Python randstate.current_randstate函数代码示例

    def random_element(self):
        """
        Return a random element of this group.
        
        EXAMPLES::
        
            sage: G = Sp(4,GF(3))
            sage: G.random_element()  # random
            [2 1 1 1]
            [1 0 2 1]
            [0 1 1 0]
            [1 0 0 1]
            sage: G.random_element() in G
            True

        ::
        
            sage: F = GF(5); MS = MatrixSpace(F,2,2)
            sage: gens = [MS([[1,2],[-1,1]]),MS([[1,1],[0,1]])]
            sage: G = MatrixGroup(gens)
            sage: G.random_element()  # random
            [1 3]
            [0 3]
            sage: G.random_element() in G
            True
        """
        # Note: even with fixed random seed, the Random() element
        # returned by gap does depend on execution order and
        # architecture. Presumably due to different memory loctions.
        current_randstate().set_seed_gap()
        F = self.field_of_definition()
        return self.element_class(gap(self).Random()._matrix_(F), self, check=False)

 def conjugacy_class_representatives(self):
     """
     Return a set of representatives for each of the conjugacy classes
     of the group.
     
     EXAMPLES::
     
         sage: G = SU(3,GF(2))
         sage: len(G.conjugacy_class_representatives())
         16
         sage: len(GL(2,GF(3)).conjugacy_class_representatives())
         8
         sage: len(GU(2,GF(5)).conjugacy_class_representatives())
         36
     """
     current_randstate().set_seed_gap()
     try:
         return self.__reps
     except AttributeError:
         pass
     G    = self._gap_().ConjugacyClasses()
     reps = list(gap.List(G, 'x -> Representative(x)'))
     F    = self.field_of_definition()
     self.__reps = Sequence([self(g._matrix_(F)) for g in reps], cr=True, universe=self, check=False)
     return self.__reps

def RandomLinearCodeGuava(n,k,F):
    r"""
    The method used is to first construct a `k \times n` matrix of the block
    form `(I,A)`, where `I` is a `k \times k` identity matrix and `A` is a
    `k \times (n-k)` matrix constructed using random elements of `F`. Then
    the columns are permuted using a randomly selected element of the symmetric
    group `S_n`.

    INPUT:
        Integers `n,k`, with `n>k>1`.

    OUTPUT:
        Returns a "random" linear code with length n, dimension k over field F.

    EXAMPLES::
        sage: C = RandomLinearCodeGuava(30,15,GF(2)); C      # optional - gap_packages (Guava package)
        Linear code of length 30, dimension 15 over Finite Field of size 2
        sage: C = RandomLinearCodeGuava(10,5,GF(4,'a')); C      # optional - gap_packages (Guava package)
        Linear code of length 10, dimension 5 over Finite Field in a of size 2^2

    AUTHOR: David Joyner (11-2005)
    """
    current_randstate().set_seed_gap()

    q = F.order()
    gap.eval("C:=RandomLinearCode("+str(n)+","+str(k)+", GF("+str(q)+"))")
    gap.eval("G:=GeneratorMat(C)")
    k = int(gap.eval("Length(G)"))
    n = int(gap.eval("Length(G[1])"))
    G = [[gfq_gap_to_sage(gap.eval("G[%s][%s]" % (i,j)),F) for j in range(1,n+1)] for i in range(1,k+1)]
    MS = MatrixSpace(F,k,n)
    return LinearCode(MS(G))

    def RandomDirectedGNC(self, n, seed=None):
        """
        Returns a random GNC (growing network with copying) digraph with n
        vertices.

        The digraph is constructed by adding vertices with a link to one
        previously added vertex. The vertex to link to is chosen with a
        preferential attachment model, i.e. probability is proportional to
        degree. The new vertex is also linked to all of the previously
        added vertex's successors.

        INPUT:


        -  ``n`` - number of vertices.

