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 ``aij[0, k], ij[1, k] = datak``
bsr_matrix((data, indices, indptr), shape=(M, N)) is the standard BSR representation where the block column indices for row i are stored in ``indicesindptr[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.
Attributes ---------- 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 stored values, including explicit zeros data Data array of the matrix indices BSR format index array indptr BSR format index pointer array blocksize Block size of the matrix has_sorted_indices Whether indices are sorted
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])