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

#*****************************************************************************80
#
## google_rank() uses the power method on the Google matrix.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer A(N,N): the incidence matrix.
#
#  Output:
#
#    real X(N): the Google rankings.
#
  from google_from_incidence import google_from_incidence
  import numpy as np

  steps = 100

  print ( '' )
  print ( 'google_rank():' )
  print ( '  Given an NxN incidence matrix A,' )
  print ( '  compute the Google matrix G,' )
  print ( '  Then start with a vector of N values 1/N,' )
  print ( '  and repeatedly compute x <= G*x' )
  print ( '' )
  print ( '  After many steps, compare last three iterates.' )
  print ( '  If they are close, we are probably at an eigenvector' )
  print ( '  associated with the eigenvalue 1.' )

  n = A.shape[0]
#
#  Compute the Google matrix.
#
  G = google_from_incidence ( A )
#
#  Set the starting vector.
#
  x = np.ones ( n ) / float ( n )
#
#  Carry out many iterations.
#  Normalization is not necessary because T is a transition matrix.
#
  for i in range ( 0, steps ):
    x = np.dot ( G, x )
#
#  Compare three successive iterates.
#
  Gx  = np.dot ( G, x )
  GGx = np.dot ( G, Gx )

  W = np.stack ( ( x, Gx, GGx ), axis = 1 )
  print ( '' )
  print ( 'x, G*x, G*G*x' )
  print ( W )

  return x

def google_rank_test ( ):

#*****************************************************************************80
#
## google_rank_test() tests google_rank().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2022
#
#  Author:
#
#    John Burkardt
#
  from moler_incidence import moler_incidence

  print ( '' )
  print ( 'google_rank_test():' )
  print ( '  google_rank() computes the Google rankings r()' )
  print ( '  for an incidence matrix A.' )

  A = moler_incidence ( )
  print ( '' )
  print ( '  Incidence matrix A:' )
  print ( A )

  r = google_rank ( A )
  print ( '' )
  print ( '  Google rankings r:' )
  print ( r )

  return

if ( __name__ == '__main__' ):
  google_rank_test ( )