#! /usr/bin/env python3
#
def power_method ( A, its ):

#*****************************************************************************80
#
## power_method() estimates the page rank vector using the power method.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    08 April 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real A(N,N): the transition matrix or the Google matrix.
#
#    integer ITS: the number of iterations.
#
#  Output:
#
#    real R(N): the estimated page rank vector.
#
  import numpy as np

  n = A.shape[0]

  for it in range ( 0, its ):
    if ( it == 0 ):
      r = np.random.rand ( n )
    else:
      r = np.dot ( A, r )
    r = r / np.linalg.norm ( r )

  return r

def power_method_test ( ):

#*****************************************************************************80
#
## power_method_test() tests power_method().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2022
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  T = np.array ( [ \
    [ 0, 0, 0.5, 1 ], \
    [ 1, 0, 0,   0 ], \
    [ 0, 1, 0,   0 ], \
    [ 0, 0, 0.5, 0 ] ] )

  its = 60
  r = power_method ( T, its )
  print ( '' )
  print ( '  Power method result:' )
  print ( r )

if ( __name__ == "__main__" ):
  power_method_test ( )