mathematics
and
computer
science

LANS

LANS Publications

"Sparse Jacobian Computation Using ADIC2 and ColPack"

S. H. K. Narayanan, B. Norris, P. Hovland, D. C. Nguyen, and A. H. Gebremedhin

Procedia Computer Science, Singapore, , pp. 2115-2123. Also Preprint ANL/MCS-P1841-0211

Preprint Version: [pdf]

Many scientific applications benefit from the accurate and efficient computation of derivatives. Automatically generating these derivative computations from an applications source code off ers a competitive alternative to other approaches, such as less accurate numerical approximations or labor-intensive analytical implementations. ADIC2 is a source transformation tool for generating code for computing the derivatives (e.g., Jacobian or Hessian) of a function given the C or C++ implementation of that function. Often the Jacobian or Hessian is sparse and presents the opportunity to greatly reduce storage and computational requirements in the automatically generated derivative computation. ColPack is a tool that compresses structurally independent columns of the Jacobian and Hessian matrices through graph coloring approaches. In this paper, we describe the integration of ColPack coloring capabilities into ADIC2, enabling accurate and efficient sparse Jacobian computations. We present performance results for a case study of a simulated moving bed chromatography application. Overall, the computation of the Jacobian by integrating ADIC2 and ColPack is approximately 40% faster than a comparable implementation that integrates ADOL-C and ColPack when the Jacobian is computed multiple times.