A Standard and Software for Numerical Metadata

ABSTRACT

We propose a standard for generating, manipulating, and storing metadata describing numerical problems, in particular properties of matrices and linear systems. The standard comprises:

–an API for metadata generating and querying software, and

–an XML format for permanent storage of metadata.

The API is open-ended, allowing for other parties to define additional metadata categories to be generated and stored within this framework. Furthermore, we present two software libraries, NMD and AnaMod, that implement this standard, and that contain a number of computational modules for numerical metadata. The libraries, more than simply illustrating the use of the standard, provide considerable utility to numerical researchers.

REFERENCES

• 1: Allan, B. A., Armstrong, R. C., Wolfe, A. P., Ray, J., Bernholdt, D. E., and Kohl, J. A. 2002. The CCA core specification in a distributed memory SPMD framework. Concurrency Comput. Pract. Exper. 14, 5, 323--345.
• 2: Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., and Sorensen, D. 1992. LAPACK Users’ Guide. SIAM, Philadelphia, PA.
• 3: Rob Armstrong , Dennis Gannon , Al Geist , Katarzyna Keahey , Scott Kohn , Lois McInnes , Steve Parker , Brent Smolinski, Toward a Common Component Architecture for High-Performance Scientific Computing, Proceedings of the 8th IEEE International Symposium on High Performance Distributed Computing, p.13, August 03-06, 1999
• 4: Arnold, D., Blackford, S., Dongarra, J., Eijkhout, V., and Xu, T. 2000. Seamless access to adaptive solver algorithms. In SGI Users’ Conference, M. Bubak et al., Eds. Academic Computer Center CYFRONET, 23--30.
• 5: Satish Balay , William D. Gropp , Lois Curfman McInnes , Barry F. Smith, Efficient management of parallelism in object-oriented numerical software libraries, Modern software tools for scientific computing, Birkhauser Boston Inc., Cambridge, MA, 1997
• 6: Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F. 1999. PETSc home page. http://www.mcs.anl.gov/petsc.
• 7: Bhowmick, S., Eijkhout, V., Freund, Y., Fuentes, E., and Keyes, D. 2006. Application of machine learning to the selection of sparse linear solvers. Int. J. High Perf. Comput. Appl. submitted.
• 8: Bunch, J. R. 1971. Analysis of the diagonal pivoting method. SIAM J. Numer. Anal. 8, 656--680.
• 9: Common Component Architecture Forum. 2009. homepage. http://www.cca-forum.org.
• 10: A. R. Conn , N. I. M. Gould , Ph L. Toint, Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A), Springer-Verlag New York, Inc., Secaucus, NJ, 1992
• 11: Davis, T. 2009. University of Florida sparse matrix collection. http://www.cise.ufl.edu/research/sparse/matrices, ftp://ftp.cise.ufl.edu/pub/faculty/davis/matrices, described in NA Digest 92, 42, 1994, NA Digest 96, 28, 1996, and NA Digest 97, 23, 1997.
• 12: Demmel, J., Dongarra, J., Eijkhout, V., Fuentes, E., Petitet, A., Vuduc, R., Whaley, R. C., and Yelick, K. 2005. Self adapting linear algebra algorithms and software. Proc. IEEE 93, 293--312.
• 13: J. Dongarra , G. Bosilca , Z. Chen , V. Eijkhout , G. E. Fagg , E. Fuentes , J. Langou , P. Luszczek , J. Pjesivac-Grbovic , K. Seymour , H. You , S. S. Vadhiyar, Self-adapting numerical software (SANS) effort, IBM Journal of Research and Development, v.50 n.2/3, p.223-238, March 2006 [doi>10.1147/rd.502.0223]
• 14: Dongarra, J. and Eijkhout, V. 2003a. Self-Adapting numerical software and automatic tuning of heuristics. In Proceedings of the International Conference on Computational Science, Lecture Notes in Computer Science, vol. 2660. Springer, 759--770.
• 15: Dongarra J. and Eijkhout V. 2003b. Self-Adapting numerical software for next generation applications. Int. J. High Perf. Comput. Appl. 17, 125--131. also Lapack Working Note 157, ICL-UT-02-07.
