sparse.bsr

Compressed Block Sparse Row matrix format

Module Contents

Classes

bsr_matrix(self,arg1,shape=None,dtype=None,copy=False,blocksize=None) Block Sparse Row matrix

Functions

isspmatrix_bsr(x) Is x of a bsr_matrix type?
class bsr_matrix(arg1, shape=None, dtype=None, copy=False, blocksize=None)

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.
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
has_sorted_indices
Whether indices are sorted

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.

Blocksize

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]])
__init__(arg1, shape=None, dtype=None, copy=False, blocksize=None)
check_format(full_check=True)

check whether the matrix format is valid

Parameters:
full_check:
True - rigorous check, O(N) operations : default False - basic check, O(1) operations
_get_blocksize()
getnnz(axis=None)
__repr__()
diagonal(k=0)
__getitem__(key)
__setitem__(key, val)
matvec(other)

Multiply matrix by vector.

matmat(other)

Multiply this sparse matrix by other matrix.

_add_dense(other)
_mul_vector(other)
_mul_multivector(other)
_mul_sparse_matrix(other)
tobsr(blocksize=None, copy=False)

Convert this matrix into Block Sparse Row Format.

With copy=False, the data/indices may be shared between this matrix and the resultant bsr_matrix.

If blocksize=(R, C) is provided, it will be used for determining block size of the bsr_matrix.

tocsr(copy=False)
tocsc(copy=False)
tocoo(copy=True)

Convert this matrix to COOrdinate format.

When copy=False the data array will be shared between this matrix and the resultant coo_matrix.

toarray(order=None, out=None)
transpose(axes=None, copy=False)
eliminate_zeros()

Remove zero elements in-place.

sum_duplicates()

Eliminate duplicate matrix entries by adding them together

The is an in place operation

sort_indices()

Sort the indices of this matrix in place

prune()

Remove empty space after all non-zero elements.

_binopt(other, op, in_shape=None, out_shape=None)

Apply the binary operation fn to two sparse matrices.

_with_data(data, copy=True)

Returns a matrix with the same sparsity structure as self, but with different data. By default the structure arrays (i.e. .indptr and .indices) are copied.

isspmatrix_bsr(x)

Is x of a bsr_matrix type?

x
object to check for being a bsr matrix
bool
True if x is a bsr matrix, False otherwise
>>> from scipy.sparse import bsr_matrix, isspmatrix_bsr
>>> isspmatrix_bsr(bsr_matrix([[5]]))
True
>>> from scipy.sparse import bsr_matrix, csr_matrix, isspmatrix_bsr
>>> isspmatrix_bsr(csr_matrix([[5]]))
False