scipy.sparse.bsr_matrix#
- class scipy.sparse.bsr_matrix(arg1, shape=None, dtype=None, copy=False, blocksize=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
andij
satisfya[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 indata[ indptr[i]: indptr[i+1] ]
. If the shape parameter is not supplied, the matrix dimensions are inferred from the index arrays.
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
andN % 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_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]])
- Attributes:
- dtypedtype
Data type of the matrix
shape
2-tupleShape 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_indices
boolWhether the indices are sorted
has_canonical_format
boolWhether 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])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.
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.
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
Remove zero elements in-place.
expm1
()Element-wise expm1.
floor
()Element-wise floor.
getH
()Return the Hermitian transpose of this matrix.
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).
Matrix storage format
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])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
()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 the indices of this array/matrix in place
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.
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 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.
trunc
()Element-wise trunc.
__getitem__