M**athematics and **A**utomatic **D**ifferentiation library in OCaml!🐫
Nomad is a comprehensive OCaml library designed for symbolic expression manipulation and optimization. It provides functionalities for evaluating expressions, computing derivatives, and performing various optimization algorithms such as Gradient Descent, Newton-Raphson, and the Bisection method. This project serves as a practical assignment for the Functional Programming course at the University of Wrocław.
## Table of Contents
- [Features](#features)
- [Requirements](#requirements)
- [Installation](#installation)
- [Usage](#usage)
- [Testing](#testing)
- [Contributing](#contributing)
- [License](#license)
- [Acknowledgments](#acknowledgments)
## Features
- **Symbolic Expression Handling**
- Define and manipulate mathematical expressions symbolically.
- Simplify expressions using algebraic rules.
- Convert expressions to their string representations.
- **Evaluation and Environment Management**
- Evaluate expressions given a set of variable assignments.
- Update and manage environments for variable values.
- **Derivatives and Gradients**
- Compute first and higher-order derivatives of expressions.
- Calculate gradients for multivariable functions.
- **Optimization Algorithms**
- **Gradient Descent**: Optimize expressions by iteratively moving towards the minimum.
- **Newton-Raphson**: Solve equations using the Newton-Raphson method.
- **Bisection Method**: Find roots of continuous functions.
- **Comprehensive Testing**
- Robust test suite to ensure correctness of all functionalities.
## Requirements
- **OCaml**: Version 4.14.2 or newer
- **Dune**: Version 3.17.0 or newer
## Installation
1. **Install Dune**
```bash
opam install dune.3.17.0
```
2. **Clone the Repository**
```bash
git clone https://github.com/igorjakus/nomad.git
cd nomad
```
3. **Build project**
```bash
dune build
```
## Usage
### Evaluating Expressions
```ocaml
open Nomad.Expr
open Nomad.Eval
let x, y = Var "x", Var "y"
let env = [("x", 2.0); ("y", 3.0)]
let expression = x +: y
let result = eval env expression
(* result = 5.0 *)
```
### Simplifying Expressions
```ocaml
open Nomad.Expr
open Nomad.Simplify
let expr = x +: Float 0.
let simplified = simplify expr
(* simplified = x *)
```
### Computing Derivatives
```ocaml
open Nomad.Derivatives
let expr = x *: x
let derivative = derivative "x" expr
(* derivative = Float 2. *: x *)
```
### Performing Gradient Descent
```ocaml
open Nomad.Gradient_descent
let expr = x *: x +: y *: y
let initial_env = [("x", 1.0); ("y", 1.0)]
let learning_rate = 0.1
let result = gradient_descent ~expr ~env:initial_env ~learning_rate ~max_iter:100
```
## Testing
Nomad includes a comprehensive test suite to validate its functionalities. To run the tests, execute:
```bash
dune runtest
```
This will execute all test cases defined in the test.ml file, ensuring that each component behaves as expected.
## Contributing
Contributions are welcome! Please submit issues and pull requests for any enhancements or bug fixes.
1. Fork the repository.
2. Create a new branch: git checkout -b feature/YourFeature
3. Commit your changes: git commit -m 'Add some feature'
4. Push to the branch: git push origin feature/YourFeature
5. Submit a pull request.
## License
This project is licensed under the MIT License. See the [LICENSE](LICENSE) file for details.
## Acknowledgments
- Developed as part of the Functional Programming course at the University of Wrocław.
- Inspired by various symbolic mathematics and optimization libraries.