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Many algorithms for scientific computation require second- or higher-order partial derivatives, which can be efficiently computed by a propagating a set of univariate Taylor series. We describe how to implement second-order mixed partial derivative computations in ADIFOR (Automatic Differentiation In FORtran), a Fortran-to-Fortran source transformation tool. Globally, we propagate three-term univariate Taylor series in the forward mode. Locally, we preaccumulate local gradients and Hessians for complicated expressions on the right-hand sides of assignment statements. We describe the source transformations and give an example of the transformed code.

ADIFOR working note No. 8: Hybrid evaluation of second derivatives in ADIFOR