"""
Hubs and authorities analysis of graph structure.
"""
#!/usr/bin/env python
#    Copyright (C) 2008-2010 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
#    NetworkX:http://networkx.lanl.gov/ 
__author__ = """Aric Hagberg (hagberg@lanl.gov)"""
__all__ = ['hits','hits_numpy','hits_scipy','authority_matrix','hub_matrix']

import networkx as nx
from networkx.exception import NetworkXError


def hits(G,max_iter=100,tol=1.0e-8,nstart=None):
    """Return HITS hubs and authorities values for nodes.

    The HITS algorithm computes two numbers for a node. 
    Authorities estimates the node value based on the incoming links.
    Hubs estimates the node value based on outgoing links.

    Parameters
    ----------
    G : graph
      A NetworkX graph 
       
    max_iter : interger, optional
      Maximum number of iterations in power method.

    tol : float, optional
      Error tolerance used to check convergence in power method iteration.

    nstart : dictionary, optional
      Starting value of each node for power method iteration.

    Returns
    -------
    (hubs,authorities) : two-tuple of dictionaries
       Two dictionaries keyed by node containing the hub and authority
       values.

    Examples
    --------
    >>> G=nx.path_graph(4)
    >>> h,a=nx.hits(G)

    Notes
    -----
    The eigenvector calculation is done by the power iteration method
    and has no guarantee of convergence.  The iteration will stop
    after max_iter iterations or an error tolerance of
    number_of_nodes(G)*tol has been reached.

    The HITS algorithm was designed for directed graphs but this
    algorithm does not check if the input graph is directed and will
    execute on undirected graphs.

    References
    ----------
    .. [1] A. Langville and C. Meyer, 
       "A survey of eigenvector methods of web information retrieval."  
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Jon Kleinberg, 
       Authoritative sources in a hyperlinked environment
       Journal of the ACM 46 (5): 604-32, 1999. 
       doi:10.1145/324133.324140. 
       http://www.cs.cornell.edu/home/kleinber/auth.pdf.
    """
    if type(G) == nx.MultiGraph or type(G) == nx.MultiDiGraph:
        raise Exception("hits() not defined for graphs with multiedges.")

    # choose fixed starting vector if not given
    if nstart is None:
        h=dict.fromkeys(G,1.0/G.number_of_nodes())
    else:
        h=nstart
        # normalize starting vector 
        s=1.0/sum(h.values())
        for k in x: h[k]*=s
    nnodes=G.number_of_nodes()
    i=0
    while True: # power iteration: make up to max_iter iterations
        hlast=h
        h=dict.fromkeys(hlast.keys(),0)
        a=dict.fromkeys(hlast.keys(),0)
        # this "matrix multiply" looks odd because it is
        # doing a left multiply a^T=hlast^T*G 
        for n in h:
            for nbr in G[n]:
                a[nbr]+=hlast[n]*G[n][nbr].get('weight',1)
        # now multiply h=Ga
        for n in h:
            for nbr in G[n]:
                h[n]+=a[nbr]*G[n][nbr].get('weight',1)
        # normalize vector 
        s=1.0/sum(h.values())
        for n in h: h[n]*=s
        # normalize vector 
        s=1.0/sum(a.values())
        for n in a: a[n]*=s
        # check convergence, l1 norm            
        err=sum([abs(h[n]-hlast[n]) for n in h])
        if err < tol:
            break
        if i>max_iter:
            raise NetworkXError(\
            "HITS: power iteration failed to converge in %d iterations."%(i+1))
        i+=1
    return h,a


def authority_matrix(G,nodelist=None):
    """Return the HITS authority matrix."""
    M=nx.to_numpy_matrix(G,nodelist=nodelist)
    return M.T*M

def hub_matrix(G,nodelist=None):
    """Return the HITS hub matrix."""
    M=nx.to_numpy_matrix(G,nodelist=nodelist)
    return M*M.T


def hits_numpy(G):
    """Return HITS hubs and authorities values for nodes.

    The HITS algorithm computes two numbers for a node. 
    Authorities estimates the node value based on the incoming links.
    Hubs estimates the node value based on outgoing links.

    Parameters
    -----------
    G : graph
      A NetworkX graph 

    Returns
    -------
    (hubs,authorities) : two-tuple of dictionaries
       Two dictionaries keyed by node containing the hub and authority
       values.

