DFG Research Center MATHEON


Humboldt-Universitaet zu Berlin


Index Determination in DAEs using the indexdet Library
and the
ADOL-C Package for Automatic Differentiation

Version: 1.0

Overview      Features      Software      Documentation      People      Contact


daeIndexDet stands for Index Determination in DAEs and is a program for computing the index in systems of differential algebraic equations (DAEs) with properly stated leading terms. Its current version is coded in C++.

daeIndexDet uses the indexdet library, which actually provides the functionalities for the index computation by using Automatic Differentiation techniques. These techniques provide an efficient calculation of machine-precision, accurate derivatives via truncated Taylor series arithmetic.

Related projects:

    Analysis and treatment of DAEs using Automatic Differentiation
        Head: Prof. Dr. Andreas Griewank (and Prof. Dr. Caren Tischendorf in the past)
        Funding: Humboldt University of Berlin (Since Apr. 2008) and Max-Planck Research Prize 2001 from Prof. Griewank (Jan. 2006 - Sep. 2006)

    D7 - Numerical simulation of integrated circuits for future chip generations
        Head: Prof. Dr. Andreas Griewank
        Funding: MATHEON Project, Application area D: Circuits simulation and opto-electronic devices (Oct. 2006 - Mar. 2008)

Talks and presentations:

   - R. Lamour, D. Monett. Index Determination for DAEs – A wide field for Automatic Differentiation. In T.E. Simos, G. Psihoyios, and Ch. Tsitouras (editors), AIP Conference Proceedings 1168 of the 7th International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2009, Vol. 2, pp. 727-730, Rethymno, Crete, Greece, September 2009.

   - D. Monett, R. Lamour, A. Griewank. Index Determination in DAEs Using the Library indexdet and the ADOL-C Package for Algorithmic Differentiation. In C. Bischof, M. Bücker, P. Hovland, U. Naumann, and J. Utke, editors, Advances in Automatic Differentiation, Lecture Notes in Computational Science and Engineering, Vol. 64, pp. 247-257, Springer, Berlin, Germany, 2008.
   (Paper and slides at the 5th International Conference on Automatic Differentiation, Bonn, Germany, 2008)

   - Slides of the talk at the MATHEON Center Days, Berlin, Germany, Apr. 2008.

   - D. Monett. Index determination in DAEs using AD techniques. In 6th European Workshop on Automatic Differentiation, INRIA Sophia-Antipolis, France, 2007.

   - Slides of the talk at the MATHEON D-Day, Berlin, Germany, Nov. 2007.


The main features of the indexdet library are:



        You must have a working installation of ADOL-C.

The library:

        If you are interested on the library, contact the authors.

Compile and run:

Extract: $ tar zxvf indexdet.tar.gz
Compile and link: $ ./makefile
Run: $ ./daeIndexDet

Note: See more details in the program documentation.

Documentation, References

Program documentation:

   daeIndexDet: A Program for the Index Determination in DAEs using the indexdet Library and the ADOL-C Package for Automatic Differentiation


    A. Griewank. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Number 19 in Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, 2000.

    A. Lamour. Index Determination and Calculation of Consistent Initial Values for DAEs. Computers and Mathematics with Applications, 50:1125-1140, 2005.

    R. März. The index of linear differential algebraic equations with properly stated leading terms. In Result. Math., volume 42, pages 308-338. Birkhäuser Verlag, Basel, 2002.

    R. März. Differential Algebraic Systems with Properly Stated Leading Term and MNA Equations. In K. Antreich, R. Bulirsch, A. Gilg, and P. Rentrop, editors, Modeling, Simulation and Optimization of Integrated Circuits, International Series of Numerical Mathematics, volume 146, pages 135-151. Birkhäuser Verlag, Basel, 2003.

    R. März. Fine decoupling of regular differential algebraic equations. In Result. Math., volume 46, pages 57-72. Birkhäuser Verlag, Basel, 2004.

    A. Walther, A. Kowarz, and A. Griewank. ADOL-C: A Package for the Automatic Differentiation of Algorithms Written in C/C++, Version 1.10.0, July 2005.



        Prof. Dr. Andreas Griewank (*)
        Prof. Dr. Dagmar Monett Díaz (**)
        Dr. René Lamour (*)

(*)   Institute of Mathematics
        Humboldt University of Berlin
        Unter den Linden 6, 10099 Berlin
(**)  Computer Science Dept., Berlin School of Economics and Law, HWR Berlin



Dagmar Monett Díaz

Last update: Oct.2010