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reconstruct_path(csgraph, predecessors, directed=True)
Construct a tree from a graph and a predecessor list.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array_like or sparse matrix
The N x N matrix representing the directed or undirected graph
from which the predecessors are drawn.
predecessors : array_like, one dimension
The length-N array of indices of predecessors for the tree. The
index of the parent of node i is given by predecessors[i].
directed : bool, optional
If True (default), then operate on a directed graph: only move from
point i to point j along paths csgraph[i, j].
If False, then operate on an undirected graph: the algorithm can
progress from point i to j along csgraph[i, j] or csgraph[j, i].
Returns
-------
cstree : csr matrix
The N x N directed compressed-sparse representation of the tree drawn
from csgraph which is encoded by the predecessor list.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import reconstruct_path
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 3) 3
>>> pred = np.array([-9999, 0, 0, 1], dtype=np.int32)
>>> cstree = reconstruct_path(csgraph=graph, predecessors=pred, directed=False)
>>> cstree.todense()
matrix([[ 0., 1., 2., 0.],
[ 0., 0., 0., 1.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.]])
numpy.core.multiarray failed to import
csgraph_to_masked(csgraph)
Convert a sparse graph representation to a masked array representation
.. versionadded:: 0.11.0
Parameters
----------
csgraph : csr_matrix, csc_matrix, or lil_matrix
Sparse representation of a graph.
Returns
-------
graph : MaskedArray
The masked dense representation of the sparse graph.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import csgraph_to_masked
>>> graph = csr_matrix( [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ])
>>> graph
<4x4 sparse matrix of type '<class 'numpy.int64'>'
with 4 stored elements in Compressed Sparse Row format>
>>> csgraph_to_masked(graph)
masked_array(
data=[[--, 1.0, 2.0, --],
[--, --, --, 1.0],
[--, --, --, 3.0],
[--, --, --, --]],
mask=[[ True, False, False, True],
[ True, True, True, False],
[ True, True, True, False],
[ True, True, True, True]],
fill_value=1e+20)
csgraph_to_dense(csgraph, null_value=0)
Convert a sparse graph representation to a dense representation
.. versionadded:: 0.11.0
Parameters
----------
csgraph : csr_matrix, csc_matrix, or lil_matrix
Sparse representation of a graph.
null_value : float, optional
The value used to indicate null edges in the dense representation.
Default is 0.
Returns
-------
graph : ndarray
The dense representation of the sparse graph.
Notes
-----
For normal sparse graph representations, calling csgraph_to_dense with
null_value=0 produces an equivalent result to using dense format
conversions in the main sparse package. When the sparse representations
have repeated values, however, the results will differ. The tools in
scipy.sparse will add repeating values to obtain a final value. This
function will select the minimum among repeating values to obtain a
final value. For example, here we'll create a two-node directed sparse
graph with multiple edges from node 0 to node 1, of weights 2 and 3.
This illustrates the difference in behavior:
>>> from scipy.sparse import csr_matrix, csgraph
>>> data = np.array([2, 3])
>>> indices = np.array([1, 1])
>>> indptr = np.array([0, 2, 2])
>>> M = csr_matrix((data, indices, indptr), shape=(2, 2))
>>> M.toarray()
array([[0, 5],
[0, 0]])
>>> csgraph.csgraph_to_dense(M)
array([[0., 2.],
[0., 0.]])
The reason for this difference is to allow a compressed sparse graph to
represent multiple edges between any two nodes. As most sparse graph
algorithms are concerned with the single lowest-cost edge between any
two nodes, the default scipy.sparse behavior of summming multiple weights
does not make sense in this context.
The other reason for using this routine is to allow for graphs with
zero-weight edges. Let's look at the example of a two-node directed
graph, connected by an edge of weight zero:
>>> from scipy.sparse import csr_matrix, csgraph
>>> data = np.array([0.0])
>>> indices = np.array([1])
>>> indptr = np.array([0, 1, 1])
>>> M = csr_matrix((data, indices, indptr), shape=(2, 2))
>>> M.toarray()
array([[0, 0],
[0, 0]])
>>> csgraph.csgraph_to_dense(M, np.inf)
array([[ inf, 0.],
[ inf, inf]])
In the first case, the zero-weight edge gets lost in the dense
representation. In the second case, we can choose a different null value
and see the true form of the graph.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import csgraph_to_dense
>>> graph = csr_matrix( [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ])
>>> graph
<4x4 sparse matrix of type '<class 'numpy.int64'>'
with 4 stored elements in Compressed Sparse Row format>
>>> csgraph_to_dense(graph)
array([[ 0., 1., 2., 0.],
[ 0., 0., 0., 1.],
[ 0., 0., 0., 3.],
[ 0., 0., 0., 0.]])
csgraph_masked_from_dense(graph, null_value=0, nan_null=True,
infinity_null=True, copy=True)
Construct a masked array graph representation from a dense matrix.
