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| Original file line number | Diff line number | Diff line change |
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| """ | ||
| Created on November 12, 2019 | ||
| @author: Quentin Lutz <[email protected]> | ||
| From scikit-network version 0.30 | ||
| BSD License | ||
| Copyright (c) 2018, Scikit-network Developers | ||
| Bertrand Charpentier <[email protected]> | ||
| Thomas Bonald <[email protected]> | ||
| 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 | ||
| other materials provided with the distribution. | ||
| * 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, | ||
| DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY | ||
| OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE | ||
| 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 Optional, Union, Iterable | ||
|
|
||
| import numpy as np | ||
| from scipy import sparse | ||
|
|
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|
|
||
| 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 | ||
|
|
||
|
|
||
| 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 |
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