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