.. versionadded:: 0.11.0
Parameters
----------
graph : array_like
Input graph. Shape should be (n_nodes, n_nodes).
null_value : float or None (optional)
Value that denotes non-edges in the graph. Default is zero.
infinity_null : bool
If True (default), then infinite entries (both positive and negative)
are treated as null edges.
nan_null : bool
If True (default), then NaN entries are treated as non-edges
Returns
-------
csgraph : MaskedArray
masked array representation of graph
Examples
--------
>>> from scipy.sparse.csgraph import csgraph_masked_from_dense
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> csgraph_masked_from_dense(graph)
masked_array(
data=[[--, 1, 2, --],
[--, --, --, 1],
[--, --, --, 3],
[--, --, --, --]],
mask=[[ True, False, False, True],
[ True, True, True, False],
[ True, True, True, False],
[ True, True, True, True]],
fill_value=0)
csgraph_from_masked(graph)
Construct a CSR-format graph from a masked array.
.. versionadded:: 0.11.0
Parameters
----------
graph : MaskedArray
Input graph. Shape should be (n_nodes, n_nodes).
Returns
-------
csgraph : csr_matrix
Compressed sparse representation of graph,
Examples
--------
>>> import numpy as np
>>> from scipy.sparse.csgraph import csgraph_from_masked
>>> graph_masked = np.ma.masked_array(data =[
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ],
... mask=[[ True, False, False , True],
... [ True, True , True, False],
... [ True , True, True ,False],
... [ True ,True , True , True]],
... fill_value = 0)
>>> csgraph_from_masked(graph_masked)
<4x4 sparse matrix of type '<class 'numpy.float64'>'
with 4 stored elements in Compressed Sparse Row format>
csgraph_from_dense(graph, null_value=0, nan_null=True, infinity_null=True)
Construct a CSR-format sparse graph from a dense matrix.
.. versionadded:: 0.11.0
Parameters
----------
graph : array_like
Input graph. Shape should be (n_nodes, n_nodes).
null_value : float or None (optional)
Value that denotes non-edges in the graph. Default is zero.
infinity_null : bool
If True (default), then infinite entries (both positive and negative)
are treated as null edges.
nan_null : bool
If True (default), then NaN entries are treated as non-edges
Returns
-------
csgraph : csr_matrix
Compressed sparse representation of graph,
Examples
--------
>>> from scipy.sparse.csgraph import csgraph_from_dense
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> csgraph_from_dense(graph)
<4x4 sparse matrix of type '<class 'numpy.float64'>'
with 4 stored elements in Compressed Sparse Row format>
construct_dist_matrix(graph, predecessors, directed=True, null_value=np.inf)
Construct distance matrix from a predecessor matrix
.. versionadded:: 0.11.0
Parameters
----------
graph : array_like or sparse
The N x N matrix representation of a directed or undirected graph.
If dense, then non-edges are indicated by zeros or infinities.
predecessors : array_like
The N x N matrix of predecessors of each node (see Notes below).
directed : bool, optional
If True (default), then operate on a directed graph: only move from
point i to point j along paths csgraph[i, j].
If False, then operate on an undirected graph: the algorithm can
progress from point i to j along csgraph[i, j] or csgraph[j, i].
null_value : bool, optional
value to use for distances between unconnected nodes. Default is
np.inf
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between nodes along the path specified
by the predecessor matrix. If no path exists, the distance is zero.
Notes
-----
The predecessor matrix is of the form returned by
`shortest_path`. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the path from
point i to point j. If no path exists between point i and j, then
predecessors[i, j] = -9999
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import construct_dist_matrix
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 3) 3
>>> pred = np.array([[-9999, 0, 0, 2],
... [1, -9999, 0, 1],
... [2, 0, -9999, 2],
... [1, 3, 3, -9999]], dtype=np.int32)
>>> construct_dist_matrix(graph=graph, predecessors=pred, directed=False)
array([[ 0., 1., 2., 5.],
[ 1., 0., 3., 1.],
[ 2., 3., 0., 3.],
[ 2., 1., 3., 0.]])
