Module « scipy.sparse.csgraph »

Fonction dijkstra - module scipy.sparse.csgraph

Signature de la fonction dijkstra

Description

dijkstra.__doc__

    dijkstra(csgraph, directed=True, indices=None, return_predecessors=False,
             unweighted=False, limit=np.inf, min_only=False)

    Dijkstra algorithm using Fibonacci Heaps

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of non-negative 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] and from
        point j to i along paths csgraph[j, i].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j or j to i along either
        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.
    limit : float, optional
        The maximum distance to calculate, must be >= 0. Using a smaller limit
        will decrease computation time by aborting calculations between pairs
        that are separated by a distance > limit. For such pairs, the distance
        will be equal to np.inf (i.e., not connected).

        .. versionadded:: 0.14.0
    min_only : bool, optional
        If False (default), for every node in the graph, find the shortest path
        from every node in indices.
        If True, for every node in the graph, find the shortest path from any
        of the nodes in indices (which can be substantially faster).

        .. versionadded:: 1.3.0

    Returns
    -------
    dist_matrix : ndarray, shape ([n_indices, ]n_nodes,)
        The matrix of distances between graph nodes. If min_only=False,
        dist_matrix has shape (n_indices, n_nodes) and dist_matrix[i, j]
        gives the shortest distance from point i to point j along the graph.
        If min_only=True, dist_matrix has shape (n_nodes,) and contains for
        a given node the shortest path to that node from any of the nodes
        in indices.
    predecessors : ndarray, shape ([n_indices, ]n_nodes,)
        If min_only=False, this has shape (n_indices, n_nodes),
        otherwise it has shape (n_nodes,).
        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 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

    sources : ndarray, shape (n_nodes,)
        Returned only if min_only=True and return_predecessors=True.
        Contains the index of the source which had the shortest path
        to each target.  If no path exists within the limit,
        this will contain -9999.  The value at the indices passed
        will be equal to that index (i.e. the fastest way to reach
        node i, is to start on node i).

    Notes
    -----
    As currently implemented, Dijkstra's algorithm does not work for
    graphs with direction-dependent distances when directed == False.
    i.e., if csgraph[i,j] and csgraph[j,i] are not equal and
    both are nonzero, setting directed=False will not yield the correct
    result.

    Also, this routine does not work for graphs with negative
    distances.  Negative distances can lead to infinite cycles that must
    be handled by specialized algorithms such as Bellman-Ford's algorithm
    or Johnson's algorithm.

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

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

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