#! /usr/bin/env python
#
def goldstein_price ( m, x ):

#*****************************************************************************80
#
## GOLDSTEIN_PRICE evaluates the Goldstein-Price polynomial.
#
#  Discussion:
#
#    The minimizer is
#
#      X* = [ 0.0, -1.0 ]
#      F(X*) = 3.0
#
#    Suggested starting point:
#
#      X = [ -0.5, 0.25 ] (easy convergence)
#      X = [ -4.0, 5.00 ] (harder convergence)
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Zbigniew Michalewicz,
#    Genetic Algorithms + Data Structures = Evolution Programs,
#    Third Edition,
#    Springer Verlag, 1996,
#    ISBN: 3-540-60676-9,
#    LC: QA76.618.M53.
#
#  Parameters:
#
#    Input, integer M, the number of variables.
#
#    Input, real X(M), the argument of the function.
#
#    Output, real F, the value of the function at X.
#
  a = x[0] + x[1] + 1.0

  b = 19.0 - 14.0 * x[0] + 3.0 * x[0] * x[0] - 14.0 * x[1] \
    + 6.0 * x[0] * x[1] + 3.0 * x[1] * x[1]

  c = 2.0 * x[0] - 3.0 * x[1]

  d = 18.0 - 32.0 * x[0] + 12.0 * x[0] * x[0] + 48.0 * x[1] \
    - 36.0 * x[0] * x[1] + 27.0 * x[1] * x[1]

  f = ( 1.0 + a * a * b ) * ( 30.0 + c * c * d )

  return f

def goldstein_price_test ( ):

#*****************************************************************************80
#
## GOLDSTEIN_PRICE_TEST works with the Goldstein-Price function.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from compass_search import compass_search
  from r8vec_print import r8vec_print

  print ( '' )
  print ( 'GOLDSTEIN_PRICE_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test COMPASS_SEARCH with the Goldstein-Price function.' )
  m = 2
  delta_tol = 0.00001
  delta = 0.3
  k_max = 20000

  x = np.array ( [ -0.5, 0.25 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( goldstein_price ( m, x ) ) )

  x, fx, k = compass_search ( goldstein_price, m, x, delta_tol, delta, k_max )
  r8vec_print ( m, x, '  Estimated minimizer X1:' )
  print ( '' )
  print ( '  F(X1) = %g, number of steps = %d' % ( fx, k ) )
#
#  Repeat with more difficult start.
#
  x = np.array ( [ -4.0, 5.0 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( goldstein_price ( m, x ) ) )

  x, fx, k = compass_search ( goldstein_price, m, x, delta_tol, delta, k_max )
  r8vec_print ( m, x, '  Estimated minimizer X1:' )
  print ( '' )
  print ( '  F(X1) = %g, number of steps = %d' % ( fx, k ) )
#
#  Demonstrate correct minimizer.
#
  x = np.array ( [ 0.0, -1.0 ] )
  r8vec_print ( m, x, '  Correct minimizer X*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( goldstein_price ( m, x ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'GOLDSTEIN_PRICE_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  goldstein_price_test ( )
  timestamp ( )