#! /usr/bin/env python3
#
def pagerank_test ( A ):

  import numpy as np

  print ( '' )
  print ( 'pagerank_test():' )

  n = A.shape[0]
#
#  Print the digraph.
#
  print ( '' )
  print ( '  The digraph adjacency matrix A.' )
  print ( A )
  input ( '  Press RETURN' )
#
#  Plot the digraph.
#
  print ( '' )
  print ( '  Plot the digraph A.' )
  digraph_plot ( A )
  input ( '  Press RETURN' )
#
#  Define the transition matrix T1:
#
  print ( '' )
  print ( '  Define transition matrix T:' )
  T = transition_matrix ( A )
  input ( '  Press RETURN' )
#
#  100 people start at node 0.  T * x moves them.  Take STEPS steps.
#
  print ( '' )
  print ( '  Watch 100 people move around digraph, x <- T * x:' )
  travel ( T )
  input ( '  Press RETURN' )
#
#  Eigenvalues of T.
#
  print ( '' )
  print ( '  Eigenvalues of T?' )
  eigen = np.linalg.eigvals ( T )
  print ( np.round ( eigen, 2 ) )
  input ( '  Press RETURN' )

  return

def digraph1 ( ):
  import numpy as np
  A1 = np.array ( [ \
    [ 0, 1, 0, 0 ], \
    [ 0, 0, 1, 0 ], \
    [ 0, 0, 0, 1 ], \
    [ 1, 0, 0, 0 ] ] )
  return A1

def digraph2 ( ):
  import numpy as np
  A2 = np.array ( [ \
    [ 0, 1, 1, 0 ], \
    [ 0, 0, 1, 0 ], \
    [ 0, 0, 0, 1 ], \
    [ 1, 0, 0, 0 ] ] )
  return A2

def digraph3 ( ):
  import numpy as np
  A3 = np.array ( [ \
    [ 0, 1, 0, 0, 0, 1, 0 ], \
    [ 0, 0, 1, 0, 0, 0, 0 ], \
    [ 1, 0, 0, 1, 0, 0, 0 ], \
    [ 1, 0, 0, 0, 0, 0, 0 ], \
    [ 0, 0, 1, 0, 0, 0, 0 ], \
    [ 0, 0, 0, 0, 0, 0, 0 ], \
    [ 0, 0, 0, 0, 0, 0, 0 ] ] )
  return A3

def digraph_plot ( A ):

#*****************************************************************************80
#
## digraph_plot plots a digraph.
#
  from graphviz import Digraph
  import numpy as np

  n = A.shape[0]

  names = np.zeros ( n, dtype = str )
  for i in range ( 0, n ):
    names[i] = chr ( i+65 )

  dot = Digraph ( format = 'png' )
  for i in range ( 0, n ):
    dot.node ( names[i] )
  for i in range ( 0, n ):
    for j in range ( 0, n ):
      if ( A[i,j] ):
        dot.edge ( names[i], names[j] )
  dot.render ( 'digraph.dot', view = True )

  return

def transition_matrix ( A ):

#*****************************************************************************80
#
## transition_matrix() computes a transition matrix.
#
  global google
  global option

  import numpy as np

  n = A.shape[0]
  s = np.sum ( A, axis = 1 )
  T = np.zeros ( [ n, n ], dtype = float )
  for i in range ( 0, n ):
    if ( s[i] != 0.0 ):
      T[i,:] = A[i,:] / s[i]
    else:
      if ( option == 0 ):
        pass
      elif ( option == 1 ):
        T[i,i] = 1.0
      else:
        T[i,:] = 1.0 / n

  if ( google ):
    p = 0.15
    T = ( 1.0 - p ) * T + ( p / n ) * np.ones ( [ n, n ] )

  T = np.transpose ( T )
  print ( np.round ( T, 2 ) )
  return T

def travel ( T ):
  import numpy as np
  global steps

  n = T.shape[0]
  for i in range ( 0, steps ):
    if ( i == 0 ):
      x = np.zeros ( n )
      x[0] = 100.0
    else:
      x = np.dot ( T, x )
    print ( i, np.round ( x, 2 ) )
#
#  Script to run examples.
#
global google
global option
global steps

if ( True ):
  google = False
  option = 2
  steps = 10
  print ( '' )
  print ( '  A1: Simple 4 node loop' )
  print ( '  Verify that the crowd walks around in a bunch.' )
  input ( '  Press RETURN...' )
  A1 = digraph1 ( )
  pagerank_test ( A1 )

if ( True ):
  google = False
  option = 2
  steps = 30
  print ( '' )
  print ( '  A2: 4 node loop with 1 branch' )
  print ( '  The initial crowd spreads out.' )
  A2 = digraph2 ( )
  pagerank_test ( A2 )

if ( True ):
  google = False
  option = 0
  steps = 15
  print ( '' )
  print ( '  A3: 7 nodes, with a source, a sink, and an island' )
  print ( '  option 0: "sinks" drain.' )
  print ( '  People who go to room F disappear.' )
  A3 = digraph3 ( )
  pagerank_test ( A3 )

if ( True ):
  google = False
  option = 1
  steps = 15
  print ( '' )
  print ( '  A3: 7 nodes, with a source, a sink, and an island' )
  print ( '  option 1: "sinks" stagnate.' )
  print ( '  People who go to room F can never leave.' )
  A3 = digraph3 ( )
  pagerank_test ( A3 )

if ( True ):
  google = False
  option = 2
  steps = 15
  print ( '' )
  print ( '  A3: 7 nodes, with a source, a sink, and an island' )
  print ( '  option 2: "sinks" evaporate.' )
  print ( '  People who go to room F next visit any random room.' )
  A3 = digraph3 ( )
  pagerank_test ( A3 )

if ( True ):
  google = True
  option = 2
  steps = 15
  print ( '' )
  print ( '  A3: 7 nodes, with a source, a sink, and an island' )
  print ( '  Use Google smoothing option.' )
  print ( '  Small probability that anyone can pop over to anywhere.' )
  A3 = digraph3 ( )
  pagerank_test ( A3 )

print ( '' )
print ( 'pagerank_test():' )
print ( '  Normal end of execution.' )\