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.


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.


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.


>>> 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]])


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


arcsin() Element-wise arcsin.
arcsinh() Element-wise arcsinh.
arctan() Element-wise arctan.
arctanh() Element-wise arctanh.
asformat(format) Return this matrix in a given sparse format
asfptype() Upcast matrix to a floating point format (if necessary)
ceil() Element-wise ceil.
check_format([full_check]) check whether the matrix format is valid
deg2rad() Element-wise deg2rad.
diagonal() Returns the main diagonal of the matrix
dot(other) Ordinary dot product ..
expm1() Element-wise expm1.
floor() Element-wise floor.
getcol(j) Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).
getrow(i) Returns a copy of row i of the matrix, as a (1 x n) sparse matrix (row vector).
log1p() Element-wise log1p.
max([axis]) Maximum of the elements of this matrix.
mean([axis]) Average the matrix over the given axis.
min([axis]) Minimum of the elements of this matrix.
multiply(other) Point-wise multiplication by another matrix, vector, or scalar.
nonzero() nonzero indices
power(n[, dtype]) This function performs element-wise power.
prune() Remove empty space after all non-zero elements.
rad2deg() Element-wise rad2deg.
rint() Element-wise rint.
setdiag(values[, k]) Set diagonal or off-diagonal elements of the array.
sign() Element-wise sign.
sin() Element-wise sin.
sinh() Element-wise sinh.
sort_indices() Sort the indices of this matrix in place
sorted_indices() Return a copy of this matrix with sorted indices
sqrt() Element-wise sqrt.
sum([axis]) Sum the matrix over the given axis.
tan() Element-wise tan.
tanh() Element-wise tanh.
toarray([order, out]) See the docstring for spmatrix.toarray.
tobsr([blocksize, copy])
tocoo([copy]) Convert this matrix to COOrdinate format.
todense([order, out]) Return a dense matrix representation of this matrix.
trunc() Element-wise trunc.