Module « scipy.sparse.csgraph »

Fonction floyd_warshall - module scipy.sparse.csgraph

Signature de la fonction floyd_warshall

Description

floyd_warshall.__doc__

    floyd_warshall(csgraph, directed=True, return_predecessors=False,
                   unweighted=False, overwrite=False)

    Compute the shortest path lengths using the Floyd-Warshall algorithm

    .. 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]
    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.
    overwrite : bool, optional
        If True, overwrite csgraph with the result.  This applies only if
        csgraph is a dense, c-ordered array with dtype=float64.

    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

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

    >>> 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 = floyd_warshall(csgraph=graph, directed=False, return_predecessors=True)
    >>> dist_matrix
    array([[ 0.,  1.,  2.,  2.],
           [ 1.,  0.,  3.,  1.],
           [ 2.,  3.,  0.,  3.],
           [ 2.,  1.,  3.,  0.]])
    >>> predecessors
    array([[-9999,     0,     0,     1],
           [    1, -9999,     0,     1],
           [    2,     0, -9999,     2],
           [    1,     3,     3, -9999]], dtype=int32)