Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Recipes for adjoint code construction
ACM Transactions on Mathematical Software (TOMS)
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Automatic Differentiation of Computer Programs
ACM Transactions on Mathematical Software (TOMS)
Automatic differentiation of algorithms: from simulation to optimization
Automatic differentiation of algorithms: from simulation to optimization
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph
Mathematical Programming: Series A and B
ACM Transactions on Mathematical Software (TOMS)
A differentiation-enabled Fortran 95 compiler
ACM Transactions on Mathematical Software (TOMS)
Automatic Differentiation: Applications, Theory, and Implementations (Lecture Notes in Computational Science and Engineering)
Optimal Jacobian accumulation is NP-complete
Mathematical Programming: Series A and B
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The source transformation tool for automatic differentiation of Fortran programs ADIFOR uses a preaccumulation technique to speed up tangent-linear codes significantly compared to the standard forward mode. Reverse mode automatic differentiation is applied to all scalar assignments to generate efficient code for the computation of local gradients. It has been well known for some time that reverse mode is not necessarily the optimal choice for the computation of these statement-level gradients as it does not minimize the number of operations required. This article presents an efficient algorithm for the solution of this combinatorial optimization problem. The corresponding software is freely available for downloading on our website. Developers of software for automatic differentiation are invited to integrate the algorithm into their tools. Gradients of scalar multivariate functions can be computed by elimination methods on the linearized computational graph. The combinatorial optimization problem that aims to minimize the number of arithmetic operations performed by the elimination algorithm is known to be NP-complete. In this article we present a polynomial algorithm for solving a relevant subclass of this problem's instances. The proposed method relies on the ability to compute vertex covers in bipartite graphs in polynomial time. A simplified version of this graph algorithm is used in a research prototype of the differentiation-enabled NAGWare Fortran compiler for the preaccumulation of local gradients of scalar assignments in the context of automatic generation of efficient tangent-linear code for numerical programs.