"""
Graph products.
"""
#    Copyright (C) 2011 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
import networkx as nx
from itertools import product

__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
                            'Pieter Swart (swart@lanl.gov)',
                            'Dan Schult(dschult@colgate.edu)'
                            'Ben Edwards(bedwards@cs.unm.edu)'])

__all__ = ['tensor_product','cartesian_product',
           'lexicographic_product', 'strong_product']

def _dict_product(d1,d2):
    return dict((k,(d1.get(k),d2.get(k))) for k in set(d1)|set(d2))


# Generators for producting graph products
def _node_product(G,H):
    for u,v in product(G, H):
        yield ((u,v), _dict_product(G.node[u], H.node[v]))

def _directed_edges_cross_edges(G,H):
    if not G.is_multigraph() and not H.is_multigraph():
        for u,v,c in G.edges_iter(data=True):
            for x,y,d in H.edges_iter(data=True):
                yield (u,x),(v,y),_dict_product(c,d)
    if not G.is_multigraph() and H.is_multigraph():
        for u,v,c in G.edges_iter(data=True):
            for x,y,k,d in H.edges_iter(data=True,keys=True):
                yield (u,x),(v,y),k,_dict_product(c,d)
    if G.is_multigraph() and not H.is_multigraph():
        for u,v,k,c in G.edges_iter(data=True,keys=True):
            for x,y,d in H.edges_iter(data=True):
                yield (u,x),(v,y),k,_dict_product(c,d)
    if G.is_multigraph() and H.is_multigraph():
        for u,v,j,c in G.edges_iter(data=True,keys=True):
            for x,y,k,d in H.edges_iter(data=True,keys=True):
                yield (u,x),(v,y),(j,k),_dict_product(c,d)

def _undirected_edges_cross_edges(G,H):
    if not G.is_multigraph() and not H.is_multigraph():
        for u,v,c in G.edges_iter(data=True):
            for x,y,d in H.edges_iter(data=True):
                yield (v,x),(u,y),_dict_product(c,d)
    if not G.is_multigraph() and H.is_multigraph():
        for u,v,c in G.edges_iter(data=True):
            for x,y,k,d in H.edges_iter(data=True,keys=True):
                yield (v,x),(u,y),k,_dict_product(c,d)
    if G.is_multigraph() and not H.is_multigraph():
        for u,v,k,c in G.edges_iter(data=True,keys=True):
            for x,y,d in H.edges_iter(data=True):
                yield (v,x),(u,y),k,_dict_product(c,d)
    if G.is_multigraph() and H.is_multigraph():
        for u,v,j,c in G.edges_iter(data=True,keys=True):
            for x,y,k,d in H.edges_iter(data=True,keys=True):
                yield (v,x),(u,y),(j,k),_dict_product(c,d)

def _edges_cross_nodes(G,H):
    if G.is_multigraph():
        for u,v,k,d in G.edges_iter(data=True,keys=True):
            for x in H:
                yield (u,x),(v,x),k,d
    else:
        for u,v,d in G.edges_iter(data=True):
            for x in H:
                if H.is_multigraph():
                    yield (u,x),(v,x),None,d
                else:
                    yield (u,x),(v,x),d


def _nodes_cross_edges(G,H):
    if H.is_multigraph():
        for x in G:
            for u,v,k,d in H.edges_iter(data=True,keys=True):
                yield (x,u),(x,v),k,d
    else:
        for x in G:
            for u,v,d in H.edges_iter(data=True):
                if G.is_multigraph():
                    yield (x,u),(x,v),None,d
                else:
                    yield (x,u),(x,v),d

def _edges_cross_nodes_and_nodes(G,H):
    if G.is_multigraph():
        for u,v,k,d in G.edges_iter(data=True,keys=True):
            for x in H:
                for y in H:
                    yield (u,x),(v,y),k,d
    else:
        for u,v,d in G.edges_iter(data=True):
            for x in H:
                for y in H:
                    if H.is_multigraph():
                        yield (u,x),(v,y),None,d
                    else:
                        yield (u,x),(v,y),d

def _init_product_graph(G,H):
    if not G.is_directed() == H.is_directed():
        raise nx.NetworkXError("G and H must be both directed or",
                               "both undirected")
    if G.is_multigraph() or H.is_multigraph():
        GH = nx.MultiGraph()
    else:
        GH = nx.Graph()
    if G.is_directed():
        GH = GH.to_directed()
    return GH


def tensor_product(G,H):
    r"""Return the tensor product of G and H.

    The tensor product P of the graphs G and H has a node set that
    is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
    P has an edge ((u,v),(x,y)) if and only if (u,v) is an edge in G
    and (x,y) is an edge in H.

    Sometimes referred to as the categorical product. 


    Parameters
    ----------
    G, H: graphs
     Networkx graphs. 

    Returns
    -------
    P: NetworkX graph
     The tensor product of G and H. P will be a multi-graph if either G
     or H is a multi-graph. Will be a directed if G and H are directed,
     and undirected if G and H are undirected.

    Raises
    ------
    NetworkXError
     If G and H are not both directed or both undirected.

    Notes
    -----
    Node attributes in P are two-tuple of the G and H node attributes.
    Missing attributes are assigned None.