• 16: I. S. Duff , Roger G. Grimes , John G. Lewis, Sparse matrix test problems, ACM Transactions on Mathematical Software (TOMS), v.15 n.1, p.1-14, March 1989 [doi>10.1145/62038.62043]
• 17: Thomas Eidson , Jack Dongarra , Victor Eijkhout, Applying Aspect-Orient Programming Concepts to a Component-Based Programming Model, Proceedings of the 17th International Symposium on Parallel and Distributed Processing, p.205.2, April 22-26, 2003
• 18: Elsner L. and Paardekoper, M. 1979. On measures of non-normality for matrices. Lin. Alg. Appl. 307/308, 107--124.
• 19: Greenbaum, A. 2002. Generalizations of the field of values useful in the study of polynomial functions of a matrix. Lin. Alg. Appl. 347, 233--249.
• 20: Laboratory for High Performance Scientific Computing & Computer Simulation. 2009. Online condition number query system. http://www.cs.uky.edu/~hipscns/HiPSCCS_Projects/OCNQS/done.htm.
• 21: Steven L. Lee, A Practical Upper Bound for Departure from Normality, SIAM Journal on Matrix Analysis and Applications, v.16 n.2, p.462-468, April 1995 [doi>10.1137/S0895479893255184]
• 22: Steven L. Lee, Best Available Bounds For Departure From Normality, SIAM Journal on Matrix Analysis and Applications, v.17 n.4, p.984-991, Oct. 1996 [doi>10.1137/S0895479895285263]
• 23: National Council for Supercomputing Applications. 2009. HDF home page. http://www.hdfgroup.org/.
• 24: National Institute of Standards and Technology. 2009a. Matrix market. http://math.nist.gov/MatrixMarket.
• 25: National Institute of Standards and Technology. 2009b. Matrix market: File formats: Harwell Boeing format. http://math.nist.gov/MatrixMarket/formats.html#hb.
• 26: National Institute of Standards and Technology. 2009c. Matrix market: File formats: Matrix market format. http://math.nist.gov/MatrixMarket/formats.html#mm.
• 27: Perl Foundation. 2009. Perl database interface. http://dbi.perl.org/.
• 28: Naren Ramakrishnan , Calvin J. Ribbens, Mining and visualizing recommendation spaces for elliptic PDEs with continuous attributes, ACM Transactions on Mathematical Software (TOMS), v.26 n.2, p.254-273, June 2000 [doi>10.1145/353474.353481]
• 29: Rew, R. K., Davis, G. P., Emmerson, S., and Davies, H. 2009. NetCDF user’s guide for C, An interface for data access, version 3 april 1997. Available from Unidata or in PostScript form by anonymous FTP from ftp://ftp.unidata.ucar.edu/pub/netcdf/guidec.ps.Z.
• 30: Youcef Saad , Martin H Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing, v.7 n.3, p.856-869, July 1986 [doi>10.1137/0907058]
• 31: Salsa Project. 2009. AnaMod reference manual. http://www.tacc.utexas.edu/~eijkhout/doc/anamod/latex/refman.pdf.
• 32: Solutions, I. V. I. 2009. IDL, the data visualization & analysis platform. homepage. http://www.ittvis.com/idl/.
• 33: Lloyd N. Trefethen, Pseudospectra of Linear Operators, SIAM Review, v.39 n.3, p.383-406, Sept. 1997 [doi>10.1137/S0036144595295284]
• 34: UniData. 2009. NetCDF (network common data form). http://www.unidata.ucar.edu/software/netcdf/.
• 35: Universitat Politecnica de Valencia. 2009. SLEPC -- Scalable software for Eigenvalue problem computations. http://www.grycap.upv.es/slepc/.
• 36: (W3C), W. W. W. C. 2001. XML schema: Formal description. W3C Working Draft, http://www.w3.org/TR/xmlschema-formal/.
• 37: (W3C), W. W. W. C. 2006a. Extensible markup language (XML). W3C Recommendation, http://www.w3.org/TR/REC-xml.
• 38: (W3C), W. W. W. C. 2006b Extensible stylesheet language (xsl). W3C Recommendation, http://www.w3.org/TR/xsl/.
• 39: Xu, S., Lee, E.-J., and Zhang J. 2003. An interim analysis report on preconditioners and matrices. Tech. rep. 388-03, University of Kentucky, Lexington. Department of Computer Science.

INDEX TERMS

Primary Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.2 Design Tools and Techniques
          Subjects: Software libraries

General Terms:
Design, Standardization