Computational Differentiation Technical Reports

This directory contains reports from the Computational Differentiation Project. Most documents have been published by both the Mathematics and Computer Science Division at Argonne National Laboratory and the Center for Research on Parallel Computation at Rice University. You can download these reports as compressed postscript by clicking on the links below. To obtain a hard copy of a report, please contact Judy Beumer([email protected]).

This page includes the following sections:

Getting Started: Intros to AD Tools and Theory
Applications of ADIFOR and ADIC
General AD Theory and Techniques
Design and Use of the ADIFOR and ADIC tools

The following links may also be useful

All ANL/MCS technical reports
All CRPC technical reports
An automatic differentiation bibliography created by George Corliss. You can also access it using a search engine.
Reports from researchers not affiliated with the Computational Differentiation Project who have used our tools in their research

Getting Started: Intros to AD Tools and Theory

Andreas Griewank. "On Automatic Differentiation" in Mathematical Programming: Recent Developments and Applications, edited by M. Iri and K. Tanabe, pages 83-108, Kluwer Academic Publishers, Amsterdam, 1989. CRPC version.
Christian Bischof, Alan Carle, Peyvand Khademi, Andrew Mauer, and Paul Hovland. "ADIFOR 2.0 User's Guide (Revision C)," Technical Report ANL/MCS-TM-192, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1995. CRPC version.
Christian Bischof, Alan Carle, Peyvand Khademi, and Andrew Mauer. "ADIFOR 2.0: Automatic Differentiation of Fortran 77 Programs,"IEEE Computational Science & Engineering, 3:18-32, 1996. CRPC version.
Christian Bischof, Lucas Roh, and Andrew Mauer. "ADIC --- An Extensible Automatic Differentiation Tool for ANSI-C," Technical Report ANL/MCS-P626-1196, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1996. CRPC version.
Christian Bischof, Alan Carle, George Corliss, Andreas Griewank, and Paul Hovland. "ADIFOR: Generating Derivative Codes from Fortran Programs,"Scientific Programming, 1:11-29, 1992.
Christian Bischof and Andreas Griewank. "Tools for the automatic differentiation of computer programs" in ICIAM/GAMM 95: Issue 1: Numerical Analysis, Scientific Computing, Computer Science, edited by G. Alefeld, O. Mahrenholtz, and R. Mennicken, pages 267-272, 1996. Special Issue of Zeitschrift f\"ur Angewandte Mathematik und Mechanik (ZAMM).

Applications of ADIFOR and ADIC

Paul Hovland, Bijan Mohammadi, and Christian Bischof. "Automatic Differentiation of Navier-Stokes Computations," Technical Report ANL/MCS-P687-0997, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1997.
Christian Bischof, Lucas Roh, Norman Chang, Ken Lee, Valery Kanevsky, O. Sam Nakagawa, and Soo-Young Oh. "Statistical On-Chip Interconnect Modelling: An Application of Automatic Differentiation," Technical Report 8, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1997.
Seon-Ki Park, Kelvin Droegemeier, and Christian Bischof. "Automatic Differentiation as a Tool for Sensitivity Analysis of a Convective Storm in a 3-D Cloud Model" in Computational Differentiation: Techniques, Applications, and Tools, edited by Martin Berz, Christian Bischof, George Corliss, and Andreas Griewank, pages 205-214, SIAM, Philadelphia, PA, 1996.
Christian H. Bischof, William T. Jones, Andrew Mauer, and Jamshid Samareh. "Experiences with the Application of the ADIC automatic differentiation tool to the CSCMDO 3-D Volume Grid Generation Code" in Proceedings of the 34th AIAA Aerospace Sciences Meeting, AIAA Paper 96-0716, American Institute of Aeronautics and Astronomics, Washington, 1996.
Christian Bischof, Gordon Pusch, and Ralf Knoesel. "Sensitivity Analysis of the MM5 Weather Model using Automatic Differentiation,"Computers in Physics, 0:605-612, 1996.
Alan Carle, Lawrence Green, Christian Bischof, and Perry Newman. "Applications of Automatic Differentiation in CFD" in Proceedings of the 25th AIAA Fluid Dynamics Conference, AIAA Paper 94-2197, 1994.
Gregory Whiffen, Christine Shoemaker, Christian Bischof, Aaron Ross, and Alan Carle. "Application of Automatic Differentiation to Groundwater Transport Codes," Technical Report MCS-P441-0594, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1994.
Christian Bischof, Greg Whiffen, Christine Shoemaker, Alan Carle, and Aaron Ross. "Application of Automatic Differentiation to Groundwater Transport Models" in Computational Methods in Water Resources X, edited by Alexander Peters, pages 173-182, Kluwer Academic Publishers, Dordrecht, 1994.
George F. Corliss, Christian Bischof, Andreas Griewank, Steven Wright, and Thomas Robey. "Automatic Differentiation for PDE's -- Unsaturated Flow Case Study" in Advances in Computer Methods for Partial Differential Equations -- VII, edited by Robert Vichnevetski, Doyle Knight, and Gerard Richter, pages 150-156, IMACS, New Brunswick, 1992.
Christian Bischof, George Corliss, Larry Green, Andreas Griewank, Kara Haigler, and Perry Newman. "Automatic Differentiation of Advanced CFD Codes for Multidisciplinary Design,"Journal on Computing Systems in Engineering, 3:625-638, 1992.
George F. Corliss. "ADIFOR Case Study: VODE+ADIFOR," ADIFOR Working Note #10, MCS--TM--168, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1992.
Christian Bischof, Larry Green, Kitty Haigler, and Tim Knauff. "Parallel Calculation of Sensitivity Derivatives for Aircraft Design Using Automatic Differentiation" (Part 1, Part 2), in Proceedings of the 5th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, \rm AIAA 94-4261, pages 73-84, American Institute of Aeronautics and Astronautics, 1994.

