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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.
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
>>> import numpy as np
>>> 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]])
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