#! /usr/bin/env python3
#
def hex2_gradient2 ( ):

#*****************************************************************************80
#
## hex2_gradient2 uses gradient descent on the hex2 function.
#
#  Discussion:
#
#    Gradient descent for a function of 2 variables.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 September 2019
#
#  Author:
#
#    John Burkardt
#
# import matplotlib.pyplot as plt
  import numpy as np
  from gradient_descent2 import gradient_descent2

  print ( '' )
  print ( 'hex2_gradient2:' )
  print ( '  Seek minimizer of a function z(x,y).' )
#
#  Choose a random initial guess.
# 
  x0 = np.array ( [ \
    - 3.0 + 6.0 * np.random.rand ( ), \
    - 3.0 + 6.0 * np.random.rand ( ) ] )

  x0 = np.array ( [ 2.0, 1.5 ] )
#
#  Choose a small learning rate.
#
  r = 0.10
#
#  Choose a small tolerance for the stepsize.
#
  dxtol = 0.00001
#
#  Choose a small tolerance for the derivative.
#
  dftol = 0.001
#
#  Maximum number of iterations
#
  itmax = 100

  x, it = gradient_descent2 ( hex2, hex2_df, x0, r, dxtol, dftol, itmax )

  print ( '' )
  print ( '  ', it, 'gradient descent steps were taken.' )
  print ( '  Initial x = ', x0, '  f(x) = ', hex2 ( x0 ), ' f\'(x) = ', hex2_df(x0) )
  print ( '  Final x = ', x, '  f(x) = ', hex2 ( x ), ' f\'(x) = ', hex2_df(x) )
#
#  Terminate.
#
  print ( '' )
  print ( 'hex2_gradient2:' )
  print ( '  Normal end of execution.' )
  return

def hex2 ( x ):

#*****************************************************************************80
#
## hex2 evaluates the function to be minimized.
#
  value = 2.0 * x[0]**2 - 1.05 * x[0]**4 + x[0]**6 / 6.0 + x[0] * x[1] + x[1]**2

  return value

def hex2_df ( x ):

#*****************************************************************************80
#
## hex2_df evaluates the derivative of the function to be minimized.
#
  import numpy as np

  df = np.array ( [ \
    4.0 * x[0] - 4.2 * x[0]**3 + x[0]**5 + x[1], \
    x[0] + 2.0 * x[1] ] )

  return df

if ( __name__ == '__main__' ):
  hex2_gradient2 ( )