General AD Theory and Techniques

Paul Hovland and Michael Heath. "Adaptive SOR: A Case Study in Automatic Differentiation of Algorithm Parameters," Technical Report ANL/MCS-P673-0797, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1997.
Christian Bischof and Po-Ting Wu. "Time-Parallel Computation of Pseudo-Adjoints for a Leapfrog Scheme," Technical Report ANL/MCS-P639-0197, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1997.
Christian H. Bischof and Mohammad R. Haghighat. "On Hierarchical Differentiation" in Computational Differentiation: Techniques, Applications, and Tools, edited by Martin Berz, Christian Bischof, George Corliss, and Andreas Griewank, pages 83-94, SIAM, Philadelphia, PA, 1996. CRPC version.
Christian H. Bischof and Po-Ting Wu. "Exploiting Intermediate Sparsity in Computing Derivatives of a Leapfrog Scheme," Technical Report ANL/MCS-P572-0396, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1996.
Amit K. Sinha, Christian H. Bischof, and Dmitri Shiriaev. "Application of Automatic Differentiation to Reservoir Design Models," Technical Report ANL/MCS-P585-0496, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1996.
Peter Eberhard and Christian Bischof. "Automatic Differentiation of Numerical Integration Algorithms," Technical Report ANL/MCS-P621-1196, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1996.
Steve Altus, Christian Bischof, Paul Hovland, and Ilan Kroo. "Using Automatic Differentiation with the Quasi-Procedural Method for Multidisciplinary Design Optimization" in Proceedings of the 34th AIAA Aerospace Sciences Meeting, AIAA Paper 96-0090, American Institute for Aeronautics and Astronomics, 1996.
Christian Bischof, Ali Bouaricha, Peyvand Khademi, and Jorge Mor\'e. "Computing Gradients in Large-Scale Optimization Using Automatic Differentiation," Technical Report MCS-P488-0195, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1995. CRPC version.
C. Bischof, A. Carle, P. Khademi, and G. Pusch. "Automatic Differentiation: Obtaining Fast and Reliable Derivatives--Fast" in Control Problems in Industry, edited by I. Lasiecka and B. Morton, pages 1-16, Birkh\"auser, Boston, 1995. CRPC version.
Paul Hovland, Christian Bischof, Donna Spiegelman, and Mario Casella. "Efficient Derivative Codes through Automatic Differentiation and Interface Contraction: An Application in Biostatistics," Technical Report MCS-P491-0195, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1995. CRPC version.
Gordon Pusch, Christian Bischof, and Alan Carle. "On Automatic Differentiation of Codes with Complex Arithmetic with Respect ot Real Variables," Technical Report ANL/MCS-TM-188, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1994.
Christian Bischof and Andreas Griewank. "Computational Differentiation and Multidisciplinary Design" in Inverse Problems and Optimal Design in Industry, edited by H. Engl and J. McLaughlin, pages 187-211, Teubner Verlag, Stuttgart, 1994.
Christian H. Bischof. "Automatic Differentiation, Tangent Linear Models and Pseudo-Adjoints" in High-Performance Computing in the Geosciences, edited by Le Dimet, Francois-Xavier, pages 59-80, Kluwer Academic Publishers, Boston, Mass., 1995. CRPC version.
Christian H. Bischof, Andreas Griewank, and Peyvand M. Khademi. "Workshop Report on First Theory Institute on Computational Differentiation," Technical Report ANL/MCS-TM-183, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1993.
Brett Averick, Jorge Mor\'e, Christian Bischof, Alan Carle, and Andreas Griewank. "Computing Large Sparse Jacobian Matrices using Automatic Differentiation,"SIAM Journal on Scientific Computing, 5:285-294, 1994.
Andreas Griewank. "Some Bounds on the Complexity of Gradients, Jacobians, and Hessians," Technical Report MCS-P355-0393, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1993.
Andreas Griewank, Christian Bischof, George Corliss, Alan Carle, and Karen Williamson. "Derivative Convergence of Iterative Equation Solvers,"Optimization Methods and Software, 2:321-355, 1993.
Christian Bischof, George Corliss, and Andreas Griewank. "Structured Second- and Higher-Order Derivatives through Univariate Taylor Series,"Optimization Methods and Software, 2:211-232, 1993.
Andreas Griewank. "Achieving Logarithmic Growth of Temporal and Spatial Complexity in Reverse Automatic Differentiation,"Optimization Methods and Software, 1:35-54, 1992.
Griewank, Andreas and Reese, Shawn. "On the Calculation of Jacobian matrices by the Markowitz Rule" in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, edited by Griewank, Andreas and Corliss, George F., pages 126-135, SIAM, Philadelphia, PA, 1991.
David Juedes. "A Taxonomy of Automatic Differentiation Tools" in Proceedings of the Workshop on Automatic Differentiation of Algorithms: Theory, Implementation, and Application, edited by Andreas Griewank and George Corliss, pages 315-330, SIAM, Philadelphia, PA, 1991.
Andreas Griewank. "On Automatic Differentiation" in Mathematical Programming: Recent Developments and Applications, edited by M. Iri and K. Tanabe, pages 83-108, Kluwer Academic Publishers, Amsterdam, 1989. CRPC version.

