Roscoe A. Bartlett
Michael A. Heroux
Abstract
Development of flexible linear algebra interfaces is an increasingly critical issue. Efficient and expressive interfaces are well established for some linear algebra abstractions, but not for vectors. Vectors differ from other abstractions in the diversity of necessary operations, sometimes requiring dozens for a given algorithm (e.g. interior-point methods for optimization). We discuss a new approach based on operator objects that are transported to the underlying data by the linear algebra library implementation, allowing developers of abstract numerical algorithms to easily extend the functionality regardless of computer architecture, application or data locality/organization. Numerical experiments demonstrate efficient implementation.
- Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenny, A., Ostrouchov, S., and Sorensen, D. 1995. LAPACK User's Guide. SIAM. Google Scholar
Digital Library
- Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F. PETSc, portable extensible toolkit for scientific computing. http://www.mcs.anl.gov/petsc.Google Scholar
- Bartlett, R. A. 2001. Object oriented approaches to large-scale nonlinear programming for process systems engineering. Ph.D. thesis, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
- Benson, S., McInnes, L. C., and Moré, J. TAO : Toolkit for advanced optimization, http://www-fp.mcs.anl.gov./tao.Google Scholar
- Blackford, L. S., Choi, J., Cleary, A., Azevedo, E. D., Demmel, J., Dhilon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walder, D., and Whaley, R. 1997. ScalLAPACK User's Guide. SIAM, Philadelphia, PA.Google Scholar
- Booch, G., Rumbaugh, J., and Jacobson, I. 1999. The Unified Modeling Language User Guide. Addison-Wesley. Google ScholarDigital Library
- Byrne, G. D. and Hindmarsh, A. C. 1999. PVODE, an ODE solver for parallel computers. Int. J. High Perf. Comput. Applic 13, 354--365. Google ScholarDigital Library
- Cai, X. 1999. Two object-oriented approaches to the parallelism of diffpack. http://www.ifi.uio.no/∼xingca/.Google Scholar
- Clay, R., Allan, B., Mish, L., and Williams, A. 1999a. ISIS++ reference guide (iterative scalable implicit solver in c++) version 1.1. Tech. Rep. SAND99-8231, Sandia National Laboratories.Google Scholar
- Clay, R. L., Mish, K. D., Otero, I. J., Taylor, L. M., and Williams, A. B. 1999b. An annotated reference guide to the finite-element interface (FEI) specification : Version 1.0. Tech. Rep. SAND99-8229, Sandia National Laboratories.Google Scholar
- Demmel, J. 1997. Applied Numerical Linear Algebra. SIAM. Google ScholarDigital Library
- Dennis, J. E., Heinkenschloss, M., and Vicente, L. N. 1998. Trust-region interior-point sqp algorithms for a class of nonlinear programming problems. SIAM J. Control and Optimization 36, 5, 1750--1794. Google ScholarDigital Library
- Dongarra, J. J., Du Croz, J., Hammarling, S., and Hanson, R. J. 1988. An extended set of FORTRAN Basic Linear Algebra Subprograms. ACM Trans. Math. Soft. 14, 1--17. Google ScholarDigital Library
- Gamma, E., Helm, R., Johnson, R., and Vlissides, J. 1995. Design Patterns: Elements fo Reusable Object-Oriented Software. Addison-Wesley. Google ScholarDigital Library
- Gertz, M. and Wright, S. 2001. Object-oriented software for quadratic programming. http://www.cs.wisc.edu/∼swright/ooqp/.Google Scholar
- Gockenbach, M. and Symes, W. The Hilbert class library. http://www.trip.caam.rice.edu/txt/ hcldoc/html/index.html.Google Scholar
- Heinkenschloss, M. and Vicente, L. N. 1999. An interface between optimization and application for the numerical solution of optimal control problems. ACM Trans. Math. Soft. 25, 2 (June), 157--190. Google ScholarDigital Library
- Heroux, M. A., Barth, T., Day, D., Hoekstra, R., Lehoucq, R., Long, K., Pawlowski, R., Tuminaro, R., and Williams, A. 2003. An overview of Trilinos. Tech. rep. SAND2003-2927, Sandia National Laboratories.Google Scholar
- Lumsdanie, A. and Siek, J. 1998a. ITL : the iterative template library. http://www.osl.iu.edu/ research/itl/.Google Scholar
- Lumsdanie, A. and Siek, J. 1998b. The matrix template library. http://www.lsc.nd.edu/ research/mtl/.Google Scholar
- Nocedal, J. and Wright, S. 1999. Numerical Optimization. Springer, New York.Google Scholar
- Pozo, R. TNT: Template Numerical Toolkit. http://math.nist.gov/tnt.Google Scholar
- Pozo, R. 1996. LAPACK++ v 1.1: High Performance Linear Algebra User's Guide. NIST.Google Scholar
- Riesen, R., Brightwell, R., Fisk, L. A., Hudson, T., Otto, J., and Maccabe, A. B. 1999. Cplant. http://www.sandia.gov/cplant.Google Scholar
- Sandia National Labs. 2001. ESI: Equation Solver Interface. http://z.ca.sandia.gove/esi.Google Scholar
- Tuminaro, R., Heroux, M., Hutchinson, S., and Shadid, J. 1999. Official Aztec User's Guide: Version 2.1. Albuquerque, NM 87185.Google Scholar
Index Terms
- Vector reduction/transformation operators
Recommendations
Performance improvement for machine learning‐based cooperative spectrum sensing by feature vector selection
To explore the potential of machine learning‐based cooperative spectrum sensing (CSS) in training time, classification speed and classification performance, this study mainly focuses on studying the problem of the feature vectors selecting for machine ...
Combined outputs framework for twin support vector machines
Twin support vector machine (TWSVM) is regarded as a milestone in the development of powerful SVMs. However, there are some inconsistencies with TWSVM that can lead to many reasonable modifications with different outputs. In order to obtain better ...
Sparse pinball twin support vector machines
AbstractThe original twin support vector machine (TWSVM) formulation works by solving two smaller quadratic programming problems (QPPs) as compared to the traditional hinge-loss SVM (C-SVM) which solves a single large QPP — this makes the ...
Highlights- A novel twin support vector machine with sparse pinball loss (SPTWSVM) is proposed.
Comments