When performing computations on sparse matrices, latency in the memory hierarchy becomes much…

When performing computations on sparse matrices, latency in the memory hierarchy becomes much more of a factor. Sparse matrices lack the spatial locality in the datastream typically found in matrix operations. As a result, new matrix representations have been proposed.

One of the earliest sparse matrix representations is the Yale Sparse Matrix Format. It stores an initial sparse m × n matrix, M in row form using three onedimensional arrays. Let R be the number of nonzero entries in M. We construct an array A of length R that contains all nonzero entries of M (in left-to-right topto-bottom order). We also construct a second array IA of length m+1 (i.e., one entry per row, plus one). IA(i) contains the index in A of the first nonzero element of row i. Row i of the original matrix extends from A(IA(i)) to A(IA(i+1)−1). The third array, JA, contains the column index of each element of A, so it also is of length R.

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