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

#*****************************************************************************80
#
## logistic evaluates the sigmoid or logistic function.
#
#  Discussion:
#
#    An R8 is a double precision real value.
#
#    The sigmoid function is useful for classification problems in
#    machine learning.  Its value is always between 0 and 1.
#
#  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.
#
  import numpy as np

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

  return value

def logistic_test ( ):

#*****************************************************************************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.' )

  l = 1.0
  b = 2.0
  m = 3.0
  x_test = np.linspace ( -2.0, 8.0, 21 )

  print ( '' )
  print ( '      X         logistic(',l,',',b,',',m,',x)' )
  print ( '' )

  for i in range ( 0, 21 ):
    x = x_test[i]
    value = logistic ( l, b, m, x )
    print ( '  %10.6g  %10.6g' % ( x, value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'logistic_test' )
  print ( '  Normal end of execution.' )
  return

def logistic_plot ( l, b, m, x1, x2 ):

#*****************************************************************************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.
#
#    real x1, x2, the x range of the plot.
#
  import matplotlib.pyplot as plt
  import numpy as np

  print ( '' )
  print ( 'logistic_plot:' )
  print ( '  Plot the function logistic(',l,',',b,',',m,').' )
#
#  Read the pairs "Year, Population" from the file.
#
  x = np.linspace ( x1, x2, 101 )
  y = logistic ( l, b, m, x )
#
#  Plot the data.
#
  plt.plot ( x, y, linewidth = 3, color = 'b' )
  plt.plot ( [ x1, x2 ], [ 0, 0 ], linewidth = 3, color = 'k' )
  plt.plot ( [ b, b ], [ 0.0, 1.0 ], '--', linewidth = 3, color = 'r' )
  plt.grid ( True )
  plt.xlabel ( '<--- X --->', fontsize = 16 )
  plt.ylabel ( '<--- Logistic(l,b,m) --->', fontsize = 16 )
  s = 'Logistic(' + str ( l ) + ',' + str ( b ) + ',' + str ( m ) + ')'
  plt.title ( s, fontsize = 16 )

  filename = 'logistic_plot.png'
  plt.savefig ( filename )
  print ( '' )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.show ( )

  plt.clf ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'logistic_plot' )
  print ( '  Normal end of execution.' )

  return

if ( __name__ == '__main__' ):
  logistic_test ( )
  logistic_plot ( 1.0, 2.0, 3.0, -2.0, 8.0 )