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Sparse matrices and linear algebra are at the heart of scientificsimulations. More than 70 sparse matrix storage formats have been developedover the years, targeting a wide range of hardware architectures and matrixtypes. Each format is developed to exploit the particular strengths of anarchitecture, or the specific sparsity patterns of matrices, and the choice ofthe right format can be crucial in order to achieve optimal performance. Theadoption of dynamic sparse matrices that can change the underlyingdata-structure to match the computation at runtime without introducingprohibitive overheads has the potential of optimizing performance throughdynamic format selection.  In this paper, we introduce Morpheus, a library that provides an efficientabstraction for dynamic sparse matrices. The adoption of dynamic matrices aimsto improve the productivity of developers and end-users who do not need to knowand understand the implementation specifics of the different formats available,but still want to take advantage of the optimization opportunity to improve theperformance of their applications. We demonstrate that by porting HPCG to useMorpheus, and without further code changes, 1) HPCG can now targetheterogeneous environments and 2) the performance of the SpMV kernel isimproved up to 2.5x and 7x on CPUs and GPUs respectively, through runtimeselection of the best format on each MPI process.

Exploiting dynamic sparse matrices for performance portable linear algebra operations