Block Compressed Row Format (BSR)

  • basically a CSR with dense sub-matrices of fixed shape instead of scalar items

    • block size (R, C) must evenly divide the shape of the matrix (M, N)

    • three NumPy arrays: indices, indptr, data

      • indices is array of column indices for each block

      • data is array of corresponding nonzero values of shape (nnz, R, C)

      • …

    • subclass of _cs_matrix (common CSR/CSC functionality)

      • subclass of _data_matrix (sparse matrix classes with .data attribute)

  • fast matrix vector products and other arithmetic (sparsetools)

  • constructor accepts:

    • dense matrix (array)

    • sparse matrix

    • shape tuple (create empty matrix)

    • (data, ij) tuple

    • (data, indices, indptr) tuple

  • many arithmetic operations considerably more efficient than CSR for sparse matrices with dense sub-matrices

  • use:

    • like CSR

    • vector-valued finite element discretizations

Examples

  • create empty BSR matrix with (1, 1) block size (like CSR…):

    >>> mtx = sp.sparse.bsr_matrix((3, 4), dtype=np.int8)

    >>> mtx

    <3x4 sparse matrix of type '<... 'numpy.int8'>'

            with 0 stored elements (blocksize = 1x1) in Block Sparse Row format>

    >>> mtx.todense()

    matrix([[0, 0, 0, 0],

            [0, 0, 0, 0],

            [0, 0, 0, 0]], dtype=int8)

  • create empty BSR matrix with (3, 2) block size:

    >>> mtx = sp.sparse.bsr_matrix((3, 4), blocksize=(3, 2), dtype=np.int8)

    >>> mtx

    <3x4 sparse matrix of type '<... 'numpy.int8'>'

            with 0 stored elements (blocksize = 3x2) in Block Sparse Row format>

    >>> mtx.todense()

    matrix([[0, 0, 0, 0],

            [0, 0, 0, 0],

            [0, 0, 0, 0]], dtype=int8)

    • a bug?

  • create using (data, ij) tuple with (1, 1) block size (like CSR…):

    >>> row = np.array([0, 0, 1, 2, 2, 2])

    >>> col = np.array([0, 2, 2, 0, 1, 2])

    >>> data = np.array([1, 2, 3, 4, 5, 6])

    >>> mtx = sp.sparse.bsr_matrix((data, (row, col)), shape=(3, 3))

    >>> mtx

    <3x3 sparse matrix of type '<... 'numpy.int64'>'

            with 6 stored elements (blocksize = 1x1) in Block Sparse Row format>

    >>> mtx.todense()

    matrix([[1, 0, 2],

            [0, 0, 3],

            [4, 5, 6]]...)

    >>> mtx.data

    array([[[1]],

    

           [[2]],

    

           [[3]],

    

           [[4]],

    

           [[5]],

    

           [[6]]]...)

    >>> mtx.indices

    array([0, 2, 2, 0, 1, 2], dtype=int32)

    >>> mtx.indptr

    array([0, 2, 3, 6], dtype=int32)

  • create using (data, indices, indptr) tuple with (2, 2) block size:

    >>> indptr = np.array([0, 2, 3, 6])

    >>> indices = np.array([0, 2, 2, 0, 1, 2])

    >>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)

    >>> mtx = sp.sparse.bsr_matrix((data, indices, indptr), shape=(6, 6))

    >>> mtx.todense()

    matrix([[1, 1, 0, 0, 2, 2],

            [1, 1, 0, 0, 2, 2],

            [0, 0, 0, 0, 3, 3],

            [0, 0, 0, 0, 3, 3],

            [4, 4, 5, 5, 6, 6],

            [4, 4, 5, 5, 6, 6]])

    >>> data

    array([[[1, 1],

            [1, 1]],

    

           [[2, 2],

            [2, 2]],

    

           [[3, 3],

            [3, 3]],

    

           [[4, 4],

            [4, 4]],

    

           [[5, 5],

            [5, 5]],

    

           [[6, 6],

            [6, 6]]])