Tools and utilities for working with compressed sparse graphs
graph should be a square array construct_dist_matrix (line 500) scipy.sparse.csgraph._tools ndarray is not C contiguous csgraph_from_masked (line 18) csgraph_from_dense (line 172) csgraph_to_masked (line 338) reconstruct_path (line 412) csgraph_to_dense (line 222) csgraph_masked_from_dense construct_dist_matrix csgraph_from_masked csgraph_from_dense cline_in_traceback csgraph_to_masked reconstruct_path csgraph_to_dense validate_graph masked_invalid isspmatrix_lil isspmatrix_csr isspmatrix_csc masked_values infinity_null copy_if_dense searchsorted scipy.sparse predecessors masked_array dense_output RuntimeError dist_matrix ImportError _validation null_value isspmatrix csr_output csr_matrix compressed ValueError _tools.pyx nan_null idx_grid directed todense minimum indices float64 csgraph asarray argsort indptr __import__ cumsum astype arange zeros tocsr shape range order numpy nnull isnan isinf int32 graph getA1 empty dtype data2 array ITYPE DTYPE __test__ pind ones ndim __name__ mask __main__ fill data copy bool sum nan inf np ma c N C Buffer dtype mismatch, expected %s%s%s but got %s Buffer dtype mismatch, expected '%s' but got %s in '%s.%s' %.200s.%.200s is not a type object %.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject %s.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject Does not understand character buffer dtype format string ('%c') Cannot convert %.200s to %.200s %s() got multiple values for keyword argument '%U' %.200s() keywords must be strings %s() got an unexpected keyword argument '%U' calling %R should have returned an instance of BaseException, not %R raise: exception class must be a subclass of BaseException __int__ returned non-int (type %.200s). The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python. __%.4s__ returned non-%.4s (type %.200s) value too large to convert to int Unexpected format string character: '%c' Expected a dimension of size %zu, got %zu Expected %d dimensions, got %d Python does not define a standard format string size for long double ('g').. Buffer dtype mismatch; next field is at offset %zd but %zd expected Big-endian buffer not supported on little-endian compiler Buffer acquisition: Expected '{' after 'T' Cannot handle repeated arrays in format string Expected a dimension of size %zu, got %d Expected a comma in format string, got '%c' Expected %d dimension(s), got %d Unexpected end of format string, expected ')' Buffer has wrong number of dimensions (expected %d, got %d) Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s) scipy.sparse.csgraph._tools.csgraph_to_masked scipy.sparse.csgraph._tools.csgraph_from_dense %.200s() takes %.8s %zd positional argument%.1s (%zd given) Out of bounds on buffer access (axis %d) scipy.sparse.csgraph._tools._construct_dist_matrix scipy.sparse.csgraph._tools._populate_graph scipy.sparse.csgraph._tools.construct_dist_matrix scipy.sparse.csgraph._tools.csgraph_masked_from_dense scipy.sparse.csgraph._tools.csgraph_to_dense scipy.sparse.csgraph._tools.csgraph_from_masked scipy.sparse.csgraph._tools.reconstruct_path compiletime version %s of module '%.100s' does not match runtime version %s init scipy.sparse.csgraph._tools ð¿ @ ; þÿ ðþÿH þÿ° øþÿ(
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construct_dist_matrix(graph, predecessors, directed=True, null_value=np.inf)
Construct distance matrix from a predecessor matrix
.. versionadded:: 0.11.0
Parameters
----------
graph : array_like or sparse
The N x N matrix representation of a directed or undirected graph.
If dense, then non-edges are indicated by zeros or infinities.
predecessors : array_like
The N x N matrix of predecessors of each node (see Notes below).
directed : bool, optional
If True (default), then operate on a directed graph: only move from
point i to point j along paths csgraph[i, j].
If False, then operate on an undirected graph: the algorithm can
progress from point i to j along csgraph[i, j] or csgraph[j, i].
null_value : bool, optional
value to use for distances between unconnected nodes. Default is
np.inf
Returns
-------
dist_matrix : ndarray
The N x N matrix of distances between nodes along the path specified
by the predecessor matrix. If no path exists, the distance is zero.