    Examples
    --------
    >>> G=nx.path_graph(4)
    >>> h,a=nx.hits(G)

    Notes
    -----
    The eigenvector calculation uses NumPy's interface to LAPACK.

    The HITS algorithm was designed for directed graphs but this
    algorithm does not check if the input graph is directed and will
    execute on undirected graphs.

    References
    ----------
    .. [1] A. Langville and C. Meyer, 
       "A survey of eigenvector methods of web information retrieval."  
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Jon Kleinberg, 
       Authoritative sources in a hyperlinked environment
       Journal of the ACM 46 (5): 604-32, 1999. 
       doi:10.1145/324133.324140. 
       http://www.cs.cornell.edu/home/kleinber/auth.pdf.
    """
    try:
        import numpy as np
    except ImportError:
        raise ImportError(\
            "hits_numpy() requires NumPy: http://scipy.org/")
    H=nx.hub_matrix(G,G.nodes())
    e,ev=np.linalg.eig(H)
    m=e.argsort()[-1] # index of maximum eigenvalue
    h=np.array(ev[:,m]).flatten()
    A=nx.authority_matrix(G,G.nodes())
    e,ev=np.linalg.eig(A)
    m=e.argsort()[-1] # index of maximum eigenvalue
    a=np.array(ev[:,m]).flatten()
    hubs=dict(zip(G.nodes(),h/h.sum()))
    authorities=dict(zip(G.nodes(),a/a.sum()))
    return hubs,authorities


def hits_scipy(G,max_iter=100,tol=1.0e-6):
    """Return HITS hubs and authorities values for nodes.

    The HITS algorithm computes two numbers for a node. 
    Authorities estimates the node value based on the incoming links.
    Hubs estimates the node value based on outgoing links.

    Parameters
    -----------
    G : graph
      A NetworkX graph 
       
    max_iter : interger, optional
      Maximum number of iterations in power method.

    tol : float, optional
      Error tolerance used to check convergence in power method iteration.

    nstart : dictionary, optional
      Starting value of each node for power method iteration.

    Returns
    -------
    (hubs,authorities) : two-tuple of dictionaries
       Two dictionaries keyed by node containing the hub and authority
       values.

    Examples
    --------
    >>> G=nx.path_graph(4)
    >>> h,a=nx.hits(G)

    Notes
    -----
    This implementation uses SciPy sparse matrices.

    The eigenvector calculation is done by the power iteration method
    and has no guarantee of convergence.  The iteration will stop
    after max_iter iterations or an error tolerance of
    number_of_nodes(G)*tol has been reached.

    The HITS algorithm was designed for directed graphs but this
    algorithm does not check if the input graph is directed and will
    execute on undirected graphs.

    References
    ----------
    .. [1] A. Langville and C. Meyer, 
       "A survey of eigenvector methods of web information retrieval."  
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Jon Kleinberg, 
       Authoritative sources in a hyperlinked environment
       Journal of the ACM 46 (5): 604-632, 1999. 
       doi:10.1145/324133.324140. 
       http://www.cs.cornell.edu/home/kleinber/auth.pdf.
    """
    try:
        import scipy.sparse
        import numpy as np
    except ImportError:
        raise ImportError(\
            "hits_scipy() requires SciPy: http://scipy.org/")
    M=nx.to_scipy_sparse_matrix(G,nodelist=G.nodes())
    (n,m)=M.shape # should be square
    A=M.T*M # authority matrix
    x=scipy.ones((n,1))/n  # initial guess
    # power iteration on authority matrix
    i=0
    while True:
        xlast=x
        x=A*x
        x=x/x.sum()
        # check convergence, l1 norm            
        err=scipy.absolute(x-xlast).sum()
        if err < tol:
            break
        if i>max_iter:
            raise NetworkXError(\
            "HITS: power iteration failed to converge in %d iterations."%(i+1))
        i+=1

    a=np.asarray(x).flatten()
    # h=M*a
    h=np.asarray(M*a).flatten()
    hubs=dict(zip(G.nodes(),h/h.sum()))
    authorities=dict(zip(G.nodes(),a/a.sum()))
    return hubs,authorities


# fixture for nose tests
def setup_module(module):
    from nose import SkipTest
    try:
        import numpy
    except:
        raise SkipTest("NumPy not available")
    try:
        import scipy
    except:
        raise SkipTest("SciPy not available")
