#! /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:
#
#    21 January 2022
#
#  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,Quiet) observations.' )
#
#  Read the data.
#
  data = np.loadtxt ( 'faithful_data.txt' )

  n, d = np.shape ( data )
  print ( '' )
  print ( '  Data involves ', n, ' values of ', d, ' dimension.' )
#
#  Normalize the data
#
  data[:,0] = ( data[:,0] - np.min ( data[:,0] ) ) / ( np.max ( data[:,0] ) - np.min ( data[:,0] ) )
  data[:,1] = ( data[:,1] - np.min ( data[:,1] ) ) / ( np.max ( data[:,1] ) - np.min ( data[:,1] ) )
#
#  Guess two good centers.
#
  C = np.array ( [ \
    [ 0.05, 0.2  ],\
    [ 0.8, 0.75 ] ] )
#
#  Display normalized data and centers.
#
  plt.plot ( data[:,0], data[:,1], 'c.', markersize = 10 )
  plt.plot ( C[:,0], C[:,1], 'k*', markersize = 20 )
  plt.xlabel ( '<-- Erupt -->', fontsize = 16 )
  plt.ylabel ( '<-- Quiet -->', 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 ( )
  plt.clf ( )
#
#  Compute distance to each center
#
  d = np.zeros ( [ n, 2 ] )
  d[:,0] = ( C[0,0] - data[:,0] )**2 + ( C[0,1] - data[:,1] )**2
  d[:,1] = ( C[1,0] - data[:,0] )**2 + ( C[1,1] - data[:,1] )**2
#
#  Y assigns data to nearest center
#
  y0 = np.where ( d[:,0] <= d[:,1] )
  y1 = np.where ( d[:,1] < d[:,0] )
#
#  Display data in clusters.
#
  plt.plot ( data[y0,0], data[y0,1], 'c.', markersize = 10 )
  plt.plot ( data[y1,0], data[y1,1], 'r.', markersize = 10 )
  plt.plot ( C[:,0], C[:,1], 'k*', markersize = 20 )
  plt.xlabel ( '<-- Erupt -->', fontsize = 16 )
  plt.ylabel ( '<-- Quiet -->', 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 ( )
  plt.clf ( )
#
#  Compute variances.
#  Careful!
#  A) np.cov() requires the rowvar = False argument!
#  B) y0 and y1 are arrays of a single entry, which is the array you want,
#     because you applied where() to a matrix.
#
  covar = np.cov ( data, rowvar = False )
  var = covar[0,0] + covar[1,1]

  n0 = len ( y0[0] )
  var0 = np.sum ( ( C[0,0] - data[y0,0] )**2 + ( C[0,1] - data[y0,1] )**2 ) / n0
  n1 = len ( y1[0] )
  var1 = np.sum ( ( C[1,0] - data[y1,0] )**2 + ( C[1,1] - data[y1,1] )**2 ) / n1

  print ( "" )
  print ( "  1 Cluster size = ", n )
  print ( "  2 Cluster size = ", n0 + n1, ' = ', n0, ' + ', n1 )
  print ( "" )
  print ( "  1 Cluster variance = ", var )
  print ( "  2 Cluster variance = ", var0 + var1, ' = ', var0, ' + ', var1 )
#
#  Terminate.
#
  print ( '' )
  print ( 'faithful_guess:' )
  print ( '  Normal end of execution.' )

  return

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