        -  ``seed`` - for the random number generator


        EXAMPLE::

            sage: D = digraphs.RandomDirectedGNC(25)
            sage: D.edges(labels=False)
            [(1, 0), (2, 0), (2, 1), (3, 0), (4, 0), (4, 1), (5, 0), (5, 1), (5, 2), (6, 0), (6, 1), (7, 0), (7, 1), (7, 4), (8, 0), (9, 0), (9, 8), (10, 0), (10, 1), (10, 2), (10, 5), (11, 0), (11, 8), (11, 9), (12, 0), (12, 8), (12, 9), (13, 0), (13, 1), (14, 0), (14, 8), (14, 9), (14, 12), (15, 0), (15, 8), (15, 9), (15, 12), (16, 0), (16, 1), (16, 4), (16, 7), (17, 0), (17, 8), (17, 9), (17, 12), (18, 0), (18, 8), (19, 0), (19, 1), (19, 4), (19, 7), (20, 0), (20, 1), (20, 4), (20, 7), (20, 16), (21, 0), (21, 8), (22, 0), (22, 1), (22, 4), (22, 7), (22, 19), (23, 0), (23, 8), (23, 9), (23, 12), (23, 14), (24, 0), (24, 8), (24, 9), (24, 12), (24, 15)]
            sage: D.show()  # long time

        REFERENCE:

        - [1] Krapivsky, P.L. and Redner, S. Network Growth by
          Copying, Phys. Rev. E vol. 71 (2005), p. 036118.
        """
        if seed is None:
            seed = current_randstate().long_seed()
        import networkx
        return DiGraph(networkx.gnc_graph(n, seed=seed))

    def RandomDirectedGN(self, n, kernel=lambda x:x, seed=None):
        """
        Returns a random GN (growing network) digraph with n vertices.

        The digraph is constructed by adding vertices with a link to one
        previously added vertex. The vertex to link to is chosen with a
        preferential attachment model, i.e. probability is proportional to
        degree. The default attachment kernel is a linear function of
        degree. The digraph is always a tree, so in particular it is a
        directed acyclic graph.

        INPUT:

        -  ``n`` - number of vertices.

        -  ``kernel`` - the attachment kernel

        -  ``seed`` - for the random number generator

        EXAMPLE::

            sage: D = digraphs.RandomDirectedGN(25)
            sage: D.edges(labels=False)
            [(1, 0), (2, 0), (3, 1), (4, 0), (5, 0), (6, 1), (7, 0), (8, 3), (9, 0), (10, 8), (11, 3), (12, 9), (13, 8), (14, 0), (15, 11), (16, 11), (17, 5), (18, 11), (19, 6), (20, 5), (21, 14), (22, 5), (23, 18), (24, 11)]
            sage: D.show()  # long time

        REFERENCE:

        - [1] Krapivsky, P.L. and Redner, S. Organization of Growing
          Random Networks, Phys. Rev. E vol. 63 (2001), p. 066123.
        """
        if seed is None:
            seed = current_randstate().long_seed()
        import networkx
        return DiGraph(networkx.gn_graph(n, kernel, seed=seed))

def RandomLobster(n, p, q, seed=None):
    """
    Returns a random lobster.

    A lobster is a tree that reduces to a caterpillar when pruning all
    leaf vertices. A caterpillar is a tree that reduces to a path when
    pruning all leaf vertices (q=0).

    INPUT:

    -  ``n`` - expected number of vertices in the backbone

    -  ``p`` - probability of adding an edge to the
       backbone

    -  ``q`` - probability of adding an edge (claw) to the
       arms

    -  ``seed`` - for the random number generator

    EXAMPLE: We show the edge list of a random graph with 3 backbone
    nodes and probabilities `p = 0.7` and `q = 0.3`::

        sage: graphs.RandomLobster(3, 0.7, 0.3).edges(labels=False)
        [(0, 1), (1, 2)]

    ::

        sage: G = graphs.RandomLobster(9, .6, .3)
        sage: G.show()  # long time
    """
    if seed is None:
        seed = current_randstate().long_seed()
    import networkx
    return graph.Graph(networkx.random_lobster(n, p, q, seed=seed))

def DegreeSequenceExpected(deg_sequence, seed=None):
    """
    Returns a random graph with expected given degree sequence. Raises
    a NetworkX error if the proposed degree sequence cannot be that of
    a graph.

    One requirement is that the sum of the degrees must be even, since
    every edge must be incident with two vertices.

    INPUT:

    -  ``deg_sequence`` - a list of integers with each
       entry corresponding to the expected degree of a different vertex.

    -  ``seed`` - for the random number generator.


