Automatic differentiation and its program realization

Jan Hartman; Ladislav Lukšan; Jan Zítko

Kybernetika (2009)

  • Volume: 45, Issue: 5, page 865-883
  • ISSN: 0023-5954

Abstract

top
Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its principles can be applied in other systems. We describe, how the operations are stored in the first part of the derivative computation and how the obtained records are effectively used in the second part of the computation.

How to cite

top

Hartman, Jan, Lukšan, Ladislav, and Zítko, Jan. "Automatic differentiation and its program realization." Kybernetika 45.5 (2009): 865-883. <http://eudml.org/doc/37695>.

@article{Hartman2009,
abstract = {Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its principles can be applied in other systems. We describe, how the operations are stored in the first part of the derivative computation and how the obtained records are effectively used in the second part of the computation.},
author = {Hartman, Jan, Lukšan, Ladislav, Zítko, Jan},
journal = {Kybernetika},
keywords = {automatic differentiation; modeling languages; systems for optimization; automatic differentiation; functions given by computer programs; algorithmic differentiation; program realization; modeling language; universal functional optimization},
language = {eng},
number = {5},
pages = {865-883},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Automatic differentiation and its program realization},
url = {http://eudml.org/doc/37695},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Hartman, Jan
AU - Lukšan, Ladislav
AU - Zítko, Jan
TI - Automatic differentiation and its program realization
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 5
SP - 865
EP - 883
AB - Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its principles can be applied in other systems. We describe, how the operations are stored in the first part of the derivative computation and how the obtained records are effectively used in the second part of the computation.
LA - eng
KW - automatic differentiation; modeling languages; systems for optimization; automatic differentiation; functions given by computer programs; algorithmic differentiation; program realization; modeling language; universal functional optimization
UR - http://eudml.org/doc/37695
ER -

References

top
  1. Automatic Differentiation of Algorithms: Theory, Implementation, and Application, SIAM, Philadelphia 1992. Zbl0747.00030MR1143784
  2. Automatic Differentiation: Applications, Theory, and Implementations, Springer–Verlag, Berlin 2005. Zbl1084.65002
  3. Computational Differentiation – Techniques, Applications, and Tools, SIAM, Philadelphia 1996. Zbl0857.00033MR1431037
  4. Evaluating gradients in optimal control – Continuous adjoints versus automatic differentiation, J. Optim. Theory Appl. 122 (2004), 1, 63–86. MR2092472
  5. Evaluation Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia 2000. MR1753583
  6. Introduction to automatic differentiation, PAMM 2 (2003), 45–49. 
  7. Realizace metod pro automatické derivování (Implementation of Methods for Automatic Differentiation), Diploma Thesis. Faculty of Mathematics and Physics, Charles University, Prague 2001. 
  8. Automatické derivování v systému UFO (Automatic Differentiation in System UFO), Technical Report V-1002. ICS AS CR, Prague 2007. 
  9. Principy automatického derivování (Principles of Automatic Differentiation), Technical Report, Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Prague 2006. 
  10. UFO 2006 – Interactive System for Universal Functional Optimization, Technical Report V-977. ICS AS CR, Prague 2006. 
  11. Structured Automatic Differentiation, Ph.D. Thesis, Cornell University, 1988. 
  12. ADOL-C: Automatic differentiation using operator overloading in C++, PAMM 2 (2003), 41–44. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.