Block Compressed Row Format (BSR)

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import numpy as np
import scipy as sp

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 array/matrix

    • sparse array/matrix

    • shape tuple (create empty array)

    • (data, coords) 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 array with (1, 1) block size (like CSR…):#

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

<Block Sparse Row sparse array of dtype 'int8'
	with 0 stored elements (blocksize=1x1) and shape (3, 4)>

mtx.toarray()

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

Create empty BSR array with (3, 2) block size:#

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

<Block Sparse Row sparse array of dtype 'int8'
	with 0 stored elements (blocksize=3x2) and shape (3, 4)>

mtx.toarray()

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

Create using (data, coords) 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_array((data, (row, col)), shape=(3, 3))
mtx

<Block Sparse Row sparse array of dtype 'int64'
	with 6 stored elements (blocksize=1x1) and shape (3, 3)>

mtx.toarray()

array([[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])

mtx.indptr

array([0, 2, 3, 6])

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_array((data, indices, indptr), shape=(6, 6))
mtx.toarray()

array([[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]]])
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