    EXAMPLES::

        sage: G = graphs.DegreeSequenceExpected([1,2,3,2,3])
        sage: G.edges(labels=False)
        [(0, 2), (0, 3), (1, 1), (1, 4), (2, 3), (2, 4), (3, 4), (4, 4)]
        sage: G.show()  # long time

    REFERENCE:

    .. [ChungLu2002] Chung, Fan and Lu, L. Connected components in random
      graphs with given expected degree sequences.
      Ann. Combinatorics (6), 2002 pp. 125-145.
    """
    if seed is None:
        seed = current_randstate().long_seed()
    import networkx
    return Graph(networkx.expected_degree_graph([int(i) for i in deg_sequence], seed=seed), loops=True)

    def RandomDirectedGNR(self, n, p, seed=None):
        """
        Returns a random GNR (growing network with redirection) digraph
        with n vertices and redirection probability p.

        The digraph is constructed by adding vertices with a link to one
        previously added vertex. The vertex to link to is chosen uniformly.
        With probability p, the arc is instead redirected to the successor
        vertex. The digraph is always a tree.

        INPUT:

        -  ``n`` - number of vertices.

        -  ``p`` - redirection probability

        -  ``seed`` - for the random number generator.

        EXAMPLE::

            sage: D = digraphs.RandomDirectedGNR(25, .2)
            sage: D.edges(labels=False)
            [(1, 0), (2, 0), (2, 1), (3, 0), (4, 0), (4, 1), (5, 0), (5, 1), (5, 2), (6, 0), (6, 1), (7, 0), (7, 1), (7, 4), (8, 0), (9, 0), (9, 8), (10, 0), (10, 1), (10, 2), (10, 5), (11, 0), (11, 8), (11, 9), (12, 0), (12, 8), (12, 9), (13, 0), (13, 1), (14, 0), (14, 8), (14, 9), (14, 12), (15, 0), (15, 8), (15, 9), (15, 12), (16, 0), (16, 1), (16, 4), (16, 7), (17, 0), (17, 8), (17, 9), (17, 12), (18, 0), (18, 8), (19, 0), (19, 1), (19, 4), (19, 7), (20, 0), (20, 1), (20, 4), (20, 7), (20, 16), (21, 0), (21, 8), (22, 0), (22, 1), (22, 4), (22, 7), (22, 19), (23, 0), (23, 8), (23, 9), (23, 12), (23, 14), (24, 0), (24, 8), (24, 9), (24, 12), (24, 15)]
            sage: D.show()  # long time

        REFERENCE:

        - [1] Krapivsky, P.L. and Redner, S. Organization of Growing
          Random Networks, Phys. Rev. E vol. 63 (2001), p. 066123.
        """
        if seed is None:
            seed = current_randstate().long_seed()
        import networkx
        return DiGraph(networkx.gnc_graph(n, seed=seed))

def RandomShell(constructor, seed=None):
    """
    Returns a random shell graph for the constructor given.

    INPUT:

    -  ``constructor`` - a list of 3-tuples (n,m,d), each
       representing a shell

    -  ``n`` - the number of vertices in the shell

    -  ``m`` - the number of edges in the shell

    -  ``d`` - the ratio of inter (next) shell edges to
       intra shell edges

    -  ``seed`` - for the random number generator


    EXAMPLE::

        sage: G = graphs.RandomShell([(10,20,0.8),(20,40,0.8)])
        sage: G.edges(labels=False)
        [(0, 3), (0, 7), (0, 8), (1, 2), (1, 5), (1, 8), (1, 9), (3, 6), (3, 11), (4, 6), (4, 7), (4, 8), (4, 21), (5, 8), (5, 9), (6, 9), (6, 10), (7, 8), (7, 9), (8, 18), (10, 11), (10, 13), (10, 19), (10, 22), (10, 26), (11, 18), (11, 26), (11, 28), (12, 13), (12, 14), (12, 28), (12, 29), (13, 16), (13, 21), (13, 29), (14, 18), (16, 20), (17, 18), (17, 26), (17, 28), (18, 19), (18, 22), (18, 27), (18, 28), (19, 23), (19, 25), (19, 28), (20, 22), (24, 26), (24, 27), (25, 27), (25, 29)]
        sage: G.show()  # long time
    """
    if seed is None:
        seed = current_randstate().long_seed()
    import networkx
    return Graph(networkx.random_shell_graph(constructor, seed=seed))

def RandomHolmeKim(n, m, p, seed=None):
    """
    Returns a random graph generated by the Holme and Kim algorithm for
    graphs with power law degree distribution and approximate average
    clustering.

