FADBAD/TADIFF
FADBAD is a C++ library which combines the two basic ways of applying the chain rule, namely forward and backward automatic differentiation. Both the forward and the backward differentiation methods use operator overloading to redefine the arithmetic operations, so that the program is capable of calculating first order derivatives. The only thing a user has to provide is the C++ program that performs the evaluation of the function. Since the computation of the derivatives is itself a C++ program, we can obtain higher order derivatives by building the forward and the backward automatic differentiation classes on top of each other. Using this approach, we can obtain derivatives of order p in 2^p different ways  hereby giving the possibility to minimize time/space usage of the computations by choosing the optimal combination of the algorithms. Depending, of course, on the function which we want to differentiate. 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. 
Current Version: 2.0/1.0
License Type: Free

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