# scipy.sparse.bsr_matrix¶

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

Block Sparse Row matrix

This can be instantiated in several ways:
bsr_matrix(D, [blocksize=(R,C)])
with a dense matrix or rank-2 ndarray D
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]:indices[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 *
>>> from scipy import *
>>> bsr_matrix( (3,4), dtype=int8 ).todense()
matrix([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]], dtype=int8)
```
```>>> row  = array([0,0,1,2,2,2])
>>> col  = array([0,2,2,0,1,2])
>>> data = array([1,2,3,4,5,6])
>>> bsr_matrix( (data,(row,col)), shape=(3,3) ).todense()
matrix([[1, 0, 2],
[0, 0, 3],
[4, 5, 6]])
```
```>>> indptr  = array([0,2,3,6])
>>> indices = array([0,2,2,0,1,2])
>>> data    = array([1,2,3,4,5,6]).repeat(4).reshape(6,2,2)
>>> bsr_matrix( (data,indices,indptr), shape=(6,6) ).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]])
```

Attributes

 dtype shape ndim int(x[, base]) -> integer nnz blocksize has_sorted_indices Determine whether the matrix has sorted indices
 data Data array of the matrix indices BSR format index array indptr BSR format index pointer array

Methods

 asformat(format) Return this matrix in a given sparse format asfptype() Upcast matrix to a floating point format (if necessary) astype(t) check_format([full_check]) check whether the matrix format is valid conj() conjugate() copy() diagonal() Returns the main diagonal of the matrix dot(other) eliminate_zeros() getH() get_shape() getcol(j) Returns a copy of column j of the matrix, as an (m x 1) sparse getdata(ind) getformat() getmaxprint() getnnz() getrow(i) Returns a copy of row i of the matrix, as a (1 x n) sparse matmat(other) matvec(other) mean([axis]) Average the matrix over the given axis. multiply(other) Point-wise multiplication by another matrix nonzero() nonzero indices prune() Remove empty space after all non-zero elements. reshape(shape) set_shape(shape) setdiag(values[, k]) Fills the diagonal elements {a_ii} with the values from the given sequence. sort_indices() Sort the indices of this matrix in place sorted_indices() Return a copy of this matrix with sorted indices sum([axis]) Sum the matrix over the given axis. sum_duplicates() toarray() tobsr([blocksize, copy]) tocoo([copy]) Convert this matrix to COOrdinate format. tocsc() tocsr() todense() todia() todok() tolil() transpose()

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