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

#*****************************************************************************80
#
## google_from_incidence() converts an incidence matrix to a Google transition matrix.
#
#  Discussion:
#
#    If the input incidence matrix has a node I with no connectivity,
#    (A(I,1:N) = 0) then we artificially set T(1:N,I)=1/N, so that
#    the transition matrix property of having unit column sums is preserved.
#
#    For nodes with connectivity, we assume that 85 percent of the time
#    we will take a link at random, and 15 percent of the time, we will
#    jump to an arbitrary link.  
#
#  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 G(N,N): the Google matrix.
#
  import numpy as np

  n = A.shape[0]
  p = 0.15
  G = np.zeros ( [ n, n ] )

  s = sum ( A, 2 );
  for i in range ( 0, n ):
    s = np.sum ( A[i,:] )
    if ( s == 0.0 ):
      G[i,:] = 1.0 / float ( n )
    else:
      G[i,:] = ( 1.0 - p ) * A[i,:] / s + p / float ( n )

  G = np.transpose ( G )

  return G

def google_from_incidence_test ( ):

#*****************************************************************************80
#
## google_from_incidence_test() tests google_from_incidence().
#
#  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_from_incidence_test():' )
  print ( '  google_from_incidence() computes the Google matrix G' )
  print ( '  from an incidence matrix A.' )

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

  G = google_from_incidence ( A )
  print ( '' )
  print ( '  Google matrix G(A):' )
  print ( G )

  return

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