Matrix Market and Dynamically Generated Content

The decomposition, solution, and eigenanalysis of systems of linear equations remain important problems in scientific computation for which new algorithms and software packages are continually being developed. In order to make reliable, reproducible quantitative assessments of the value of new algorithmic developments, it is useful to have a common collection of representative problems through which methods can be compared. For sparse matrices the Harwell-Boeing Sparse Matrix Collection has served this purpose for some time. However, one of the difficulties with such collections is that their size and diversity makes them unwieldy to manage and use effectively. Consequently, the Harwell-Boeing collection has not been used as much as it should, and new matrices have not been regularly added to the collection. Recent developments in Web techologies are opening up new possibilities for improving the access to and usability of test corpora of this type.

The Matrix Market provides convenient Web access to a repository of test data for use in comparative studies of algorithms for numerical linear algebra. Matrices and related data from problems in linear systems, least squares, and eigenvalue calculations in a wide variety of scientific and engineering disciplines are provided. Tools for browsing through the collection or for searching for matrices with special properties are included. Additional background on the project can be found in [3]. In this paper, we discuss work on the user interface to Matrix Market.

Matrices in Matrix Market are gathered together into sets. Matrices in a set are related by application area or are contributed from a single source. Sets can be further grouped into collections managed by a single group, such as the Harwell-Boeing collection. Individual matrices may be stored expecitily as dense or sparse matrices, or may be made available via a code which generates them. For each matrix, we provide a summary page in HTML format outlining the properties of the matrix and displaying a graphical representation of its structure. Clicking on the GIF image providing the view of the nonzero structure retrieves another image at a finer level of detail. Similarly, we have developed an HTML page for each set, which gives its background (e.g., source and application area), references, as well as a thumbnail sketch of the nonzero pattern of each matrix in the set. Clicking on the matrix identifier or thumbnail retrieves the home page for that particular matrix. A separate database contains all the information in a highly strucutured form, allowing us to manipulate the data in various ways. All the matrix and set HTML pages are automatically generated from this database. The database also supports both structured and free-text retrieval. The matrix collection may also be browsed by collection, application domain, or contributor.

Matrix Market provides a Database Query tool with an HTML form interface that allows the user to specify a large variety of attributes describing selection criteria for matrices. Lists allow selection based on predefined attributes in the database, such as linear algebra problem type, arithmetic field (real, complex, pattern, symmetry property, definiteness, type of nonzero structure, storage mode, and shape. Text fields allow the user to specify the minimum and maximum number of rows, columns, and nonzeros. Additional buttons allow the user to request that right-hand sides, exact solution, or initial vectors be made available. A text field allows the user to specify patterns to match in the database text descriptions of the matrices. Help text is provided for each of the available selection criteria. Only matrices that satisfy all of the requirements specified by the user are retrieved. Matches are returned on an HTML page organized by matrix set. Links to the home pages of individual matrices as well as the sets are provided.

We have a variety of plans for improving the Matrix Market. Among these are the following:

• Automated submission. We intend that Matrix Market provide a real marketplace for the exchange of matrix test data. For this to happen there must be a convenient way for users to submit their own matrices for possible inclusion in the collection. We envision a set of HTML forms or a Java applet that allows users to describe their matrices and to either provide a URL where the matrix data can be picked up or upload the data to the Matrix Market site. Submitting the form would construct prototype database entries for the new matrix and would notify the maintainers that a new matrix has been submitted. We believe that it will still be necessary to review contributions to determine if they are in the public domain, represent a significant application area, are of interest to algorithm developers, and do not substantially duplicate other matrices already in the collection.
• Matrix generators (Matrix Market Deli). Many of the matrices found in Matrix Market were obtained by running application codes that generated them. In many cases these codes are parameterized so that a wide range of matrices can be produced. We plan to incorporate programs which generate matrices useful for testing linear algebra software into our collection. These may be made available either as links to downloadable codes or access to remote execution servers which exercise the generation software on demand. The latter method could provide access to proprietary matrix generators, with permission of the authors. One way to supply matrix generation software is to develop Java applets which present a class of matrices whose individual members can be computed on demand inside a Web browser. We are currently experimenting with such tools. This is a more scalable approach than providing a remote execution service, but presents some challenges in that there has yet been little experience in developing portable, reliable, and efficient floating-point applications in the Java environment.
• Issuing the collection on CD-ROM. We plan to issue the entire Matrix Market collection on CD-ROM to facilitate easier local access.

A service that currently provides dynamically generated content is the source code request service for the NIST Sparse BLAS, a set of sparse matrix computational kernels . The request dynamically generates specific routines from the library according to user specifications. The user is provided with an HTML form for selecting the matrix storage format, the BLAS operation, the type of scaling, the number of right-hand sides, and scalar factors. Help text is provided for each of the selection criteria.