Design and Use of the ADIFOR and ADIC tools

Jason Abate, Christian Bischof, Alan Carle, and Lucas Roh. "Algorithms and Design for a Second-Order Automatic Differentiation Module" in Proc. Int. Symposium on Symbolic and Algebraic Computing (ISSAC) '97, pages 149-155, Association of Computing Machinery, New York, 1997.
Christian Bischof, Alan Carle, Peyvand Khademi, Andrew Mauer, and Paul Hovland. "ADIFOR 2.0 User's Guide (Revision C)," Technical Report ANL/MCS-TM-192, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1995. CRPC version.
Christian Bischof, Lucas Roh, and Andrew Mauer. "ADIC --- An Extensible Automatic Differentiation Tool for ANSI-C," Technical Report ANL/MCS-P626-1196, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1996. CRPC version.
Christian Bischof and Alan Carle. "User's Experience with ADIFOR 2.0" in Computational Differentiation: Techniques, Applications, and Tools, edited by Martin Berz, Christian Bischof, George Corliss, and Andreas Griewank, pages 385-392, SIAM, Philadelphia, PA, 1996. CRPC version.
Christian Bischof, Alan Carle, Peyvand Khademi, and Andrew Mauer. "ADIFOR 2.0: Automatic Differentiation of Fortran 77 Programs,"IEEE Computational Science & Engineering, 3:18-32, 1996. CRPC version.
Christian Bischof, Peyvand Khademi, and Timothy Knauff. "ADIFOR Strategies related to Pointer Usage in MM5," Technical Report ANL/MCS-TM-187, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1994.
Paul Hovland. "Using ADIFOR 1.0 to Compute Hessians," Technical Report MCS--TM--195, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1994.
Christian Bischof, Alan Carle, George Corliss, and Andreas Griewank. "ADIFOR: Automatic Differentiation in a Source Translator Environment" in International Symposium on Symbolic and Algebraic Computing 92, edited by Paul Wang, pages 294-302, ACM, Washington, D.C., 1992.
Christian H. Bischof and Moe El-Khadiri. "Extending Compile-Time Reverse Mode and Exploiting Partial Separability in ADIFOR," Technical Report ANL/MCS-TM-163, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1992.
Christian H. Bischof, Alan Carle, George Corliss, Andreas Griewank, and Paul Hovland. "Getting Started with ADIFOR," Technical Report ANL/MCS-TM-164, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1992.
Christian Bischof, George Corliss, and Andreas Griewank. "Hybrid Evaluation of Second Derivatives in ADIFOR," Technical Report ANL/MCS-TM-166, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1992.
Christian Bischof and Andreas Griewank. "ADIFOR: A Fortran System for Portable Automatic Differentiation" in Proceedings of the 4th Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper 92-4744, pages 433-441, American Institute of Aeronautics and Astronautics, Washington, 1992.
Christian Bischof, Alan Carle, George Corliss, Andreas Griewank, and Paul Hovland. "ADIFOR: Generating Derivative Codes from Fortran Programs,"Scientific Programming, 1:11-29, 1992.
Christian Bischof and Paul Hovland. "Using ADIFOR to Compute Dense and Sparse Jacobians," Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1991.
Christian Bischof, George Corliss, and Andreas Griewank. "ADIFOR Exception Handling," Technical Report ANL/MCS-TM-159, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1991.
Christian Bischof, Alan Carle, George Corliss, Andreas Griewank, and Paul Hovland. "ADIFOR: Fortran Source Translation for Efficient Derivatives," Technical Report MCS--P278--1291, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, 1991.

Argonne National Laboratory/Mathematics and Computer Science Division/ [email protected]