2D-Automatic-Differentation: C++ Forward-Mode Automatic Differentation Library

A high-performance, header-only C++ library for Forward-Mode Automatic Differentation(AD). The lib uses Jet propagation (an extension of dual numbers) to simultaneously compute the function's value and its exact first and second-order partial derivatives.

Key features

• Header-only Architecture: The mathematical logic resides entirely in jet.hpp, allowing the compiler to perform aggressive optimizations (inline) and eliminating function-call overhead.
• Full Hessian Matrix: Computes all second-order partial derivatives for functions of two variables.
• Operator Overloading: The mathematical code looks natural. It supports addition, subtraction, multiplication, and division between Jets and scalars.
• Elementary Functions: Built-in support for sin(x), cos(x), and exp(x), along with their propagation to higher-order derivatives via the Chain Rule.

Project Structure

2D-automatic-differentation/
├── Makefile                # Build script for the application and tests
├── README.md               #
├── .gitignore              
├── include/
│   ├── jet.hpp             # CORE ENGINE: Jet structure and algebra
│   └── function.hpp        # Testing function definition
├── src/
│   └── main.cpp            # Entry point (CLI), handles I/O streams
└── tests/
    ├── test_jet.cpp        # Unit tests for Jet operations with assertions
    └── test_function.cpp   # Integration tests verified with Mathematica

Build & Run

This project uses make. It requires a compiles that supports the C++17 standard.

1. Clone the repository

git clone https://github.com/szampen/2D-automatic-differentation.git
cd 2D-automatic-differentation

2. Build the application

To compile the main program and all the tests, run the following command:

make all

3. Run the solver

The application expects data from standard input(stdin).

./autodiff_solver

Clean binaries

To remove all compiled executable files:

make clean

Input/Output format

This program calculates derivatives at specific points provided by user.

Input data:

The first line is the number of points N. The following M lines contain the coordinates x_i and y_i

4
0.0 1.0
1.0 -1.0
-2.0 2.0
10.0 0.1

Output data:

For each point, the program outputs 6-space separated values with 15-decimal precision: f, f_x, f_y, f_xx, f_xy, f_yy.

0.756802495307928 0.000000000000000 2.820892232343080 -0.550484746419296 0.000000000000000 6.742753957524750
...

How to define your own function?

To compute Jets for a new function, simply edit include/function.hpp file. The function must be defined as a template template<typename T>, which allows it to be evaluated using both standard double types and the Jet structures.

After updating the function, simply rebuild the project (make all). The gradient vector and Hessian matrix values will be automatically updated for every tested point.