#! /usr/bin/env python3
#
def logistic ( l, b, m, x ):

#*****************************************************************************80
#
## logistic evaluates the sigmoid or logistic function.
#
#  Discussion:
#
#    The sigmoid function is useful for classification problems in
#    machine learning.  Its value is always between 0 and l.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 October 2019
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real l, the maximum value of the function.  This is often 1.
#
#    real b, the cutoff value, where the function equals l/2.
#    This is often 0.
#
#    real m, the slope, which determines the steepness of the curve
#    and the width of the uncertainty interval.  This is often 1.
#
#    real x, the argument.
#
#  Output:
#
#    real value, the value of the logistic function at x.
#
  import numpy as np

  value = l / ( 1.0 + np.exp ( - m * ( x - b ) ) )

  return value

def logistic_test ( l, b, m ):

#*****************************************************************************80
#
## logistic_test() tests logistic().
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 October 2019
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'logistic_test():' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  logistic() evaluates the logistic function.' )

  x = np.linspace ( b - 2.0, b + 2.0, 21 )
  y = logistic ( l, b, m, x )

  print ( '' )
  print ( '  X     Logistic(l=',l,'b=',b,'m=',m,',X)' )
  print ( '' )
  print ( np.c_ [ x, y ] )

def logistic_plot ( l, b, m ):

#*****************************************************************************80
#
## logistic_plot() plots the logistic function.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 October 2019
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real l, the maximum value of the function.  This is often 1.
#
#    real b, the cutoff value, where the function equals l/2.
#    This is often 0.
#
#    real m, the slope, which determines the steepness of the curve
#    and the width of the uncertainty interval.  This is often 1.
#
  import matplotlib.pyplot as plt
  import numpy as np

  print ( '' )
  print ( 'logistic_plot():' )
  print ( '  Plot logistic(l=',l,',b=',b,',m=',m,').' )
#
#  Sample the function y(x) over [x1,x2].
#
  x = np.linspace ( b - 2.0, b + 2.0, 101 )
  y = logistic ( l, b, m, x )
#
#  Plot the data.
#
  plt.clf ( )
  plt.plot ( x, y, linewidth = 3, color = 'b' )
  plt.plot ( [ b-2.0, b+2.0 ], [ 0, 0 ], linewidth = 3, color = 'k' )
  plt.plot ( [ b, b ], [ 0.0, l ], '--', linewidth = 3, color = 'r' )
  plt.grid ( True )
  plt.xlabel ( '<--- X --->', fontsize = 16 )
  plt.ylabel ( '<--- Y = Logistic(l,b,m;x) --->', fontsize = 16 )
  s = 'Logistic(l=' + str ( l ) + ',b=' + str ( b ) + ',m=' + str ( m ) + ')'
  plt.title ( s, fontsize = 16 )

  filename = 'logistic_l' + str(l) + '_b' + str ( b ) + '_m' + str ( m ) + '.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.show ( )
  plt.close ( )

  return

if ( __name__ == '__main__' ):
  logistic_test ( 1.0, 2.0, 3.0 )
  logistic_plot ( 1.0, 2.0, 3.0 )
  logistic_plot ( 10.0, 2.0, 3.0 )
  logistic_plot ( 1.0, 10.0, 3.0 )
  logistic_plot ( 1.0, 2.0, 10.0 )