A Proposed Standard for Matrix Metadata∗

We propose a standard for storing metadata describing numerical matrix data. The standard consists of an XML file format and an internal data format. We give the abstract description of the XML storage format, APIs (Application Programmer Interfaces) for access to the stored data inside a program, and a core set of categories of data to be stored. The standard defines an open-ended format, allowing for other parties to define additional metadata categories to be stored within this framework. 1 General discussion Matrix storage formats, both file formats and data structures, traditionally limit themselves to specifying only the minimally necessary description of the data: the matrix size, and the matrix elements themselves with a fairly explicit description of the nonzero structure for sparse matrices. However, we can associate with matrix data any number of derived properties, such as norms, spectral properties, or graph properties in the sparse case. There is no standard way of storing such data, making interoperability hard between software modules written by different authors. Such interoperability would be valuable in a number of contexts. For instance, linear algebra algorithms often need, or at least have a use for, difficult to compute matrix statistics, such as condition number estimates. Thus, the total algorithm consists of two disparate modules: one analyser that estimates the numerical quantity, and the algorithm proper which uses this quantity to fine-tune its workings. While any ad hoc fit can be made between such analysis-producing and analysis-consuming software, a more general solution would make componentization of such software possible. We note that analysis modules need not limit themselves, as in the example just given, to calculation or estimation of numerical quantities from the problem data. We can also envision that an application annotate its data before passing it to the numerical routine. Thus, information like the nature of a differential equation or its discretisation can be preserved, and translated to useful numerical information by a different kind of analysis module. There is also use for a more permanent storage format of numerical metadata. We will argue both points, the programmatic and the storage aspects of metadata, in detail below. The existence of a metadata standard for numerical data – we limit ourselves here to matrix data, though extension of these ideas to other fields is natural (see for instance [2, ch. 7]) – makes the following software functionalities possible. • First of all, it allows numerical algorithms to request metadata, not easily derivable from more traditional inputs, that will assist in the computation process. ∗ This work was funded in part by the Los Alamos Computer Science Institute through the subcontract # R71700J-29200099 from Rice University, and by the National Science Foundation under grant # 0203984.