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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],
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