# scipy.sparse.bsr_array#

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

Block Sparse Row format sparse array.

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

where D is a 2-D ndarray.

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

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

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

to construct an empty sparse array 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 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 array (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

```>>> import numpy as np
>>> from scipy.sparse import bsr_array
>>> 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

`shape`2-tuple

The shape of the array.

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 array

indices

BSR format index array of the array

indptr

BSR format index pointer array of the array

`blocksize`

Block size of the matrix.

`has_sorted_indices`bool

Whether the indices are sorted

`has_canonical_format`bool

Whether the array/matrix has sorted indices and no duplicates

`T`

Transpose.

Methods

 Element-wise arcsin. Element-wise arcsinh. Element-wise arctan. 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/matrix in the passed format. Upcast array/matrix to a floating point format (if necessary) `astype`(dtype[, casting, copy]) Cast the array/matrix elements to a specified type. 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. Returns a copy of this array/matrix. Number of non-zero entries, equivalent to Element-wise deg2rad. `diagonal`([k]) Returns the kth diagonal of the array/matrix. `dot`(other) Ordinary dot product Remove zero elements in-place. Element-wise expm1. Element-wise floor. Return the Hermitian transpose of this array/matrix. Get shape of a sparse array/matrix. Returns a copy of column j of the array/matrix, as an (m x 1) sparse array/matrix (column vector). Sparse array/matrix storage format. Maximum number of elements to display when printed. `getnnz`([axis]) Number of stored values, including explicit zeros. Returns a copy of row i of the array/matrix, as a (1 x n) sparse array/matrix (row vector). Element-wise log1p. `max`([axis, out]) 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]) 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 another array/matrix, vector, or scalar. `nanmax`([axis, out]) Return the maximum of the array/matrix or maximum along an axis, ignoring any NaNs. `nanmin`([axis, out]) Return the minimum of the array/matrix or minimum along an axis, ignoring any NaNs. Nonzero indices of the array/matrix. `power`(n[, dtype]) This function performs element-wise power. Remove empty space after all non-zero elements. 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` Element-wise rint. `set_shape`(shape) `setdiag`(values[, k]) Set diagonal or off-diagonal elements of the array/matrix. Element-wise sign. Element-wise sin. Element-wise sinh. Sort the indices of this array/matrix in place Return a copy of this array/matrix with sorted indices Element-wise sqrt. `sum`([axis, dtype, out]) Sum the array/matrix elements over a given axis. Eliminate duplicate array/matrix entries by adding them together Element-wise tan. 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 array/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. Element-wise trunc.
 __getitem__ __mul__