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

#*****************************************************************************80
#
## quartic_gradient1() applies gradient descent to the quartic function.
#
#  Discussion:
#
#    f (x) = 2 * x**4 - 4 * x**2 + x + 20
#    f'(x) = 8 * x**3 - 8 * x + 1
#
#    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
#
  from gradient_descent1 import gradient_descent1
  import matplotlib.pyplot as plt
  import numpy as np

  print ( '' )
  print ( 'quartic_gradient1:' )
  print ( '  Seek minimizer of a quartic scalar function f(x)' )
#
#  Plot the function.
#
  xmin = -2.0
  xmax = +2.0;

  xp = np.linspace ( xmin, xmax, 101 )
  fp = quartic_f ( xp )
  plt.plot ( xp, fp, linewidth = 3 )
  plt.plot ( [ xmin, xmax ], [ 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 as "%s"' % ( filename ) )
  plt.show ( )
  plt.close ( )
#
#  Choose a random initial guess.
#
  r = 0.05
  dxtol = 0.00001
  dftol = 0.001
  itmax = 100

  for x0 in [ -1.6, 1.8 ]:

    print ( '' )
    print ( '  %12.8g  %12.8g  %12.8g' % ( x0, quartic_f ( x0 ), quartic_df ( x0 ) ) )
    x, it = gradient_descent1 ( quartic_f, quartic_df, x0, r, dxtol, dftol, itmax )
    print ( '  %12.8g  %12.8g  %12.8g' % ( x, quartic_f ( x ), quartic_df ( x ) ) )
#
#  Plot the function with initial point and local minimizer
#
    xvec = np.linspace ( xmin, xmax, 101 )
    fxvec = quartic_f ( xvec )
    plt.plot ( xvec, fxvec, linewidth = 3 )
    plt.plot ( [ x0, x0 ], [ 0, quartic_f ( x0 ) ], 'b', linewidth = 3 )
    plt.plot ( x0,  0.0, 'bo', markersize = 10 )
    plt.plot ( x0,  quartic_f ( x0 ), 'bo', markersize = 10 )
    plt.plot ( [ x, x ], [ 0, quartic_f ( x ) ], 'r', linewidth = 3 )
    plt.plot ( x,  0.0, 'ro', markersize = 10 )
    plt.plot ( x,  quartic_f ( x ), 'ro', markersize = 10 )
    plt.plot ( [ xmin, xmax ], [ 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 )
    plt.show ( )
    plt.close ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'quartic_gradient1:' )
  print ( '  Normal end of execution.' )
  return

def quartic_f ( x ):

#*****************************************************************************80
#
## quartic_f() evaluates the quartic function.
#
  f = 2.0 * x**4 - 4.0 * x**2 + x + 20.0

  return f

def quartic_df ( x ):

#*****************************************************************************80
#
## quartic_df() evaluates the derivative of the quartic function.
#
  df = 8.0 * x**3 - 8.0 * x + 1.0

  return df

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