#! /usr/bin/env python3
#
def faithful_guess ( ):

#*****************************************************************************80
#
## faithful_guess() guesses a good clustering of the Old Faithful data.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 September 2023
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np
  import platform

  print ( '' )
  print ( 'faithful_guess():' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Guess a good clustering of the Old Faithful (Erupt,Wait) observations.' )
  print ( '  Then do a few steps of Lloyd iteration for improvement.' )
#
#  Read the data.
#
  data = np.loadtxt ( 'faithful_normalized.txt' )
  n = data.shape[0]
#
#  Guess two good centers.
#
  Z = np.array ( [ \
    [ 0.05, 0.2  ],\
    [ 0.8, 0.75 ] ] )
#
#  Display normalized data and centers.
#
  plt.clf ( )
  plt.plot ( data[:,0], data[:,1], 'c.', markersize = 10 )
  plt.plot ( Z[:,0], Z[:,1], 'k*', markersize = 20 )
  plt.xlabel ( '<-- Erupt -->', fontsize = 16 )
  plt.ylabel ( '<-- Wait -->', fontsize = 16 )
  plt.title ( 'Estimated centers for Old Faithful data', fontsize = 16 )
  plt.grid ( True )
  filename = 'faithful_guess_centers.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.show ( )
#
#  Compute distance to each center
#
  d = np.zeros ( [ n, 2 ] )
  d[:,0] = ( data[:,0] - Z[0,0] )**2 + ( data[:,1] - Z[0,1] )**2
  d[:,1] = ( data[:,0] - Z[1,0] )**2 + ( data[:,1] - Z[1,1] )**2
#
#  C assigns data to nearest center
#
  C = np.zeros ( n, dtype = int )

  c0 = np.where ( d[:,0] <= d[:,1] )
  n0 = np.sum ( d[:,0] <= d[:,1] )
  C[c0] = 0

  c1 = np.where ( d[:,1] <  d[:,0] )
  n1 = np.sum ( d[:,1] <  d[:,0] )
  C[c1] = 1
#
#  Display data in clusters.
#
  plt.clf ( )
  plt.plot ( data[C==0,0], data[C==0,1], 'c.', markersize = 10 )
  plt.plot ( data[C==1,0], data[C==1,1], 'r.', markersize = 10 )
  plt.plot ( Z[:,0], Z[:,1], 'k*', markersize = 20 )
  plt.xlabel ( '<-- Erupt -->', fontsize = 16 )
  plt.ylabel ( '<-- Wait -->', fontsize = 16 )
  plt.title ( 'Estimated clusters for Old Faithful data', fontsize = 16 )
  plt.grid ( True )
  filename = 'faithful_guess_clusters.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.show ( )
#
#  Compute 1-cluster energy.
#
  xmean = np.mean ( data[:,0] )
  ymean = np.mean ( data[:,1] )
  E = np.sum ( ( xmean - data[:,0] )**2 + ( ymean - data[:,1] )**2 )
#
#  Compute 2-cluster energies.
#
  e0 = np.sum ( ( data[C==0,0] - Z[0,0] )**2 + ( data[C==0,1] - Z[0,1] )**2 )
  e1 = np.sum ( ( data[C==1,0] - Z[1,0] )**2 + ( data[C==1,1] - Z[1,1] )**2 )

  print ( "" )
  print ( "  Single cluster size = ", n )
  print ( "  Two cluster size    = ", n0 + n1, ' = ', n0, ' + ', n1 )
  print ( "" )
  print ( "  Single cluster energy = ", E )
  print ( "  Two cluster energy    = ", e0 + e1, ' = ', e0, ' + ', e1 )
#
#  Terminate.
#
  print ( '' )
  print ( 'faithful_guess():' )
  print ( '  Normal end of execution.' )

  return

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