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layout.py

00001 """
Layout (positioning) algorithms for graph drawing.
"""
__author__ = """Aric Hagberg (hagberg@lanl.gov)\nDan Schult(dschult@colgate.edu)"""
__date__ = "$Date: 2005-06-15 08:53:26 -0600 (Wed, 15 Jun 2005) $"
__credits__ = """"""
__revision__ = "$Revision: 1033 $"
#    Copyright (C) 2004,2005 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    Distributed under the terms of the GNU Lesser General Public License
#    http://www.gnu.org/copyleft/lesser.html
from math import pi,sin,cos,sqrt
import sys
from networkx.utils import uniform_sequence


# try numpy first and Numeric, second. Fail if neither is available. 
try:
    import numpy as N
except ImportError:
    try:
        import Numeric as N
    except ImportError:
        raise ImportError,"Neither Numeric nor numpy can be imported."

00028 def circular_layout(G, dim=2):
    """
    Circular layout.

    Crude version that doesn't try to minimize edge crossings.

    """
    vpos={}
    r=1.0  # radius of circle
    t=0
    dt=2.0*pi/G.order()
    # should test for dim < 2 here
    for v in G:
        p=dim*[0.0]
        p[0]=r*cos(t)
        p[1]=r*sin(t)
        vpos[v]=N.array(p)
        t=t+dt
    return vpos        

00048 def shell_layout(G, nlist=None, dim=2 ):
    """
    Shell layout.
    Crude version that doesn't try to minimize edge crossings.

    nlist is an optional list of lists of nodes to be drawn
    at each shell level.  Only one shell with all nodes will
    be drawn if not specified.

    """
    if nlist==None:
        nlist=[G.nodes()] # draw the whole graph in one shell

    nshells=len(nlist)
    vpos={}
    if len(nlist[0])==1:
        initial_radius=0.0 # single node at center
    else:
        initial_radius=1.0

    for s in range(nshells):
        r=float(s+initial_radius)  # radius of circle
        t=0
        slist=[n for n in nlist[s] if G.has_node(n)]
        dt=2.0*pi/len(slist)
        for n in slist:
            p=dim*[0.0]
            p[0]=r*cos(t)
            p[1]=r*sin(t)
            vpos[n]=N.array(p)
            t=t+dt
    return vpos        

00081 def random_layout(G, dim=2):
    """ Random layout."""
    import random
    vpos={}
    for v in G.nodes():
        vpos[v]=N.array([random.random() for i in range(dim)])
    return vpos        

00089 def spring_layout(G, iterations=50, dim=2, node_pos=None):
    """Spring force model layout"""
    if node_pos==None :  # set the initial positions randomly in 1x1 box
        vpos=random_layout(G, dim=dim) 
    else:
        vpos=node_pos
    if iterations==0:
        return vpos
    if G.order()==0:
        k=1.0
    else:
        k=N.sqrt(1.0/G.order()) # optimal distance between nodes
    disp={}         # displacements

    # initial "temperature" (about .1 of domain area)
    # this is the largest step allowed in the dynamics
    # linearly step down by dt on each iteration so
    # on last iteration it is size dt.
    t=0.1
    dt=0.1/float(iterations+1)
    for i in range(0,iterations):
        for v in G:
            disp[v]=N.zeros(dim)
            for u in G:
                delta=vpos[v]-vpos[u]
                dn=max(sqrt(N.dot(delta,delta)),0.01)
                # repulsive force between all
                deltaf=delta*k**2/dn**2
                disp[v]=disp[v]+deltaf
                # attractive force between neighbors
                if G.has_edge(v,u):
                    deltaf=-delta*dn**2/(k*dn)
                    disp[v]=disp[v]+deltaf

        # update positions
        for v in G:
            l=max(sqrt(N.dot(disp[v],disp[v])),0.01)
            vpos[v]=vpos[v]+ disp[v]*t/l
        t-=dt
    return vpos
                   

00131 def spectral_layout(G, dim=2, vpos=None, iterations=1000, eps=1.e-3):
    """
    Return the position vectors for drawing G using spectral layout.
    """
    # check silly cases
    n=G.order()
    if iterations==0 or n==0:
        return vpos or {}
    # create initial guesses for positions
    if vpos is None:
        # start with random positions
        nodes=G.nodes()
        uhat=[ ]
        for p in range(dim):
            rx=uniform_sequence(n)
            uhat.append( dict( zip(nodes,rx) ) )
    else:
        # use given positions
        uhat=[]
        for p in range(dim):
            rx=[(v,pos[p]) for (v,pos) in vpos.iteritems()]   
            uhat.append( dict(rx) )
    # Find lowest eigenvectors
    vhat=graph_low_ev_pi(uhat,G,eps,iterations)
    # form position dict
    vpos={}
    for n in nodes:
        poslist=[ vhat[p].get(n,0) for p in range(dim) ]
        vpos[n]=N.array( poslist )
    return vpos

