PCOMP

Algorithm 746: PCOMP: A Fortran code for automatic differentiation Automatic differentiation is an interesting and important tool for all numerical algorithms that require derivatives, e.g., in nonlinear programming, optimal control, parameter estimation, and differential equations. The basic idea is to avoid not only numerical approximations, which are expensive with respect to CPU time and contain round-off errors, but also hand-coded differentiation. This article introduces the forward and backward accumulation methods and describes the numerical implementation of a computer code with the name PCOMP. The main intention of the approach used is to provide a flexible and portable Fortran code for practical applications. The underlying language is described in terms of a formal grammar and is a subset of Fortran with a few extensions. Besides a parser that generates an intermediate code and that can be executed independently from the evaluation routines, there are other subroutines for the direct computation of function and gradient values, which can be called directly from a user program. On the other hand, it is possible to generate a Fortran code for function and gradient evaluation that can be compiled and linked separately


References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Patterson, Michael A.; Weinstein, Matthew; Rao, Anil V.: An efficient overloaded method for computing derivatives of mathematical functions in MATLAB (2013)
  2. Boisvert, Jason J.; Donaldson, Matthew W.; Spiteri, Raymond J.: Solving parameter estimation problems with $\Bbb S\Bbb O\Bbb C\Bbb X$ (2012)
  3. Chudej, K.; Bauer, Marco; Pesch, H.J.; Schittkowski, K.: Numerical simulation of a Molten carbonate fuel cell by partial differential algebraic equations (2008)
  4. Griewank, Andreas; Walther, Andrea: Evaluating derivatives. Principles and techniques of algorithmic differentiation (2008)
  5. Schittkowski, Klaus: Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery (2008)
  6. Schittkowski, K.: Parameter identification in one-dimensional partial differential algebraic equations (2007)
  7. Kallrath, Josef (ed.): Modeling languages in mathematical optimization. (2004)
  8. Schittkowski, K.: Data fitting in partial differential algebraic equations: Some academic and industrial applications. (2004)
  9. Frías, Jesús M.; Oliveira, Jorge C.; Schittkowski, Klaus: Modeling and parameter identification of a maltodextrin DE 12 drying process in a convection oven (2001)
  10. Liepelt, Michael; Schittkowski, Klaus: Optimal control of distributed systems with break points (2001)
  11. Blatt, M.; Schittkowski, K.: Optimal control of one-dimensional partial differential algebraic equations with applications (2000)
  12. Schittkowski, Klaus: Parameter estimation in a mathematical model for substrate diffusion in a metabolically active cutaneous tissue (2000)
  13. Schittkowski, K.: PDEFIT: A FORTRAN code for data fitting in partial differential equations (1999)
  14. Jerrell, Max E.: Automatic differentiation and interval arithmetic for estimation of disequilibrium models (1997)
  15. Dobmann, M.; Liepelt, M.; Schittkowski, K.: Algorithm 746: PCOMP: A Fortran code for automatic differentiation (1995)
  16. Mehlhorn, Rainer; Dinkelmann, Michael; Sachs, Gottfried: Application of automatic differentiation to optimal control problems (1994)
  17. Juedes, David W.: A taxonomy of automatic differentiation tools (1991)