auto_deriv: Tool for automatic differentiation of a Fortran code

Abstract auto_deriv is a module comprised of a set of fortran 95 procedures which can be used to calculate the first and second partial derivatives (mixed or not) of any continuous function with many independent variables. The mathematical function should be expressed as one or more fortran 77/90/95 procedures. A new type of variables is defined and the overloading mechanism of functions and operators provided by the fortran 95 language is extensively used to define the differentiation rules. Proper (... Title of program: AUTO_DERIV Catalogue Id: ADLS_v2_0 Nature of problem The need to calculate accurate derivatives of a multivariate function frequently arises in computational physics and chemistry. The most versatile approach to evaluate them by a computer, automatically and to machine precision, is via user-defined types and operator overloading. AUTO_DERIV is a Fortran 95 implementation of them, designed to evaluate the first and second derivatives of a function of many variables. Versions of this program held in the CPC repository in Mendeley Data ADLS_v1_0; AUTO_DERIV; 10.1016/S0010-4655(99)00513-5 ADLS_v2_0; AUTO_DERIV; 10.1016/j.cpc.2010.06.043 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)### 摘要 auto_deriv模块由一组Fortran 95子程序构成，可用于计算任意多自变量连续函数的一阶、二阶偏导数（含混合偏导数）。待求解的数学函数需以一个或多个Fortran 77/90/95子程序的形式进行定义。本模块定义了一种新型变量，并充分利用Fortran 95语言提供的函数与运算符重载机制来构建求导规则。（原文此处截断） 程序标题：AUTO_DERIV 编目编号：ADLS_v2_0 问题背景 在计算物理与计算化学领域，时常需要求解多变量函数的精确导数。通过计算机自动求解并达到机器精度的最通用方案，是借助用户自定义类型与运算符重载机制。AUTO_DERIV即为该方案的Fortran 95实现，专为求解多变量函数的一阶、二阶偏导数而设计。 Mendeley Data收录的CPC程序库中该程序的版本： ADLS_v1_0; AUTO_DERIV; 10.1016/S0010-4655(99)00513-5 ADLS_v2_0; AUTO_DERIV; 10.1016/j.cpc.2010.06.043 本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019年）