TADIFF, A Flexible C++ Package for Automatic Differentiation, Using Taylor Series Expansion

Claus Bendtsen and Ole Stauning

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TADIFF is a C++ program package for performing Taylor expansions on functions implemented as C++ programs. Using Taylor expansion we calculate several orders of derivatives with respect to one variable. This is actually also possible using FADBAD, but since FADBAD was designed to compute one order of derivatives at a time with respect to several variables, it is not optimal to use it for performing Taylor expansions. The TADIFF package works by overloading the arithmetic operations, used in the function evaluation. This overloading will ``record'' the dependencies of the variables used in the program so that a representation of the actual computation performed is available after the function evaluation. This recording can then be used to compute the Taylor expansion of the function, expanded in the point of evaluation with respect to one of the input variables.

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IMM Technical Report 7/97

Last modified April 15, 1997

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