"""
Created on November 12, 2019
@author: Quentin Lutz <qlutz@enst.fr>
From scikit-network version 0.30
BSD License
Copyright (c) 2018, Scikit-network Developers
Bertrand Charpentier <bertrand.charpentier@live.fr>
Thomas Bonald <thomas.bonald@telecom-paristech.fr>
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this
list of conditions and the following disclaimer in the documentation and/or
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* Neither the name of the copyright holder nor the names of its
contributors may be used to endorse or promote products derived from this
software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
OF THE POSSIBILITY OF SUCH DAMAGE.
"""
from functools import partial
from multiprocessing import Pool
from typing import Iterable, Optional, Union
import numpy as np
from scipy import sparse
[docs]
def get_distances(
adjacency: sparse.csr_matrix,
sources: Optional[Union[int, Iterable]] = None,
method: str = "D",
return_predecessors: bool = False,
unweighted: bool = False,
n_jobs: Optional[int] = None,
):
"""Compute distances between nodes.
* Graphs
* Digraphs
Based on SciPy (scipy.sparse.csgraph.shortest_path)
Parameters
----------
adjacency :
The adjacency matrix of the graph
sources :
If specified, only compute the paths for the points at the given indices. Will not work with ``method =='FW'``.
method :
The method to be used.
* ``'D'`` (Dijkstra),
* ``'BF'`` (Bellman-Ford),
* ``'J'`` (Johnson).
return_predecessors :
If ``True``, the size predecessor matrix is returned
unweighted :
If ``True``, the weights of the edges are ignored
n_jobs :
If an integer value is given, denotes the number of workers to use (-1 means the maximum number will be used).
If ``None``, no parallel computations are made.
Returns
-------
dist_matrix : np.ndarray
Matrix of distances between nodes. ``dist_matrix[i,j]`` gives the shortest
distance from the ``i``-th source to node ``j`` in the graph (infinite if no path exists
from the ``i``-th source to node ``j``).
predecessors : np.ndarray, optional
Returned only if ``return_predecessors == True``. The matrix of predecessors, which can be used to reconstruct
the shortest paths. Row ``i`` of the predecessor matrix contains information on the shortest paths from the
``i``-th source: each entry ``predecessors[i, j]`` gives the index of the previous node in the path from
the ``i``-th source to node ``j`` (-1 if no path exists from the ``i``-th source to node ``j``).
"""
n_jobs, directed = 1, True
if method == "FW" and n_jobs != 1:
raise ValueError("The Floyd-Warshall algorithm cannot be used with parallel computations.")
if sources is None:
sources = np.arange(adjacency.shape[0])
elif np.issubdtype(type(sources), np.integer):
sources = np.array([sources])
n = len(sources)
local_function = partial(
sparse.csgraph.shortest_path,
adjacency,
method,
directed,
return_predecessors,
unweighted,
False,
)
if n_jobs == 1 or n == 1:
try:
res = sparse.csgraph.shortest_path(
adjacency,
method,
directed,
return_predecessors,
unweighted,
False,
sources,
)
except sparse.csgraph.NegativeCycleError:
raise ValueError(
"The shortest path computation could not be completed because a negative cycle is present."
)
else:
try:
with Pool(n_jobs) as pool:
res = np.array(pool.map(local_function, sources))
except sparse.csgraph.NegativeCycleError:
pool.terminate()
raise ValueError(
"The shortest path computation could not be completed because a negative cycle is present."
)
if return_predecessors:
res[1][res[1] < 0] = -1
if n == 1:
return res[0].ravel(), res[1].astype(int).ravel()
else:
return res[0], res[1].astype(int)
else:
if n == 1:
return res.ravel()
else:
return res
[docs]
def get_shortest_path(
adjacency: sparse.csr_matrix,
sources: Union[int, Iterable],
targets: Union[int, Iterable],
method: str = "D",
unweighted: bool = False,
n_jobs: Optional[int] = None,
):
"""Compute the shortest paths in the graph.
Parameters
----------
adjacency :
The adjacency matrix of the graph
sources : int or iterable
Sources nodes.
targets : int or iterable
Target nodes.
method :
The method to be used.
* ``'D'`` (Dijkstra),
* ``'BF'`` (Bellman-Ford),
* ``'J'`` (Johnson).
unweighted :
If ``True``, the weights of the edges are ignored
n_jobs :
If an integer value is given, denotes the number of workers to use (-1 means the maximum number will be used).
If ``None``, no parallel computations are made.
Returns
-------
paths : list
If single source and single target, return a list containing the nodes on the path from source to target.
If multiple sources or multiple targets, return a list of paths as lists.
An empty list means that the path does not exist.
Examples
--------
>>> from sknetwork.data import linear_digraph
>>> adjacency = linear_digraph(3)
>>> get_shortest_path(adjacency, 0, 2)
[0, 1, 2]
>>> get_shortest_path(adjacency, 2, 0)
[]
>>> get_shortest_path(adjacency, 0, [1, 2])
[[0, 1], [0, 1, 2]]
>>> get_shortest_path(adjacency, [0, 1], 2)
[[0, 1, 2], [1, 2]]
"""
if np.issubdtype(type(sources), np.integer):
sources = [sources]
if np.issubdtype(type(targets), np.integer):
targets = [targets]
if len(sources) == 1:
source2target = True
source = sources[0]
elif len(targets) == 1:
source2target = False
source = targets[0]
targets = sources
else:
raise ValueError(
"This request is ambiguous. Either use one source and multiple targets or multiple sources and one target."
)
if source2target:
dists, preds = get_distances(adjacency, source, method, True, unweighted, n_jobs)
else:
dists, preds = get_distances(adjacency.T, source, method, True, unweighted, n_jobs)
paths = []
for target in targets:
if dists[target] == np.inf:
path = []
else:
path = [target]
node = target
while node != source:
node = preds[node]
path.append(node)
if source2target:
path.reverse()
paths.append(path)
if len(paths) == 1:
paths = paths[0]
return paths