Read e-book online Advances in Automatic Differentiation PDF

By Adrian Sandu (auth.), Christian H. Bischof, H. Martin Bücker, Paul Hovland, Uwe Naumann, Jean Utke (eds.)

This assortment covers advances in computerized differentiation idea and perform. computing device scientists and mathematicians will find out about fresh advancements in automated differentiation conception in addition to mechanisms for the development of sturdy and robust automated differentiation instruments. Computational scientists and engineers will enjoy the dialogue of varied functions, which supply perception into powerful thoughts for utilizing automated differentiation for inverse difficulties and layout optimization.

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WSEAS Transactions on Circuits and Systems (2005) 3. : Simple relational correctness proofs for static analyses and program transformations. In: POPL ’04: Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 14–25. ACM Press, New York, NY, USA (2004) 4. : Interactive theorem proving and program development: Coq’Art: the calculus of inductive constructions. Texts in theoretical computer science. SpringerVerlag (2004) 5. : Proof-carrying code from certified abstract interpretation and fixpoint compression.

Load and store costs (both ≥ 0) are associated with single read and write accesses to the persistent memory, respectively. Floating-point operations have nontrivial cost > 0. The program’s physical memory p = (p1 , . . e. one does not count on any of the pi holding useful values except right after their computation. A data-flow reversal is an algorithm that makes the values of the intermediate variables of a given program run (equivalently, its DAG) available in reverse order. 6 7 6 7 6 7 4 5 4 5 4 5 3 3 3 2 2 2 1 1 1 0 -1 (a) 0 -1 (b) 0 -1 (c) Fig.

Non-differentiable intrinsic functions can be rewritten using IF constructs. For a given statement s, if the triple {φ }s{ψ } can be proved in the Hoare calculus, then the judgement {φ }s{ψ } is valid. 2 A Hoare Logic for Active Variables The activity analysis of program variables can be justified by the following natural semantics. States are assignments of values pa or na to variables which we termed ‘active’ or ‘passive’ states. The values pa and na are understood as ‘possibly active’ Certifying AD Transformations 29 Fig.

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