TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95

Abstract
We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding mixed derivatives. Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and ...

Title of program: TaylUR
Catalogue Id: ADXR_v1_0

Nature of problem
Problems that require potentially high orders of derivatives with respect to some variables, such as e.g. expansions of Feynman diagrams in particle masses in perturbative Quantum Field Theory, and which cannot be treated using existing Fortran modules for automatic differentiation [1-2].

Versions of this program held in the CPC repository in Mendeley Data
ADXR_v1_0; TaylUR; 10.1016/j.cpc.2005.12.016
ADXR_v2_0; TaylUR; 10.1016/j.cpc.2007.03.008
ADXR_v3_0; TaylUR; 10.1016/j.cpc.2009.10.025

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要：本报告提出TaylUR，一款Fortran 95模块，旨在自动计算复值函数关于多个变量的导数，其阶数可任意设定，但不含混合导数。算术运算符与Fortran内建函数被重载，以便在定义类型taylor的对象上正确执行，该类型编码了函数及其对用户定义的独立变量的若干阶导数。该程序可用于计算乘积等运算的导数，……

程序名称：TaylUR
目录编号：ADXR_v1_0

问题性质：涉及对某些变量求高阶导数的问题，例如在微扰量子场论中费曼图的粒子质量展开，这些问题无法使用现有的自动微分Fortran模块进行处理[1-2]。

本程序在Mendeley数据中心的CPC程序库中保存的版本有：
ADXR_v1_0; TaylUR; 10.1016/j.cpc.2005.12.016
ADXR_v2_0; TaylUR; 10.1016/j.cpc.2007.03.008
ADXR_v3_0; TaylUR; 10.1016/j.cpc.2009.10.025

此程序已从贝尔法斯特女王大学（1969-2018年）所持有的CPC程序库中导入。