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 arithmetics (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 = 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 = 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 = 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 = 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]]])