Second-order adjoints by source code manipulation of numerical programs

U. Naumann, M. Maier, Jan Riehme, B. Christianson

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    The analysis and modification of numerical programs in the context of
    generating and optimizing adjoint code automatically probably ranges among the
    technically and theoretically most challenging source transformation algorithms
    known today. A complete compiler for the target language (Fortran in our case) is
    needed to cover the technical side. This amounts to a mathematically motivated
    semantic transformation of the source code that involves the reversal of the flow
    of data through the program. Both the arithmetic complexity and the memory
    requirement can be substantial for large-scale numerical simulations. Finding the
    optimal data-flow reveral schedule turns out to be an NP-complete problem. The
    same complexity result applies to other domain-specific peephole optimizations.
    In this paper we present a first research prototype of the NAGWare Fortran
    compiler with the ability to generate adjoint code automatically. Moreover, we
    discuss an approach to generating second-order adjoint code for use in Newtontype algorithms for unconstrained nonlinear optimization. While the focus of this paper is mostly on the compiler issues some information on the mathematical background will be found helpful for motivational purposes
    Original languageEnglish
    PublisherRWTH Aachen
    Number of pages17
    Publication statusPublished - 2007

    Publication series

    NameRWTH Aachen, Dept Comp Science, Technical report
    No.AIB TR 2007-13


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