#! /usr/bin/env python3
#
def ex51 ( ):

#*****************************************************************************80
#
## ex51, lab 5 exercise 1.
#
#  Discussion:
#
#    Gradient descent for a function of 1 variable.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 April 2019
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np
  import platform

  print ( '' )
  print ( 'ex51:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Seek minimizer of a scalar function f(x).' )
#
#  Plot f
#
  xvec = np.linspace ( -2.0, 2.0, 101 )
  fxvec = f ( xvec )
  plt.plot ( xvec, fxvec, linewidth = 3 )
  plt.grid ( True )
  plt.xlabel ( '<-- X -->' )
  plt.ylabel ( '<-- F(X) -->' )
  plt.title ( 'Minimize F(X)', fontsize = 16 )
  filename = 'ex51_f.png'
  plt.savefig ( filename )
  print ( '' )
  print ( '  Graphics saved in "%s"' % ( filename ) )
  plt.show ( )
  plt.clf ( )
#
#  Choose a random initial guess.
#
  x = - 2.0 + 4.0 * np.random.rand ( 1 )

  x0 = x
#
#  Choose a small learning rate.
#
  r = 0.05
#
#  Choose a small tolerance for the derivative.
#
  tol = 0.001
#
#  Loop.
#
  step = 0
  while ( tol < abs ( fp ( x ) ) ):
    step = step + 1
    x = x - r * fp ( x )
    print ( '  %d  %g  %g  %g' % ( step, x, f ( x ), fp ( x ) ) )
#
#  Plot f with minimizer
#
  xvec = np.linspace ( -2.0, 2.0, 101 )
  fxvec = f ( xvec )
  plt.plot ( xvec, fxvec, linewidth = 3 )
  plt.plot ( [ x0, x0 ], [ 0, f ( x0 ) ], 'b', linewidth = 3)
  plt.plot ( x0,  0.0, 'bo', markersize = 10 )
  plt.plot ( x0,  f ( x0 ), 'bo', markersize = 10 )
  plt.plot ( [ x, x ], [ 0, f ( x ) ], 'r', linewidth = 3)
  plt.plot ( x,  0.0, 'ro', markersize = 10 )
  plt.plot ( x,  f ( x ), 'ro', markersize = 10 )
  plt.grid ( True )
  plt.xlabel ( '<-- X -->' )
  plt.ylabel ( '<-- F(X) -->' )
  plt.title ( 'Initial point in blue, minimizer in red', fontsize = 16 )
  filename = 'ex51_minimizer.png'
  plt.savefig ( filename )
  print ( '' )
  print ( '  Graphics saved in "%s"' % ( filename ) )
  plt.show ( )
  plt.clf ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'ex51:' )
  print ( '  Normal end of execution.' )
  return

def f ( x ):

#*****************************************************************************80
#
## F evaluates the function to be minimized.
#
  value = 2.0 * x ** 4 - 4.0 * x ** 2 + x + 20.0

  return value

def fp ( x ):

#*****************************************************************************80
#
## FP evaluates the derivative of the function to be minimized.
#
  value = 8.0 * x ** 3 - 8.0 * x + 1.0

  return value

if ( __name__ == '__main__' ):
  ex51 ( )