Module « scipy.sparse.csgraph »

Fonction johnson - module scipy.sparse.csgraph

Signature de la fonction johnson

Description

johnson.__doc__

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

    Compute the shortest path lengths using Johnson's algorithm.

    Johnson's algorithm combines the Bellman-Ford algorithm and Dijkstra's
    algorithm to quickly find shortest paths in a way that is robust to
    the presence of negative cycles.  If a negative cycle is detected,
    an error is raised.  For graphs without negative edge weights,
    dijkstra may be faster.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse 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) predecesor 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.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import johnson

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3

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