00162 def graph_low_ev_pi(uhat,G,eps=1.e-3,iterations=10000):
    """ 
    Power Iteration method to find smallest eigenvectors of Laplacian(G).
    Note: constant eigenvector has eigenvalue=0 but is not included
    in the count of smallest eigenvalues.

    uhat -- list of p initial guesses (dicts) for the p eigenvectors.
    G -- The Graph from which Laplacian is calculated.
    eps -- tolerance for norm of change in eigenvalue estimate.
    iterations -- maximum number of iterations to use.
    """
    # set up element value for constant eigenvector (squared)
    constant=1.0/G.order()
    # set up data for faster iteration
    gg_data=_gershgorin_setup(G)
    # 
    v=[]  # setup v to hold eigenvectors
    p=len(uhat)   # number of guesses is number of vectors to return 
    for i in xrange(p):
        vv=uhat[i]  # get initial guess
        ##normalize(vv)
        norm=sqrt(N.sum([vals**2 for vals in vv.itervalues()]))
        nn=1.0/norm
        for k in vv:
            vv[k] *= nn
        ##
        v.append(vv)

        difference=eps+1
        iii=0
#        sys.stderr.write("drawing")
        while difference>eps:
            vhat=v[i]
            ## Orthogonal to constant vector
            dotprod=constant*sum(vhat.itervalues())
            for (k,val) in vhat.iteritems():
                vhat[k]-=dotprod
            ## Orthogonal to other already found eigenvectors
            for j in range(i):  
                ##  vhat= vhat- <vhat,v[j]> * v[j]
                s_d=sum([vhat.get(k,0)*val for (k,val) in v[j].iteritems()])
                for (k,value) in v[j].iteritems():
                    vhat[k]=vhat.get(k,0)-value*s_d
                ##
            vv=_graph_gershgorin_dot_v(gg_data,vhat)
            ##normalize(vv)     vv=vv/|vv|
            norm=sqrt(sum([vals**2 for vals in vv.itervalues()]))
            if norm==0:
                raise networkx.NetworkXError,"Eigenvector with zero eigenvalue given as input."
            nn=1.0/norm
            for k in vv:
                vv[k] *= nn
            ##
            v[i]=vv
            ##difference = |vhat-vv|
            result=vhat.copy()
            for (k,value) in vv.iteritems():
                result[k]=result.get(k,0)-value
            difference=sqrt(sum([vals**2 for vals in result.itervalues()]))
            #print "difference on iteration %s is %s"%(iii,difference)
            ##
            iii += 1
            if iii==iterations: 
                #print "Maximum iterations achieved."
                break
                raise NetworkXError, "Maximum number of iterations exceeded." 
#            if iii%20==0: sys.stderr.write(".")
    return v 
    
00231 def _gershgorin_setup(G):
    """
    Return a list of matrix properties to be used 
    to iteratively multiply B*v where v is a vector
    and B=g*I-L and g is the Gershgorin estimate of 
    the largest eigenvalue of L=Laplacian(G).

    Used as input to graph_gershgorin_dot_v()
    """
    diag=G.degree(with_labels=True)
    adj={}
    g=max(diag.itervalues())
    for (n,degree) in diag.iteritems():
        diag[n]=g-degree
        adj[n]=G.neighbors(n)
    return [diag,adj]

00248 def _graph_gershgorin_dot_v(gg_data,v):
    """
    Returns B*v where B=g*I-L and g is the Gershgorin estimate of the 
    largest eigenvalue of L.  (g=max( deg(n) + sum_u(\|w_(n,u)\|)

    We use this to iterate and find the smallest eigenvectors of L.
    """
    (diag,adj)=gg_data
    r={}
    for (n,nbrs) in adj.iteritems():
        rn=sum([ v.get(u,0) for u in nbrs ])
        #rn=sum([ v.get(u,0)*w for (u,w) in nbrs.iteritems() ])#weighted adj matrix
        r[n]=rn+v.get(n,0)*diag[n]
    return r

def _test_suite():
    import doctest
    suite = doctest.DocFileSuite('tests/drawing/layout.txt',package='networkx')
    return suite

if __name__ == "__main__":
    import os
    import sys
    import unittest
    if sys.version_info[:2] < (2, 4):
        print "Python version 2.4 or later required for tests (%d.%d detected)." %  sys.version_info[:2]
        sys.exit(-1)
    # directory of networkx package (relative to this)
    nxbase=sys.path[0]+os.sep+os.pardir
    sys.path.insert(0,nxbase) # prepend to search path
    unittest.TextTestRunner().run(_test_suite())
    

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