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

#*****************************************************************************80
#
## transition_from_incidence() computes a transition matrix from an incidence 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 for a directed graph.
#
#  Output:
#
#    real T(N,N): the transition matrix for the directed graph.
#
  import numpy as np

  T = A.copy()    # T = A doesn't do what we would expect!
  T = T.astype ( float )  # Otherwise, integer arithmetic!
  m = T.shape[0]
  for i in range ( 0, m ):
    if ( np.sum ( T[i,:] ) == 0 ):
      T[i,:] = 1
    T[i,:] = T[i,:] / np.sum ( T[i,:] )
  T = np.transpose ( T ) 
     
  return T

def transition_from_incidence_test ( ):

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

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

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

  T = transition_from_incidence ( A )
  print ( '  Transition matrix T:' )
  print ( T )

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