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

#*****************************************************************************80
#
## surf_rank uses the "random surfer" method for node rankings of a digraph.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 February 2020
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer A(N,N): the incidence matrix.
#
#  Output:
#
#    real X(N): the surfer rankings.
#
  from transition_from_incidence import transition_from_incidence
  import numpy as np

  steps = 100000

  print ( '' )
  print ( 'surf_rank():' )
  print ( '  Given an NxN incidence matrix A,' )
  print ( '  compute the transition matrix T,' )
  print ( '  and then repeatedly visit nodes, keeping track of' )
  print ( '  how often you visited.' )
  print ( '' )
  print ( '  15 per cent of the time, simply take a random jump to a node.' )
  print ( '  The rest of the time, follow a random link from the current node.' )
  print ( '' )
  print ( '  When done, the node weight is the number of visits' )
  print ( '  normalized by the total number of visits.' )

  n = A.shape[0]

  r = np.zeros ( n, dtype = np.float )
#
#  Get the transition matrix from the incidence matrix.
#
  T = transition_from_incidence ( A )
#
#  Choose J, a random starting position.
#
  j = np.random.randint ( 0, n )
#
#  Carry out many moves.
#
  for k in range ( 0, steps ):

    p1 = np.random.rand ( )
    q1 = 0.15

    if ( p1 <= q1 ):

      j = np.random.randint ( 0, n )

    else:

      p2 = np.random.rand ( )
      q2 = 0.0
      for i in range ( 0, n ):
        q2 = q2 + T[i,j]
        if ( p2 <= q2 ):
          j = i
          break
 
    r[j] = r[j] + 1.0
#
#  Normalize the counts.
#
  r = r / float ( steps )

  return r

def surf_rank_test ( ):

#*****************************************************************************80
#
## surf_rank_test() tests surf_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 ( 'surf_rank_test():' )
  print ( '  surf_rank() computes the surf rankings r()' )
  print ( '  for an incidence matrix A.' )

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

  r = surf_rank ( A )
  print ( '' )
  print ( '  Surf rankings r:' )
  print ( r )

  return

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