DNAODD

Generalized dual numbers for efficient computation of arbitrary-order directional derivatives in multiple directions

This repository provides a Fortran implementation for the efficient computation of arbitrary-order directional derivatives in multiple directions using generalized dual numbers.

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Overview

This project implements a generalized dual number framework for computing directional derivatives of arbitrary order along multiple directions. The approach is designed to be efficient and scalable, making it suitable for applications in kinematics, optimization, and automatic differentiation.

The implementation supports the computation of directional derivatives of arbitrary order along multiple independent directions, based on a generalized dual number algebra.

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📁 Project Structure

• src/ --- Fortran source modules
• app/ --- Executable programs
• docs/ --- Additional documentation and API descriptions
• fpm.toml --- Project configuration file

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📦 Requirements

• A Fortran compiler, such as gfortran or ifx
• A recent version of fpm is recommended

To install fpm, visit:

👉 https://github.com/fortran-lang/fpm

Although this project is designed to be built conveniently with fpm, the use of fpm is not strictly required. If fpm is not used, the source files must be compiled and linked manually in the correct order, taking into account the module dependencies among the Fortran source files. In addition, preprocessor flags (e.g., -cpp, -DUSE_REAL128, -DMAX_ORDER_DUALZN=<N>) may be required depending on the desired configuration.

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🛠️ Building with fpm (default: real64)

From the project root:

fpm build

For example, using Intel Fortran:

FPM_FC=ifx fpm build

Quadruple precision

To enable quadruple precision (real128), compile with:

fpm run --flag "-DUSE_REAL128" <executable_name>

For example:

fpm run --flag "-DUSE_REAL128" partialD_fun

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▶️ Running Examples

By default, MAX_ORDER_DUALZN = 5.

The example EA1 requires a minimum order of 7:

fpm run --flag "-DMAX_ORDER_DUALZN=7" EA1

Other examples can be executed directly, for instance:

fpm run RCR_KQs

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Notes

• The maximum derivative order is controlled at compile time via the MAX_ORDER_DUALZN flag.
• Increasing this value allows higher-order derivatives but may increase memory usage and computational cost.

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Status

This repository is under active development and is intended to support a research article currently in preparation and submission.