#! /usr/bin/env python
#
def bohach2 ( m, x ):

#*****************************************************************************80
#
## BOHACH2 evaluates the Bohachevsky function #2.
#
#  Discussion:
#
#    The minimizer is
#
#      X* = [ 0.0, 0.0 ]
#      F(X*) = 0.0
#
#    Suggested starting point:
#
#      X = [ 0.6, 1.3 ]
#
#  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.
#
  import numpy as np

  f =       x[0] * x[0] \
    + 2.0 * x[1] * x[1] \
    - 0.3 * np.cos ( 3.0 * np.pi * x[0] ) * np.cos ( 4.0 * np.pi * x[1] ) \
    + 0.3

  return f

def bohach2_test ( ):

#*****************************************************************************80
#
## BOHACH2_TEST works with the Bohachevsky function #2.
#
#  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 ( 'BOHACH2_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test COMPASS_SEARCH with the Bohachevsky function #2.' )
  m = 2
  delta_tol = 0.00001
  delta = 0.3
  k_max = 20000

  x = np.array ( [ 0.6, 1.3 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  f = bohach2 ( m, x )
  print ( '  F(X0) = %g' % ( f ) )

  x, fx, k = compass_search ( bohach2, 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, 0.0 ] )
  r8vec_print ( m, x, '  Correct minimizer X*:' )
  print ( '' )
  f = bohach2 ( m, x )
  print ( '  F(X*) = %g' % ( f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'BOHACH2_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  bohach2_test ( )
  timestamp ( )