TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

TL;DR

TaylUR 3 is an advanced Fortran 95 package that automatically computes complex-valued functions' derivatives up to any order, including mixed derivatives, with a new core for improved performance.

Contribution

This paper introduces TaylUR 3, a significantly improved version with a new core capable of arbitrary-order multivariate derivatives, enhancing flexibility and computational capabilities.

Findings

Supports derivatives of any order, including mixed derivatives.

Provides accurate numerical derivatives for complex-valued functions.

Improves computational efficiency over previous versions.

Abstract

This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives.