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Automatic adjoints

Computers are not only able to perform computations; they can do mathematics. Well-known software is Mathematica and Maple. Adjoints can also be done by symbol manipulation. For example, Ralf Giering offers a program for converting linear operator programs into their adjoints. Actually, it does even more. He says:[*]
Given a Fortran routine (or collection of routines) for a function, TAMC produces Fortran routines for the computation of the derivatives of this function. The derivatives are computed in the reverse mode (adjoint model) or in the forward mode (tangent-linear model). In both modes Jacobian-Matrix products can be computed.