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]])


shape Get shape of a matrix.
nnz Number of stored values, including explicit zeros.
has_sorted_indices Determine whether the matrix has sorted indices
dtype (dtype) Data type of the matrix
ndim (int) Number of dimensions (this is always 2)
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.
argmax([axis, out]) Return indices of minimum elements along an axis.
argmin([axis, out]) Return indices of minimum elements along an axis.
asformat(format) Return this matrix in a given sparse format
asfptype() Upcast matrix to a floating point format (if necessary)
astype(t) Cast the matrix elements to a specified type.
ceil() Element-wise ceil.
check_format([full_check]) check whether the matrix format is valid
conj() Element-wise complex conjugation.
conjugate() Element-wise complex conjugation.
copy() Returns a copy of this matrix.
count_nonzero() Number of non-zero entries, equivalent to
deg2rad() Element-wise deg2rad.
diagonal() Returns the main diagonal of the matrix
dot(other) Ordinary dot product
eliminate_zeros() Remove zero elements in-place.
expm1() Element-wise expm1.
floor() Element-wise floor.
getH() Return the Hermitian transpose of this matrix.
get_shape() Get shape of a matrix.
getcol(j) Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).
getformat() Format of a matrix representation as a string.
getmaxprint() Maximum number of elements to display when printed.
getnnz([axis]) Number of stored values, including explicit zeros.
getrow(i) Returns a copy of row i of the matrix, as a (1 x n) sparse matrix (row vector).
log1p() Element-wise log1p.
matmat(*args, **kwds) matmat is deprecated!
matvec(*args, **kwds) matvec is deprecated!
max([axis, out]) Return the maximum of the matrix or maximum along an axis.
maximum(other) Element-wise maximum between this and another matrix.
mean([axis, dtype, out]) Compute the arithmetic mean along the specified axis.
min([axis, out]) Return the minimum of the matrix or maximum along an axis.
minimum(other) Element-wise minimum between this and another 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.
reshape(shape[, order]) Gives a new shape to a sparse matrix without changing its data.
rint() Element-wise rint.
set_shape(shape) See reshape.
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, dtype, out]) Sum the matrix elements over a given axis.
sum_duplicates() Eliminate duplicate matrix entries by adding them together
tan() Element-wise tan.
tanh() Element-wise tanh.
toarray([order, out]) See the docstring for spmatrix.toarray.
tobsr([blocksize, copy]) Convert this matrix into Block Sparse Row Format.
tocoo([copy]) Convert this matrix to COOrdinate format.
tocsc([copy]) Convert this matrix to Compressed Sparse Column format.
tocsr([copy]) Convert this matrix to Compressed Sparse Row format.
todense([order, out]) Return a dense matrix representation of this matrix.
todia([copy]) Convert this matrix to sparse DIAgonal format.
todok([copy]) Convert this matrix to Dictionary Of Keys format.
tolil([copy]) Convert this matrix to LInked List format.
transpose([axes, copy]) Reverses the dimensions of the sparse matrix.
trunc() Element-wise trunc.