An API for Manipulating Matrices Stored by Blocks

We discuss an API that simplifies the specification of a data structure for storing hierarchical matrices (matrices stored recursively by blocks) and the manipulation of such matrices. This work addresses a recent demand for libraries that support such storage of matrices for performance reasons. We believe a move towards such libraries has been slow largely because of the difficulty that has been encountered when implementing them using more traditional coding styles. The impact on ease of coding and performance is demonstrated in examples and experiments. The applicability of the approach for sparse matrices is also discussed.