scipy.sparse.

bsr_matrix#

class scipy.sparse.bsr_matrix(arg1, shape=None, dtype=None, copy=False, blocksize=None, *, maxprint=None)[source]#

Block Sparse Row format sparse matrix.

This can be instantiated in several ways:
bsr_matrix(D, [blocksize=(R,C)])

where D is a 2-D ndarray.

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

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

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

to construct an empty sparse 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:
dtypedtype

Data type of the matrix

shape2-tuple

Shape of the matrix

ndimint

Number of dimensions (this is always 2)

nnz

Number of stored values, including explicit zeros.

size

Number of stored values.

data

BSR format data array of the matrix

indices

BSR format index array of the matrix

indptr

BSR format index pointer array of the matrix

blocksize

Block size of the matrix.

has_sorted_indicesbool

Whether the indices are sorted

has_canonical_formatbool

Whether the array/matrix has sorted indices and no duplicates

T

Transpose.

Methods

__len__()

__mul__(other)

arcsin()

Element-wise arcsin.

arcsinh()

Element-wise arcsinh.

arctan()

Element-wise arctan.

arctanh()

Element-wise arctanh.

argmax([axis, out, explicit])

Return indices of maximum elements along an axis.

argmin([axis, out, explicit])

Return indices of minimum elements along an axis.

asformat(format[, copy])

Return this array/matrix in the passed format.

asfptype()

Upcast matrix to a floating point format (if necessary)

astype(dtype[, casting, copy])

Cast the array/matrix elements to a specified type.

ceil()

Element-wise ceil.

check_format([full_check])

Check whether the array/matrix respects the BSR format.

conj([copy])

Element-wise complex conjugation.

conjugate([copy])

Element-wise complex conjugation.

copy()

Returns a copy of this array/matrix.

count_nonzero([axis])

Number of non-zero entries, equivalent to

deg2rad()

Element-wise deg2rad.

diagonal([k])

Returns the kth diagonal of the array/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 the shape of the matrix

getcol(j)

Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (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 matrix, as a (1 x n) sparse matrix (row vector).

log1p()

Element-wise log1p.

max([axis, out, explicit])

Return the maximum of the array/matrix or maximum along an axis.

maximum(other)

Element-wise maximum between this and another array/matrix.

mean([axis, dtype, out])

Compute the arithmetic mean along the specified axis.

min([axis, out, explicit])

Return the minimum of the array/matrix or maximum along an axis.

minimum(other)

Element-wise minimum between this and another array/matrix.

multiply(other)

Point-wise multiplication by array/matrix, vector, or scalar.

nanmax([axis, out, explicit])

Return the maximum, ignoring any Nans, along an axis.

nanmin([axis, out, explicit])

Return the minimum, ignoring any Nans, along an axis.

nonzero()

Nonzero indices of the array/matrix.

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/matrix without changing its data.

resize(*shape)

Resize the array/matrix 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/matrix.

sign()

Element-wise sign.

sin()

Element-wise sin.

sinh()

Element-wise sinh.

sort_indices()

Sort the indices of this array/matrix in place

sorted_indices()

Return a copy of this array/matrix with sorted indices

sqrt()

Element-wise sqrt.

sum([axis, dtype, out])

Sum the array/matrix elements over a given axis.

sum_duplicates()

Eliminate duplicate array/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/matrix.

tobsr([blocksize, copy])

Convert this array/matrix into Block Sparse Row Format.

tocoo([copy])

Convert this array/matrix to COOrdinate format.

tocsc([copy])

Convert this array/matrix to Compressed Sparse Column format.

tocsr([copy])

Convert this array/matrix to Compressed Sparse Row format.

todense([order, out])

Return a dense representation of this sparse matrix.

todia([copy])

Convert this array/matrix to sparse DIAgonal format.

todok([copy])

Convert this array/matrix to Dictionary Of Keys format.

tolil([copy])

Convert this array/matrix to List of Lists format.

trace([offset])

Returns the sum along diagonals of the sparse array/matrix.

transpose([axes, copy])

Reverses the dimensions of the sparse array/matrix.

trunc()

Element-wise trunc.

__getitem__

Notes

Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power.

Summary of BSR format

The Block Sparse 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. Such sparse 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.

Limitations

Block Sparse Row format sparse matrices do not support slicing.

Examples

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