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Module « scipy.sparse.csgraph »

Fonction bellman_ford - module scipy.sparse.csgraph

Signature de la fonction bellman_ford

def bellman_ford(csgraph, directed=True, indices=None, return_predecessors=False, unweighted=False) 

Description

help(scipy.sparse.csgraph.bellman_ford)

    bellman_ford(csgraph, directed=True, indices=None, return_predecessors=False,
                 unweighted=False)

    Compute the shortest path lengths using the Bellman-Ford algorithm.

    The Bellman-Ford algorithm can robustly deal with graphs with negative
    weights.  If a negative cycle is detected, an error is raised.  For
    graphs without negative edge weights, Dijkstra's algorithm may be faster.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array_like, or sparse array or matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    indices : array_like or int, optional
        if specified, only compute the paths from the points at the given
        indices.
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.

    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N 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 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

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    This routine is specially designed for graphs with negative edge weights.
    If all edge weights are positive, then Dijkstra's algorithm is a better
    choice.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_array
    >>> from scipy.sparse.csgraph import bellman_ford

    >>> graph = [
    ... [0, 1 ,2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_array(graph)
    >>> print(graph)
    <Compressed Sparse Row sparse array of dtype 'int64'
    	with 5 stored elements and shape (4, 4)>
    	Coords	Values
    	(0, 1)	1
    	(0, 2)	2
    	(1, 3)	1
    	(2, 0)	2
    	(2, 3)	3

    >>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    

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