TaylUR，Fortran 95的任意阶对角自动微分程序包
TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95
摘要：
我们提出了TaylUR，Fortran 95模块自动计算数值的复值函数的衍生物w.r.t.多个变量，每个变量的顺序任意，但不包括混合衍生物。算术运算符和Fortran内部函数被重载，以正确地作用于定义类型为“taylor”的对象，该类型将函数及其前几个导数w.r.t.用户自定义的独立变量。乘积和复合函数的导数使用莱布尼茨规则和Faa di Bruno公式计算。TaylUR大量使用运算符重载和其他面向对象的Fortran 95特性。
英文摘要：
We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives w.r.t. 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 defined type "taylor", which encodes a function along with its first few derivatives w.r.t. the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faa di Bruno's formula. TaylUR makes heavy use of operator overloading and other object-oriented Fortran 95 features.
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