    For example
    >>> G = nx.Graph()
    >>> H = nx.Graph()
    >>> G.add_node(0,a1=True)
    >>> H.add_node('a',a2='Spam')
    >>> P = nx.tensor_product(G,H)
    >>> P.nodes(data=True)
    [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})]

    Edge attributes and edge keys (for multigraphs) are also copied to the
    new product graph
    """
    GH = _init_product_graph(G,H)
    GH.add_nodes_from(_node_product(G,H))
    GH.add_edges_from(_directed_edges_cross_edges(G,H))
    if not GH.is_directed():
        GH.add_edges_from(_undirected_edges_cross_edges(G,H))
    GH.name = "Tensor product("+G.name+","+H.name+")"
    return GH

def cartesian_product(G,H):
    """Return the Cartesian product of G and H.

    The tensor product P of the graphs G and H has a node set that
    is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
    P has an edge ((u,v),(x,y)) if and only if (u,v) is an edge in G 
    and x==y or  and (x,y) is an edge in H and u==v.
    and (x,y) is an edge in H.

    Parameters
    ----------
    G, H: graphs
     Networkx graphs. 

    Returns
    -------
    P: NetworkX graph
     The Cartesian product of G and H. P will be a multi-graph if either G
     or H is a multi-graph. Will be a directed if G and H are directed,
     and undirected if G and H are undirected.

    Raises
    ------
    NetworkXError
     If G and H are not both directed or both undirected.

    Notes
    -----
    Node attributes in P are two-tuple of the G and H node attributes.
    Missing attributes are assigned None.

    For example
    >>> G = nx.Graph()
    >>> H = nx.Graph()
    >>> G.add_node(0,a1=True)
    >>> H.add_node('a',a2='Spam')
    >>> P = nx.tensor_product(G,H)
    >>> P.nodes(data=True)
    [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})]

    Edge attributes and edge keys (for multigraphs) are also copied to the
    new product graph
    """
    if not G.is_directed() == H.is_directed():
        raise nx.NetworkXError("G and H must be both directed or",
                               "both undirected")
    GH = _init_product_graph(G,H)
    GH.add_nodes_from(_node_product(G,H))
    GH.add_edges_from(_edges_cross_nodes(G,H))
    GH.add_edges_from(_nodes_cross_edges(G,H))
    GH.name = "Cartesian product("+G.name+","+H.name+")"
    return GH

def lexicographic_product(G,H):
    """Return the lexicographic product of G and H.

    The lexicographical product P of the graphs G and H has a node set that
    is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
    P has an edge ((u,v),(x,y)) if and only if (u,v) is an edge in G 
    or u==v and (x,y) is an edge in H.

    Parameters
    ----------
    G, H: graphs
     Networkx graphs. 

    Returns
    -------
    P: NetworkX graph
     The Cartesian product of G and H. P will be a multi-graph if either G
     or H is a multi-graph. Will be a directed if G and H are directed,
     and undirected if G and H are undirected.

    Raises
    ------
    NetworkXError
     If G and H are not both directed or both undirected.

    Notes
    -----
    Node attributes in P are two-tuple of the G and H node attributes.
    Missing attributes are assigned None.

    For example
    >>> G = nx.Graph()
    >>> H = nx.Graph()
    >>> G.add_node(0,a1=True)
    >>> H.add_node('a',a2='Spam')
    >>> P = nx.tensor_product(G,H)
    >>> P.nodes(data=True)
    [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})]

    Edge attributes and edge keys (for multigraphs) are also copied to the
    new product graph
    """
    GH = _init_product_graph(G,H)
    GH.add_nodes_from(_node_product(G,H))
    # Edges in G regardless of H designation
    GH.add_edges_from(_edges_cross_nodes_and_nodes(G,H))
    # For each x in G, only if there is an edge in H
    GH.add_edges_from(_nodes_cross_edges(G,H))
    GH.name = "Lexographic product("+G.name+","+H.name+")"
    return GH

def strong_product(G,H):
    """Return the strong product of G and H.

    The strong product P of the graphs G and H has a node set that
    is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
    P has an edge ((u,v),(x,y)) if and only if 
    u==v and (x,y) is an edge in H, or
    x==y and (u,v) is an edge in G, or
    (u,v) is an edge in G and (x,y) is an edge in H.

    Parameters
    ----------
    G, H: graphs
     Networkx graphs. 

    Returns
    -------
    P: NetworkX graph
     The Cartesian product of G and H. P will be a multi-graph if either G
     or H is a multi-graph. Will be a directed if G and H are directed,
     and undirected if G and H are undirected.

    Raises
    ------
    NetworkXError
     If G and H are not both directed or both undirected.

    Notes
    -----
    Node attributes in P are two-tuple of the G and H node attributes.
    Missing attributes are assigned None.

    For example
    >>> G = nx.Graph()
    >>> H = nx.Graph()
    >>> G.add_node(0,a1=True)
    >>> H.add_node('a',a2='Spam')
    >>> P = nx.tensor_product(G,H)
    >>> P.nodes(data=True)
    [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})]

    Edge attributes and edge keys (for multigraphs) are also copied to the
    new product graph
    """
    GH = _init_product_graph(G,H)
    GH.add_nodes_from(_node_product(G,H))
    GH.add_edges_from(_nodes_cross_edges(G,H))
    GH.add_edges_from(_edges_cross_nodes(G,H))
    GH.add_edges_from(_directed_edges_cross_edges(G,H))
    if not GH.is_directed():
        GH.add_edges_from(_undirected_edges_cross_edges(G,H))
    GH.name = "Strong product("+G.name+","+H.name+")"
    return GH