#! /usr/bin/env python3  
#
def cobweb_plot ( f, x0, N, a = 0, b = 1, filename = 'cobweb.png' ):

#*****************************************************************************80
#
## cobweb_plot() makes a cobweb plot of a function iteration.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    11 January 2023
#
#  Author:
#
#    Original Python code by John D Cook.
#    This version by John Burkardt
#
#  Reference:
#
#    John D Cook,
#    Cobweb plots,
#    https://www.johndcook.com/blog/2020/01/19/cobweb-plots/
#    Posted 19 January 2020.
#
#  Input:
#
#    function f, a function of the form y = f(x).
#
#    real x0, the initial value of x.
#
#    integer N, the number of iterates.
#
#    real a, b, the range over which the function is to be studied.
#
#    string filename: the name of the file in which to save the plot.
#
  import matplotlib.pyplot as plt
  import numpy as np

  y0 = f ( x0 )

  plt.clf ( )
#
#  Plot the function.
#
  t = np.linspace ( a, b, N )
  plt.plot ( t, f ( t ), 'k', linewidth = 2 )

  plt.grid ( True )
#
#  Plot the dotted line y = x.
#
  plt.plot ( t, t, "k:", linewidth = 2 )
#   
#  Plot the iterates.
#
  x = x0
  y = y0
  for _ in range ( N ):
    fy = f ( y )
    plt.plot ( [x, y], [y,  y], 'b', linewidth = 1 )
    plt.plot ( [y, y], [y, fy], 'b', linewidth = 1 )
    x = y
    y = fy
#
#  Plot the first and last points.
#
  plt.plot ( x0, y0, 'g.', markersize = 20 )
  plt.plot ( x, y, 'r.', markersize = 20 )
#
#  Give x and y axis the same scale.
#
  plt.axis ( 'equal' )
#
#  Save a copy of the figure.
#
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
#
#  Show the figure.
#
  plt.show ( block = False )
  plt.close ( )

  return

def cobweb_plot_test ( ):

#*****************************************************************************80
#
## cobweb_plot_test() tests cobweb_plot().
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    24 June 2022
#
#  Author:
#
#    John D Cook.
#    Modifications by John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'cobweb_plot_test():' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test cobweb_plot().' )

  cobweb_plot ( np.cos, 1.0, 20, 0.0, 1.0, 'cos.png' )
  cobweb_plot ( lambda x:0.5*x+1.0/x, 0.5, 20, 0.2, 4.0, 'sqrt2.png' )
  cobweb_plot ( lambda x:2*abs(x-0.5), 0.123, 20, 0.0, 1.0, 'tent.png' )
  cobweb_plot ( lambda x:0.5*x*(1.0-x), 0.9, 20, 0.0, 1.0, 'logistic_0.5.png' )
  cobweb_plot ( lambda x:1.5*x*(1.0-x), 0.01, 20, 0.0, 1.0, 'logistic_1.5.png' )
  cobweb_plot ( lambda x:2.5*x*(1.0-x), 0.01, 20, 0.0, 1.0, 'logistic_2.5.png' )
  cobweb_plot ( lambda x:3.5*x*(1.0-x), 0.01, 20, 0.0, 1.0, 'logistic_3.5.png' )
  cobweb_plot ( lambda x:3.6*x*(1.0-x), 0.01, 40, 0.0, 1.0, 'logistic_3.6.png' )
  cobweb_plot ( lambda x:3.7*x*(1.0-x), 0.01, 40, 0.0, 1.0, 'logistic_3.7.png' )
  cobweb_plot ( lambda x:3.8*x*(1.0-x), 0.01, 40, 0.0, 1.0, 'logistic_3.8.png' )
#
#  Terminate.
#
  print ( '' )
  print ( 'cobweb_plot_test():' )
  print ( '  Normal end of execution.' )
  return

def timestamp ( ):

#*****************************************************************************80
#
## timestamp() prints the date as a timestamp.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    21 August 2019
#
#  Author:
#
#    John Burkardt
#
  import time

  t = time.time ( )
  print ( time.ctime ( t ) )

  return

if ( __name__ == '__main__' ):
  timestamp ( )
  cobweb_plot_test ( )
  timestamp ( )