Notes
-----
The predecessor matrix is of the form returned by
`shortest_path`. Row i of the predecessor matrix contains
information on the shortest paths from point i: each entry
predecessors[i, j] gives the index of the previous node in the path from
point i to point j. If no path exists between point i and j, then
predecessors[i, j] = -9999
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import construct_dist_matrix
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 3) 3
>>> pred = np.array([[-9999, 0, 0, 2],
... [1, -9999, 0, 1],
... [2, 0, -9999, 2],
... [1, 3, 3, -9999]], dtype=np.int32)
>>> construct_dist_matrix(graph=graph, predecessors=pred, directed=False)
array([[ 0., 1., 2., 5.],
[ 1., 0., 3., 1.],
[ 2., 3., 0., 3.],
[ 2., 1., 3., 0.]])
reconstruct_path(csgraph, predecessors, directed=True)
Construct a tree from a graph and a predecessor list.
.. versionadded:: 0.11.0
Parameters
----------
csgraph : array_like or sparse matrix
The N x N matrix representing the directed or undirected graph
from which the predecessors are drawn.
predecessors : array_like, one dimension
The length-N array of indices of predecessors for the tree. The
index of the parent of node i is given by predecessors[i].
directed : bool, optional
If True (default), then operate on a directed graph: only move from
point i to point j along paths csgraph[i, j].
If False, then operate on an undirected graph: the algorithm can
progress from point i to j along csgraph[i, j] or csgraph[j, i].
Returns
-------
cstree : csr matrix
The N x N directed compressed-sparse representation of the tree drawn
from csgraph which is encoded by the predecessor list.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import reconstruct_path
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
(0, 1) 1
(0, 2) 2
(1, 3) 1
(2, 3) 3
>>> pred = np.array([-9999, 0, 0, 1], dtype=np.int32)
>>> cstree = reconstruct_path(csgraph=graph, predecessors=pred, directed=False)
>>> cstree.todense()
matrix([[ 0., 1., 2., 0.],
[ 0., 0., 0., 1.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.]])
csgraph_to_masked(csgraph)
Convert a sparse graph representation to a masked array representation
.. versionadded:: 0.11.0
Parameters
----------
csgraph : csr_matrix, csc_matrix, or lil_matrix
Sparse representation of a graph.
Returns
-------
graph : MaskedArray
The masked dense representation of the sparse graph.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import csgraph_to_masked
>>> graph = csr_matrix( [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ])
>>> graph
<4x4 sparse matrix of type '<class 'numpy.int64'>'
with 4 stored elements in Compressed Sparse Row format>
>>> csgraph_to_masked(graph)
masked_array(
data=[[--, 1.0, 2.0, --],
[--, --, --, 1.0],
[--, --, --, 3.0],
[--, --, --, --]],
mask=[[ True, False, False, True],
[ True, True, True, False],
[ True, True, True, False],
[ True, True, True, True]],
fill_value=1e+20)
csgraph_to_dense(csgraph, null_value=0)
Convert a sparse graph representation to a dense representation
.. versionadded:: 0.11.0
Parameters
----------
csgraph : csr_matrix, csc_matrix, or lil_matrix
Sparse representation of a graph.
null_value : float, optional
The value used to indicate null edges in the dense representation.
Default is 0.
Returns
-------
graph : ndarray
The dense representation of the sparse graph.
Notes
-----
For normal sparse graph representations, calling csgraph_to_dense with
null_value=0 produces an equivalent result to using dense format
conversions in the main sparse package. When the sparse representations
have repeated values, however, the results will differ. The tools in
scipy.sparse will add repeating values to obtain a final value. This
function will select the minimum among repeating values to obtain a
final value. For example, here we'll create a two-node directed sparse
graph with multiple edges from node 0 to node 1, of weights 2 and 3.
This illustrates the difference in behavior:
>>> from scipy.sparse import csr_matrix, csgraph
>>> data = np.array([2, 3])
>>> indices = np.array([1, 1])
>>> indptr = np.array([0, 2, 2])
>>> M = csr_matrix((data, indices, indptr), shape=(2, 2))
>>> M.toarray()
array([[0, 5],
[0, 0]])
>>> csgraph.csgraph_to_dense(M)
array([[0., 2.],
[0., 0.]])
