Publication: A sparse matrix approach to reverse mode automatic differentiation in Matlab
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A sparse matrix approach to reverse mode automatic differentiation in Matlab

- Article in a journal -
 

Author(s)
Shaun A. Forth , Naveen Kr. Sharma

Published in
Procedia Computer Science

Year
2010

Abstract
We review the extended Jacobian approach to automatic differentiation of a user-supplied function and highlight the Schur complement form’s forward and reverse variants. We detail a Matlab operator overloaded approach to construct the extended Jacobian that enables the function Jacobian to be computed using Matlab’s sparse matrix operations. Memory and runtime costs are reduced using a variant of the hoisting technique of Bischof (Issues in Parallel Automatic Differentiation, 1991). On five of the six mesh-based gradient test problems from The {MINPACK2} Test Problem Collection (Averick et al, 1992) the reverse variant of our extended Jacobian technique with hoisting outperforms the sparse storage forward mode of the {MAD} package (Forth, {ACM} T. Math. Software. 32, 2006). For increasing problems size the ratio of gradient to function cpu time is seen to be bounded, if not decreasing, in line with Griewank and Walther’s (Evaluating Derivatives, SIAM, 2008) cheap gradient principle.

AD Tools
MAD, TOMLAB /MAD

AD Theory and Techniques
Reverse Mode, Sparsity

BibTeX
@ARTICLE{
         Forth2010Asm,
       author = "Shaun A. Forth and Naveen Kr. Sharma",
       title = "A sparse matrix approach to reverse mode automatic differentiation in {M}atlab",
       journal = "Procedia Computer Science",
       pages = "1863--1871",
       issn = "1877-0509",
       doi = "http://dx.doi.org/10.1016/j.procs.2010.04.208",
       url = "http://www.sciencedirect.com/science/article/pii/S1877050910002097",
       keywords = "Performance",
       abstract = "We review the extended Jacobian approach to automatic differentiation of a
         user-supplied function and highlight the Schur complement form’s forward and reverse
         variants. We detail a Matlab operator overloaded approach to construct the extended Jacobian that
         enables the function Jacobian to be computed using Matlab’s sparse matrix operations.
         Memory and runtime costs are reduced using a variant of the hoisting technique of Bischof (Issues in
         Parallel Automatic Differentiation, 1991). On five of the six mesh-based gradient test problems from
         The \{MINPACK2\} Test Problem Collection (Averick et al, 1992) the reverse variant of our
         extended Jacobian technique with hoisting outperforms the sparse storage forward mode of the
         \{MAD\} package (Forth, \{ACM\} T. Math. Software. 32, 2006). For increasing
         problems size the ratio of gradient to function cpu time is seen to be bounded, if not decreasing,
         in line with Griewank and Walther’s (Evaluating Derivatives, SIAM, 2008) cheap gradient
         principle.",
       volume = "1",
       number = "1",
       year = "2010",
       ad_tools = "MAD, TOMLAB /MAD",
       ad_theotech = "Reverse Mode, Sparsity"
}


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