    INPUT:


    -  ``n`` - number of vertices.

    -  ``m`` - number of random edges to add for each new
       node.

    -  ``p`` - probability of adding a triangle after
       adding a random edge.

    -  ``seed`` - for the random number generator.


    From the NetworkX documentation: The average clustering has a hard
    time getting above a certain cutoff that depends on m. This cutoff
    is often quite low. Note that the transitivity (fraction of
    triangles to possible triangles) seems to go down with network
    size. It is essentially the Barabasi-Albert growth model with an
    extra step that each random edge is followed by a chance of making
    an edge to one of its neighbors too (and thus a triangle). This
    algorithm improves on B-A in the sense that it enables a higher
    average clustering to be attained if desired. It seems possible to
    have a disconnected graph with this algorithm since the initial m
    nodes may not be all linked to a new node on the first iteration
    like the BA model.

    EXAMPLE: We show the edge list of a random graph on 8 nodes with 2
    random edges per node and a probability `p = 0.5` of
    forming triangles.

    ::

        sage: graphs.RandomHolmeKim(8, 2, 0.5).edges(labels=False)
        [(0, 2), (0, 5), (1, 2), (1, 3), (2, 3), (2, 4), (2, 6), (2, 7),
         (3, 4), (3, 6), (3, 7), (4, 5)]

    ::

        sage: G = graphs.RandomHolmeKim(12, 3, .3)
        sage: G.show()  # long time

    REFERENCE:

    - [1] Holme, P. and Kim, B.J. Growing scale-free networks with
      tunable clustering, Phys. Rev. E (2002). vol 65, no 2,
      026107.
    """
    if seed is None:
        seed = current_randstate().long_seed()
    import networkx

    return graph.Graph(networkx.powerlaw_cluster_graph(n, m, p, seed=seed))

    def _cftp(self, start_row):
        """
        Implement coupling from the past.

        ALGORITHM:

        The set of Gelfand-Tsetlin patterns can partially ordered by
        elementwise domination.  The partial order has unique maximum
        and minimum elements that are computed by the methods
        :meth:`_cftp_upper` and :meth:`_cftp_lower`. We then run the Markov
        chain that randomly toggles each element up or down from the
        past until the state reached from the upper and lower start
        points coalesce as described in [Propp1997]_.

        EXAMPLES::

            sage: G = GelfandTsetlinPatterns(3, 5)
            sage: G._cftp(0)  # random
            [[5, 3, 2], [4, 2], [3]]
            sage: G._cftp(0) in G
            True
        """
        from sage.misc.randstate import current_randstate
        from sage.misc.randstate import seed
        from sage.misc.randstate import random

        count = self._n * self._k
        seedlist = [(current_randstate().long_seed(), count)]
        upper = []
        lower = []
        while True:
            upper = self._cftp_upper()
            lower = self._cftp_lower()
            for currseed, count in seedlist:
                with seed(currseed):
                    for _ in range(count):
                        for row in range(start_row, self._n):
                            for col in range(self._n - row):
                                direction = random() % 2
                                self._toggle_markov_chain(upper, row, col, direction)
                                self._toggle_markov_chain(lower, row, col, direction)
            if all(all(x == y for x,y in zip(l1, l2)) for l1, l2 in zip(upper, lower)):
                break
            count = seedlist[0][1] * 2
            seedlist.insert(0, (current_randstate().long_seed(), count))
        return GelfandTsetlinPattern(upper)

def RandomGNM(n, m, dense=False, seed=None):
    """
    Returns a graph randomly picked out of all graphs on n vertices
    with m edges.

    INPUT:


    -  ``n`` - number of vertices.

    -  ``m`` - number of edges.

    -  ``dense`` - whether to use NetworkX's
       dense_gnm_random_graph or gnm_random_graph


    EXAMPLES: We show the edge list of a random graph on 5 nodes with
    10 edges.

    ::

        sage: graphs.RandomGNM(5, 10).edges(labels=False)
        [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]

    We plot a random graph on 12 nodes with m = 12.

