#! /usr/bin/env python3
#
def exercise2 ( ):

#*****************************************************************************80
#
## exercise2() classifies gold coins as fake(0) or legitimate(1).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 February 2022
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np
  from logistic_regression import logistic_regression

  print ( '' )
  print ( 'exercise2():' )
  print ( '  Seek parameters for logistic regression example.' )
  print ( '  We have M samples of gold coins.' )
  print ( '  Data includes g, the weight in grams, and' )
  print ( '  y, a label of 0 for fake coins, 1 for real coins.' )
  print ( '  We seek a logistic regression model' )
  print ( '    y = 1 / ( 1 + exp ( - ( w(0) + w(1) * g(:) ) )' )
  print ( '  for which we need to estimate the weights w.' )
  print ( '' )
  print ( '  Use gradient descent.' )
#
#  Read the data file.
#
  data = np.loadtxt ( 'gold_data.txt' )
#
#  First column is weight in grams.  
#  Second column is Y (genuine = 1, counterfeit = 0).
#
  g = data[:,0]
  y = data[:,1]
  m = len ( g )
#
#  Normalize the G data.
#
  gmin = np.min ( g )
  gmax = np.max ( g )
  gn = ( g - np.min ( g ) ) / ( np.max ( g ) - np.min ( g ) )
#
#  Create a data array X = [ 1 | g ].
#
  X = np.zeros ( [ m, 2 ] )
  X[:,0] = 1
  X[:,1] = gn
#
#  Set the learning rate ALPHA
#
  alpha = 0.02
#
#  Set the number of iterations KMAX.
#
  kmax = 100000
#
#  Compute logistic weights W.
#
  w = logistic_regression ( X, y, alpha, kmax )

  print ( '' )
  print ( '  Estimated weights W = (%g,%g)' % ( w[0], w[1] ) )
#
#  Display the data.
#
  gp = np.linspace ( -1.0, 2.0, 101 )
  gpu = gmin + ( gmax - gmin ) * gp
  cutoff = - w[0] / w[1]
  cutoff2 = gmin + ( gmax - gmin ) * cutoff
  print ( '  Cutoff value for normalized data is ', cutoff )
  print ( '  Cutoff value  is ', cutoff2 )
  yp = 1.0 / ( 1.0 + np.exp ( - ( w[0] + w[1] * gp ) ) )
  plt.plot ( g, y, 'ro' )
  plt.plot ( gpu, yp, linewidth = 3 )
  plt.plot ( [cutoff2,cutoff2], [0,1], '--', color = 'r' )
  plt.grid ( True )
  plt.xlabel ( '<-- G: Weight in grams -->' )
  plt.ylabel ( '<-- Y(G): Fake = 0, Real = 1 -->' )
  plt.title ( 'Logistic regression for gold coin weights' )
  filename = 'exercise2.png'
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.savefig ( filename )
  plt.show ( )
  plt.close ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'exercise2():' )
  print ( '  Normal end of execution.' )

  return

if ( __name__ == '__main__' ):
  exercise2 ( )