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 exceptionally well for some time. Release I of that collection (Duff, Grimes and Lewis, 1989) contains nearly 300 matrices of order 9 to 35,558 from a variety of applications. One of the difficulties with such collections is that their size and diversity makes them unwieldy to manage and use effectively. As a result, 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 network communications infrastructure, such as the World Wide Web (WWW), are opening up new possibilities for improving the access to and usability of test corpora of this type. In this paper we describe a WWW resource which provides a variety of services based initially upon the Harwell-Boeing collection. We call this resource the Matrix Market.
The Matrix Market is a repository of matrices. Matrices are gathered together into sets. Matrices in a set are related by application area or contributed from a single source. Sets can further be grouped into collections managed by a single group, such as the Harwell-Boeing collection. Individual matrices may be stored explicitly as dense or sparse matrices, or may be available implicitly via a code which generates them. The matrices can be of a wide variety of types, e.g., real, complex, symmetric, nonsymmetric, Hermitian. Some are representations of nonzero patterns only. Others include supplementary data such as right-hand sides, solution vectors, and initial vectors for iterative solvers. We store matrices and associated material one per file, in a fixed format..
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. Similarly, we have developed a WWW
page for each set, which gives its background (e.g., source and application
area), references, as well as a thumbnail sketch of each matrix's nonzero
pattern. We maintain a separate database which contains all of the information
on these pages in a highly structured form. This allows us to manipulate the
data in various ways; for example, all of the matrix and set WWW pages are
automatically generated from this database. The database also supports both
structured and free-text retrieval.
In the remainder of this paper we describe each of the components of the repository in detail, with emphasis on the case of sparse matrix data. This reflects the organization and implementation of the Matrix Market prototype released in February 1996. The Matrix Market is still under active development, and some of the details of its interface and implementation may evolve over time. In the final section, we outline plans for extending this service to dense matrices and matrix generation software, as well as ideas for use of new WWW technologies such as Java (Flanagan, 1996) to enhance its the usefulness.