    ::

        sage: gnm = graphs.RandomGNM(12, 12)
        sage: gnm.show()  # long time

    We view many random graphs using a graphics array::

        sage: g = []
        sage: j = []
        sage: for i in range(9):
        ...    k = graphs.RandomGNM(i+3, i^2-i)
        ...    g.append(k)
        ...
        sage: for i in range(3):
        ...    n = []
        ...    for m in range(3):
        ...        n.append(g[3*i + m].plot(vertex_size=50, vertex_labels=False))
        ...    j.append(n)
        ...
        sage: G = sage.plot.graphics.GraphicsArray(j)
        sage: G.show()  # long time
    """
    if seed is None:
        seed = current_randstate().long_seed()
    import networkx

    if dense:
        return graph.Graph(networkx.dense_gnm_random_graph(n, m, seed=seed))
    else:
        return graph.Graph(networkx.gnm_random_graph(n, m, seed=seed))

def RandomBarabasiAlbert(n, m, seed=None):
    u"""
    Return a random graph created using the Barabasi-Albert preferential
    attachment model.

    A graph with m vertices and no edges is initialized, and a graph of n
    vertices is grown by attaching new vertices each with m edges that are
    attached to existing vertices, preferentially with high degree.

    INPUT:

    - ``n`` - number of vertices in the graph

    - ``m`` - number of edges to attach from each new node

    - ``seed`` - for random number generator

    EXAMPLES:

    We show the edge list of a random graph on 6 nodes with m = 2.

    ::

        sage: graphs.RandomBarabasiAlbert(6,2).edges(labels=False)
        [(0, 2), (0, 3), (0, 4), (1, 2), (2, 3), (2, 4), (2, 5), (3, 5)]

    We plot a random graph on 12 nodes with m = 3.

    ::

        sage: ba = graphs.RandomBarabasiAlbert(12,3)
        sage: ba.show()  # long time

    We view many random graphs using a graphics array::

        sage: g = []
        sage: j = []
        sage: for i in range(1,10):
        ...    k = graphs.RandomBarabasiAlbert(i+3, 3)
        ...    g.append(k)
        ...
        sage: for i in range(3):
        ...    n = []
        ...    for m in range(3):
        ...        n.append(g[3*i + m].plot(vertex_size=50, vertex_labels=False))
        ...    j.append(n)
        ...
        sage: G = sage.plot.graphics.GraphicsArray(j)
        sage: G.show()  # long time

    """
    if seed is None:
        seed = current_randstate().long_seed()
    import networkx

    return graph.Graph(networkx.barabasi_albert_graph(n, m, seed=seed))

    def irreducible_characters(self):
        """
        Returns the list of irreducible characters of the group.

        EXAMPLES::
        
            sage: G = GL(2,2)
            sage: G.irreducible_characters()
            [Character of General Linear Group of degree 2 over Finite Field of size 2,
             Character of General Linear Group of degree 2 over Finite Field of size 2,
             Character of General Linear Group of degree 2 over Finite Field of size 2]

        """
        current_randstate().set_seed_gap()
        Irr = self._gap_().Irr()
        L = []
        for irr in Irr:
            L.append(ClassFunction(self,irr))
        return L

def RandomRegular(d, n, seed=None):
    """
    Returns a random d-regular graph on n vertices, or returns False on
    failure.

    Since every edge is incident to two vertices, n\*d must be even.

    INPUT:


    -  ``n`` - number of vertices

    -  ``d`` - degree

    -  ``seed`` - for the random number generator


    EXAMPLE: We show the edge list of a random graph with 8 nodes each
    of degree 3.

    ::

        sage: graphs.RandomRegular(3, 8).edges(labels=False)
        [(0, 1), (0, 4), (0, 7), (1, 5), (1, 7), (2, 3), (2, 5), (2, 6), (3, 4), (3, 6), (4, 5), (6, 7)]

    ::

        sage: G = graphs.RandomRegular(3, 20)
        sage: if G:
        ...    G.show()  # random output, long time

    REFERENCES:

    - [1] Kim, Jeong Han and Vu, Van H. Generating random regular
      graphs. Proc. 35th ACM Symp. on Thy. of Comp. 2003, pp
      213-222. ACM Press, San Diego, CA, USA.
      http://doi.acm.org/10.1145/780542.780576

    - [2] Steger, A. and Wormald, N. Generating random regular
      graphs quickly. Prob. and Comp. 8 (1999), pp 377-396.
    """
    if seed is None:
        seed = current_randstate().long_seed()
    import networkx

    try:
        N = networkx.random_regular_graph(d, n, seed=seed)
        if N is False:
            return False
        return graph.Graph(N, sparse=True)
    except StandardError:
        return False