MATSELL#

MATSELL = “sell” - A matrix type to be used for sparse matrices, [ZMRS18] This matrix type is identical to MATSEQSELL when constructed with a single process communicator, and MATMPISELL otherwise. As a result, for single process communicators, MatSeqSELLSetPreallocation() is supported, and similarly MatMPISELLSetPreallocation() is supported for communicators controlling multiple processes. It is recommended that you call both of the above preallocation routines for simplicity.

Options Database Key#

  • -mat_type sell - sets the matrix type to “sell” during a call to MatSetFromOptions()

Notes#

This format is only supported for real scalars, double precision, and 32-bit indices (the defaults).

It can provide better performance on Intel and AMD processes with AVX2 or AVX512 support for matrices that have a similar number of non-zeros in contiguous groups of rows. However if the computation is memory bandwidth limited it may not provide much improvement.

Developer Notes#

On Intel (and AMD) systems some of the matrix operations use SIMD (AVX) instructions to achieve higher performance.

The sparse matrix format is as follows. For simplicity we assume a slice size of 2, it is actually 8

                            (2 0  3 4)
   Consider the matrix A =  (5 0  6 0)
                            (0 0  7 8)
                            (0 0  9 9)

   symbolically the Ellpack format can be written as

        (2 3 4 |)           (0 2 3 |)
   v =  (5 6 0 |)  colidx = (0 2 2 |)
        --------            ---------
        (7 8 |)             (2 3 |)
        (9 9 |)             (2 3 |)

    The data for 2 contiguous rows of the matrix are stored together (in column-major format) (with any left-over rows handled as a special case).
    Any of the rows in a slice fewer columns than the rest of the slice (row 1 above) are padded with a previous valid column in their "extra" colidx[] locations and
    zeros in their "extra" v locations so that the matrix operations do not need special code to handle different length rows within the 2 rows in a slice.

    The one-dimensional representation of v used in the code is (2 5 3 6 4 0 7 9 8 9)  and for colidx is (0 0 2 2 3 2 2 2 3 3)

See MatMult_SeqSELL() for how this format is used with the SIMD operations to achieve high performance.

References#

ZMRS18

Hong Zhang, Richard T. Mills, Karl Rupp, and Barry F. Smith. Vectorized parallel sparse matrix-vector multiplication in PETSc using AVX-512. In Proceedings of the 47th International Conference on Parallel Processing. 2018.

See Also#

Mat, MatCreateSeqSELL(), MatCreateSeqAIJ(), MatCreateSell(), MATSEQSELL, MATMPISELL, MATSEQAIJ, MATMPIAIJ, MATAIJ

Level#

beginner

Location#

src/mat/impls/sell/seq/sell.c

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Index of all manual pages