scipy.sparse.bsr_matrix

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

Block Sparse Row format sparse matrix.

This can be instantiated in several ways:

bsr_array(D, [blocksize=(R,C)])

where D is a dense matrix or 2-D ndarray.

bsr_array(S, [blocksize=(R,C)])

with another sparse matrix S (equivalent to S.tobsr())

bsr_array((M, N), [blocksize=(R,C), dtype])

to construct an empty sparse matrix with shape (M, N) dtype is optional, defaulting to dtype=’d’.

bsr_array((data, ij), [blocksize=(R,C), shape=(M, N)])

where data and ij satisfy a[ij[0, k], ij[1, k]] = data[k]

bsr_array((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 array dimensions are inferred from the index arrays.

Notes

Sparse arrays 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 sparse 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.

Canonical Format

In canonical format, there are no duplicate blocks and indices are sorted per row.

Examples

>>> from scipy.sparse import bsr_array
>>> import numpy as np
>>> bsr_array((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_array((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_array((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]])

Attributes:

dtypedtype

Data type of the array

shape2-tuple

Shape of the matrix

ndimint

Number of dimensions (this is always 2)

nnz

Number of stored values, including explicit zeros.

data

Data array

indices

BSR format index array

indptr

BSR format index pointer array

blocksize

Block size

has_sorted_indices

Determine whether the matrix has sorted indices

Methods

__len__()
__mul__(other)
arcsin()	Element-wise arcsin.
arcsinh()	Element-wise arcsinh.
arctan()	Element-wise arctan.
arctanh()	Element-wise arctanh.
argmax([axis, out])	Return indices of maximum elements along an axis.
argmin([axis, out])	Return indices of minimum elements along an axis.
asformat(format[, copy])	Return this array in the passed format.
asfptype()	Upcast array to a floating point format (if necessary)
astype(dtype[, casting, copy])	Cast the array elements to a specified type.
ceil()	Element-wise ceil.
check_format([full_check])	check whether the matrix format is valid
conj([copy])	Element-wise complex conjugation.
conjugate([copy])	Element-wise complex conjugation.
copy()	Returns a copy of this array.
count_nonzero()	Number of non-zero entries, equivalent to
deg2rad()	Element-wise deg2rad.
diagonal([k])	Returns the kth diagonal of the array.
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 array.
get_shape()	Get the shape of the matrix
getcol(j)	Returns a copy of column j of the array, as an (m x 1) sparse array (column vector).
getformat()	Matrix storage format
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 array, as a (1 x n) sparse array (row vector).
log1p()	Element-wise log1p.
max([axis, out])	Return the maximum of the matrix or maximum along an axis.
maximum(other)	Element-wise maximum between this and another array.
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 array.
multiply(other)	Point-wise multiplication by another matrix, vector, or scalar.
nanmax([axis, out])	Return the maximum of the matrix or maximum along an axis, ignoring any NaNs.
nanmin([axis, out])	Return the minimum of the matrix or minimum along an axis, ignoring any NaNs.
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(self, shape[, order, copy])	Gives a new shape to a sparse array without changing its data.
resize(*shape)	Resize the array in-place to dimensions given by shape
rint()	Element-wise rint.
set_shape(shape)	Set the shape of the matrix in-place
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 array 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])	Return a dense ndarray representation of this sparse array.
tobsr([blocksize, copy])	Convert this matrix into Block Sparse Row Format.
tocoo([copy])	Convert this matrix to COOrdinate format.
tocsc([copy])	Convert this array to Compressed Sparse Column format.
tocsr([copy])	Convert this array to Compressed Sparse Row format.
todense([order, out])	Return a dense matrix representation of this sparse array.
todia([copy])	Convert this array to sparse DIAgonal format.
todok([copy])	Convert this array to Dictionary Of Keys format.
tolil([copy])	Convert this array to List of Lists format.
trace([offset])	Returns the sum along diagonals of the sparse array.
transpose([axes, copy])	Reverses the dimensions of the sparse array.
trunc()	Element-wise trunc.

__getitem__