The reason for this difference is to allow a compressed sparse graph to
represent multiple edges between any two nodes. As most sparse graph
algorithms are concerned with the single lowest-cost edge between any
two nodes, the default scipy.sparse behavior of summming multiple weights
does not make sense in this context.
The other reason for using this routine is to allow for graphs with
zero-weight edges. Let's look at the example of a two-node directed
graph, connected by an edge of weight zero:
>>> from scipy.sparse import csr_matrix, csgraph
>>> data = np.array([0.0])
>>> indices = np.array([1])
>>> indptr = np.array([0, 1, 1])
>>> M = csr_matrix((data, indices, indptr), shape=(2, 2))
>>> M.toarray()
array([[0, 0],
[0, 0]])
>>> csgraph.csgraph_to_dense(M, np.inf)
array([[ inf, 0.],
[ inf, inf]])
In the first case, the zero-weight edge gets lost in the dense
representation. In the second case, we can choose a different null value
and see the true form of the graph.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import csgraph_to_dense
>>> graph = csr_matrix( [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ])
>>> graph
<4x4 sparse matrix of type '<class 'numpy.int64'>'
with 4 stored elements in Compressed Sparse Row format>
>>> csgraph_to_dense(graph)
array([[ 0., 1., 2., 0.],
[ 0., 0., 0., 1.],
[ 0., 0., 0., 3.],
[ 0., 0., 0., 0.]])
csgraph_from_dense(graph, null_value=0, nan_null=True, infinity_null=True)
Construct a CSR-format sparse graph from a dense matrix.
.. versionadded:: 0.11.0
Parameters
----------
graph : array_like
Input graph. Shape should be (n_nodes, n_nodes).
null_value : float or None (optional)
Value that denotes non-edges in the graph. Default is zero.
infinity_null : bool
If True (default), then infinite entries (both positive and negative)
are treated as null edges.
nan_null : bool
If True (default), then NaN entries are treated as non-edges
Returns
-------
csgraph : csr_matrix
Compressed sparse representation of graph,
Examples
--------
>>> from scipy.sparse.csgraph import csgraph_from_dense
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> csgraph_from_dense(graph)
<4x4 sparse matrix of type '<class 'numpy.float64'>'
with 4 stored elements in Compressed Sparse Row format>
csgraph_masked_from_dense(graph, null_value=0, nan_null=True,
infinity_null=True, copy=True)
Construct a masked array graph representation from a dense matrix.
.. versionadded:: 0.11.0
Parameters
----------
graph : array_like
Input graph. Shape should be (n_nodes, n_nodes).
null_value : float or None (optional)
Value that denotes non-edges in the graph. Default is zero.
infinity_null : bool
If True (default), then infinite entries (both positive and negative)
are treated as null edges.
nan_null : bool
If True (default), then NaN entries are treated as non-edges
Returns
-------
csgraph : MaskedArray
masked array representation of graph
Examples
--------
>>> from scipy.sparse.csgraph import csgraph_masked_from_dense
>>> graph = [
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ]
>>> csgraph_masked_from_dense(graph)
masked_array(
data=[[--, 1, 2, --],
[--, --, --, 1],
[--, --, --, 3],
[--, --, --, --]],
mask=[[ True, False, False, True],
[ True, True, True, False],
[ True, True, True, False],
[ True, True, True, True]],
fill_value=0)
csgraph_from_masked(graph)
Construct a CSR-format graph from a masked array.
.. versionadded:: 0.11.0
Parameters
----------
graph : MaskedArray
Input graph. Shape should be (n_nodes, n_nodes).
Returns
-------
csgraph : csr_matrix
Compressed sparse representation of graph,
Examples
--------
>>> import numpy as np
>>> from scipy.sparse.csgraph import csgraph_from_masked
>>> graph_masked = np.ma.masked_array(data =[
... [0, 1 , 2, 0],
... [0, 0, 0, 1],
... [0, 0, 0, 3],
... [0, 0, 0, 0]
... ],
... mask=[[ True, False, False , True],
... [ True, True , True, False],
... [ True , True, True ,False],
... [ True ,True , True , True]],
... fill_value = 0)
>>> csgraph_from_masked(graph_masked)
<4x4 sparse matrix of type '<class 'numpy.float64'>'
with 4 stored elements in Compressed Sparse Row format>
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