Module « scipy.sparse.csgraph »

Fonction shortest_path - module scipy.sparse.csgraph

Signature de la fonction shortest_path

Description

shortest_path.__doc__

    shortest_path(csgraph, method='auto', directed=True, return_predecessors=False,
                  unweighted=False, overwrite=False, indices=None)

    Perform a shortest-path graph search on a positive directed or
    undirected graph.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    method : string ['auto'|'FW'|'D'], optional
        Algorithm to use for shortest paths.  Options are:

           'auto' -- (default) select the best among 'FW', 'D', 'BF', or 'J'
                     based on the input data.

           'FW'   -- Floyd-Warshall algorithm.  Computational cost is
                     approximately ``O[N^3]``.  The input csgraph will be
                     converted to a dense representation.

           'D'    -- Dijkstra's algorithm with Fibonacci heaps.  Computational
                     cost is approximately ``O[N(N*k + N*log(N))]``, where
                     ``k`` is the average number of connected edges per node.
                     The input csgraph will be converted to a csr
                     representation.

           'BF'   -- Bellman-Ford algorithm.  This algorithm can be used when
                     weights are negative.  If a negative cycle is encountered,
                     an error will be raised.  Computational cost is
                     approximately ``O[N(N^2 k)]``, where ``k`` is the average
                     number of connected edges per node. The input csgraph will
                     be converted to a csr representation.

           'J'    -- Johnson's algorithm.  Like the Bellman-Ford algorithm,
                     Johnson's algorithm is designed for use when the weights
                     are negative.  It combines the Bellman-Ford algorithm
                     with Dijkstra's algorithm for faster computation.

    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
        method == 'FW' and csgraph is a dense, c-ordered array with
        dtype=float64.
    indices : array_like or int, optional
        If specified, only compute the paths from the points at the given
        indices. Incompatible with method == 'FW'.

    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
    -----
    As currently implemented, Dijkstra's algorithm and Johnson's algorithm
    do not work for graphs with direction-dependent distances when
    directed == False.  i.e., if csgraph[i,j] and csgraph[j,i] are non-equal
    edges, method='D' may yield an incorrect result.

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

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