Combining source transformation and operator overloading techniques to compute derivatives for MATLAB programs

Proceedings. Second IEEE International Workshop on Source Code Analysis and Manipulation Pub Date : 2002-10-01 DOI:10.1109/SCAM.2002.1134106

C. Bischof, H. M. Bücker, B. Lang, A. Rasch, A. Vehreschild

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引用次数: 114

Abstract

Derivatives of mathematical functions play a key role in various areas of numerical and technical computing. Many of these computations are done in MATLAB, a popular environment for technical computing providing engineers and scientists with capabilities for mathematical computing, analysis, visualization, and algorithmic development. For functions written in the MATLAB language, a novel software tool is proposed to automatically transform a given MATLAB program into another MATLAB program capable of computing not only the original function but also user-specified derivatives of that function. That is, a program transformation known as automatic differentiation is performed to change the semantics of the program in a fashion based on the chain rule of differential calculus. The crucial ingredient of the tool is a combination of source-to-source transformation and operator overloading. The overall design of the tool is described and numerical experiments are reported demonstrating the efficiency of the resulting code for a sample problem.

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结合源变换和算子重载技术计算MATLAB程序的导数

数学函数的导数在数值计算和技术计算的各个领域发挥着关键作用。这些计算中的许多都是在MATLAB中完成的，这是一个流行的技术计算环境，为工程师和科学家提供数学计算、分析、可视化和算法开发的能力。对于用MATLAB语言编写的函数，提出了一种新的软件工具，可以将给定的MATLAB程序自动转换为另一个MATLAB程序，该程序不仅可以计算原函数，还可以计算用户指定的该函数的导数。也就是说，执行一种称为自动微分的程序转换，以基于微分的链式法则的方式改变程序的语义。该工具的关键成分是源到源转换和操作符重载的组合。描述了该工具的总体设计，并报告了数值实验，证明了生成的代码对一个示例问题的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings. Second IEEE International Workshop on Source Code Analysis and Manipulation

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