Christian Bischof. Issues in parallel automatic differentiation. In Andreas Griewank and George F. Corliss, editors, Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia, Penn., 1991, 100-113.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....2000 The algorithm described in this note is of theoretical interest and enhances our understanding of parallel automatic differentiation. It is not intended to represent practical issues involved in a particular implementation of such software. More practical issues in this field are discussed in [1 3,5]. The structure of this note is as follows. In Sec. 2, straight line codes are specified as an abstraction of more complicated programs. For the parallel evaluation of the underlying function, a common representation of a straight line code known as an arithmetic circuit is introduced. In Sec. 3, ....

C. H. Bischof, Issues in parallel automatic differentiation, in Automatic Differentiation of Algorithms, A. Griewank and G. Corliss, eds., Philadelphia, PA, 1991, SIAM, pp. 100--113.

....Since all computation is performed as a by product of elementary operations, it is very difficult, if not impossible, to perform optimizations that transcend one elementary operation. The resulting disadvantages, especially those associated with the exploitation of parallelism, are discussed in [2]. of Efficiency: The overwhelming majority of codes for which computational scientists want derivatives are written in Fortran 77, which does not support operator overloading. While we can emulate operator overloading by associating a subroutine call with each elementary operation, this approach ....

Christian Bischof. Issues in parallel automatic differentiation. In Andreas Griewank and George F. Corliss, editors, Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia, Penn., 1991, 100-113.

....DAG case to the linear DAG case by ordering DAG nodes in a topological fashion and considering all nodes at a given level as a supernode. Since nodes in a supernode are independent, they can actually be eliminated in parallel, an approach that was explored at the elementary operation level in [9]. 4 A Case Study We now provide a concrete example illustrating that hierarchical approaches to derivative generation can do considerably better than either of the monolithic approaches largely underlying current AD tools. To this end, we employ the driven cavity problem in the MINPACK 2 test ....

C. H. Bischof, Issues in parallel automatic differentiation, in Automatic Differentiation of Algorithms, A. Griewank and G. Corliss, eds., Philadelphia, PA, 1991, SIAM, pp. 100--113.

....DAG case to the linear DAG case by ordering DAG nodes in a topological fashion and considering all nodes at a given level as a supernode. Since nodes in a supernode are independent, they can actually be eliminated in parallel, an approach that was explored at the elementary operation level in [9]. 4 A Case Study We now provide a concrete example illustrating that hierarchical approaches to derivative generation can do considerably better than either of the monolithic approaches largely underlying current AD tools. To this end, we employ the driven cavity problem in the MINPACK 2 test ....

C. H. Bischof, Issues in parallel automatic differentiation, in Automatic Differentiation of Algorithms, A. Griewank and G. Corliss, eds., Philadelphia, PA, 1991, SIAM, pp. 100--113.

....Since all computation is performed as a by product of elementary operations, it is very difficult, if not impossible, to perform optimizations that transcend one elementary operation. The resulting disadvantages, especially those associated with the exploitation of parallelism, are discussed in [2]. Loss of Efficiency: The overwhelming majority of codes for which computational scientists want derivatives are written in Fortran 77, which does not support operator overloading. While we can emulate operator overloading by associating a subroutine call with each elementary operation, this ....

Christian Bischof. Issues in parallel automatic differentiation. In Andreas Griewank and George F. Corliss, editors, Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia, Penn., 1991, 100--113.

.... to perform optimizations that transcend one elementary operation (such as the constant folding techniques that simplified the reverse mode shown in Figure 5 into that shown in Figure 6) The resulting disadvantages, especially those associated with the exploitation of parallelism, are discussed in [2]. Loss of Efficiency: The overwhelming majority of codes for which computational scientists want derivatives are written in Fortran, which does not support operator overloading. While we can emulate operator overloading by associating a subroutine call with each elementary operation, this ....

Christian Bischof. Issues in parallel automatic differentiation. In Andreas Griewank and George F. Corliss, editors, Automatic Differentiation of Algorithms: Theory, Implementation, and Application, pages 100 -- 113. SIAM, Philadelphia, Penn., 1991.

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Christian Bischof. Issues in parallel automatic differentiation. In Andreas Griewank and George F. Corliss, editors, Automatic Differentiation of Algorithms: Theory, Implementation, and Application, pages 100--113. SIAM, Philadelphia, Penn., 1991.

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