#! /usr/bin/env python3
#
def quartic_gradient1 ( ):

#*****************************************************************************80
#
## quartic_gradient1 applies gradient descent to the quartic function.
#
#  Discussion:
#
#    The quartic function is
#    f(x) = 2.0 * x ** 4 - 4.0 * x ** 2 + x + 20.0
#
#    We seek a minimizer of f(x) in the range -2 <= x <= 2.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 September 2019
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np
  from quartic import quartic
  from quartic import quartic_df
  from gradient_descent1 import gradient_descent1

  a = -2.0
  b = +2.0;

  print ( '' )
  print ( 'quartic_gradient1:' )
  print ( '  Seek local minimizer of a scalar function f(x) in [',a,',',b,']' )
#
#  Plot the function.
#
  xvec = np.linspace ( -2.0, 2.0, 101 )
  fxvec = quartic ( xvec )
  plt.plot ( xvec, fxvec, linewidth = 3 )
  plt.plot ( [ a, b ], [ 0, 0 ], 'k', linewidth = 3 )
  plt.grid ( True )
  plt.xlabel ( '<-- X -->' )
  plt.ylabel ( '<-- F(X) -->' )
  plt.title ( 'Quartic function', fontsize = 16 )
  filename = 'quartic.png'
  plt.savefig ( filename )
  print ( '' )
  print ( '  Graphics saved in "%s"' % ( filename ) )
  plt.show ( )
  plt.clf ( )
#
#  Choose a random initial guess.
#
  x0 = a + ( b - a ) * np.random.rand ( )
#
#  Choose a small learning rate.
#
  r = 0.05
#
#  Choose a small tolerance for the stepsize.
#
  dxtol = 0.001
#
#  Choose a small tolerance for the derivative.
#
  dftol = 0.001
#
#  Maximum number of iterations.
#
  itmax = 100

  x, it = gradient_descent1 ( quartic, quartic_df, x0, r, dxtol, dftol, itmax )

  print ( '' )
  print ( '  ', it, 'gradient descent steps were taken.' )
  print ( '  Initial x = ', x0, '  f(x) = ', quartic ( x0 ), ' f\'(x) = ', quartic_df(x0) )
  print ( '  Final x = ', x, '  f(x) = ', quartic ( x ), ' f\'(x) = ', quartic_df(x) )
#
#  Plot the function with initial point and local minimizer
#
  xvec = np.linspace ( a, b, 101 )
  fxvec = quartic ( xvec )
  plt.plot ( xvec, fxvec, linewidth = 3 )
  plt.plot ( [ x0, x0 ], [ 0, quartic ( x0 ) ], 'b', linewidth = 3 )
  plt.plot ( x0,  0.0, 'bo', markersize = 10 )
  plt.plot ( x0,  quartic ( x0 ), 'bo', markersize = 10 )
  plt.plot ( [ x, x ], [ 0, quartic ( x ) ], 'r', linewidth = 3 )
  plt.plot ( x,  0.0, 'ro', markersize = 10 )
  plt.plot ( x,  quartic ( x ), 'ro', markersize = 10 )
  plt.plot ( [ a, b ], [ 0, 0 ], 'k', linewidth = 3 )
  plt.grid ( True )
  plt.xlabel ( '<-- X -->' )
  plt.ylabel ( '<-- F(X) -->' )
  plt.title ( 'Initial point in blue, local minimizer in red', fontsize = 16 )
  filename = 'quartic_minimizer.png'
  plt.savefig ( filename )
  print ( '' )
  print ( '  Graphics saved in "%s"' % ( filename ) )
  plt.show ( )
  plt.clf ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'quartic_gradient1:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  quartic_gradient1 ( )