scipy.sparse.bsr_matrix

class scipy.sparse.bsr_matrix(arg1, shape=None, dtype=None, copy=False, blocksize=None)[source]

Block Sparse Row matrix

This can be instantiated in several ways:
bsr_matrix(D, [blocksize=(R,C)])
where D is a dense matrix or 2-D ndarray.
bsr_matrix(S, [blocksize=(R,C)])
with another sparse matrix S (equivalent to S.tobsr())
bsr_matrix((M, N), [blocksize=(R,C), dtype])
to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype=’d’.
bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)])
where data and ij satisfy a[ij[0, k], ij[1, k]] = data[k]
bsr_matrix((data, indices, indptr), [shape=(M, N)])
is the standard BSR representation where the block column indices for row i are stored in indices[indptr[i]:indptr[i+1]] and their corresponding block values are stored in data[ indptr[i]: indptr[i+1] ]. If the shape parameter is not supplied, the matrix dimensions are inferred from the index arrays.

Notes

Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power.

Summary of BSR format

The Block Compressed Row (BSR) format is very similar to the Compressed Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense sub matrices like the last example below. Block matrices often arise in vector-valued finite element discretizations. In such cases, BSR is considerably more efficient than CSR and CSC for many sparse arithmetic operations.

Blocksize

The blocksize (R,C) must evenly divide the shape of the matrix (M,N). That is, R and C must satisfy the relationship M % R = 0 and N % C = 0.

If no blocksize is specified, a simple heuristic is applied to determine an appropriate blocksize.

Examples

>>> from scipy.sparse import bsr_matrix
>>> bsr_matrix((3, 4), dtype=np.int8).toarray()
array([[0, 0, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 0]], dtype=int8)
>>> 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])
>>> bsr_matrix((data, (row, col)), shape=(3, 3)).toarray()
array([[1, 0, 2],
       [0, 0, 3],
       [4, 5, 6]])
>>> 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)
>>> bsr_matrix((data,indices,indptr), shape=(6, 6)).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]])

Attributes

has_sorted_indices Determine whether the matrix has sorted indices
dtype (dtype) Data type of the matrix
shape (2-tuple) Shape of the matrix
ndim (int) Number of dimensions (this is always 2)
nnz Number of nonzero elements
data Data array of the matrix
indices BSR format index array
indptr BSR format index pointer array
blocksize Block size of the matrix

Methods