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

#*****************************************************************************80
#
## LOCAL computes the local function.
#
#  Discussion:
#
#    This function has a local minimizer:
#
#      X* = ( 0.2858054412..., 0.2793263206...), F(X*) = 5.9225...
#
#    and a global minimizer:
#
#      X* = ( -21.02667179..., -36.75997872...), F(X*) = 0.
#
#    Suggested starting point for local minimizer:
#
#      X = ( 1, 1 ), F(X) = 3.33 * 10^6.
#
#    Suggested starting point for global minimizer:
#
#      X = ( -15, -35), F(X) = 1.49 * 10^8.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    David Himmelblau,
#    Applied Nonlinear Programming,
#    McGraw Hill, 1972,
#    ISBN13: 978-0070289215,
#    LC: T57.8.H55.
#
#  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.
#
  f = ( x[0] ** 2 + 12.0 * x[1] - 1.0 ) ** 2 \
    + ( 49.0 * x[0] ** 2 + 49.0 * x[1] ** 2 + 84.0 * x[0] \
    + 2324.0 * x[1] - 681.0 ) ** 2
 
  return f

def local_test ( ):

#*****************************************************************************80
#
## LOCAL_TEST works with the Local 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 ( 'LOCAL_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test COMPASS_SEARCH with the Local function.' )
  m = 2
  delta_tol = 0.00001
  delta = 0.3
  k_max = 20000

  x = np.array ( [ 1.0, 1.0 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( local ( m, x ) ) )

  x, fx, k = compass_search ( local, 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 local minimizer.
#
  x = np.array ( [ 0.2858054412, 0.2793263206 ] )
  r8vec_print ( m, x, '  Correct local minimizer X*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( local ( m, x ) ) )
#
#  Try for global minimizer.
#
  x = np.array ( [ -15.0, -35.0 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( local ( m, x ) ) )

  x, fx, k = compass_search ( local, 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 global minimizer.
#
  x = np.array ( [ -21.02667179, -36.75997872 ] )
  r8vec_print ( m, x, '  Correct global minimizer X*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( local ( m, x ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'LOCAL_TEST' )
  print ( '  Normal end of execution.' )
  return

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