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

#*****************************************************************************80
#
## HIMMELBLAU computes the Himmelblau function.
#
#  Discussion:
#
#    This function has 4 global minima:
#
#      X* = (  3,        2       ), F(X*) = 0.
#      X* = (  3.58439, -1.84813 ), F(X*) = 0.
#      X* = ( -3.77934, -3.28317 ), F(X*) = 0.
#      X* = ( -2.80512,  3.13134 ), F(X*) = 0.
#
#    Suggested starting points are
#
#      (+1,+1),
#      (-1,+1),
#      (-1,-1),
#      (+1,-1),
#
#  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 + x[1]      - 11.0 ) ** 2 \
    + ( x[0]      + x[1] ** 2 -  7.0 ) ** 2
 
  return f

def himmelblau_test ( ):

#*****************************************************************************80
#
## HIMMELBLAU_TEST works with the Himmelblau 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 ( 'HIMMELBLAU_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test COMPASS_SEARCH with the Himmelblau 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' % ( himmelblau ( m, x ) ) )

  x, fx, k = compass_search ( himmelblau, 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 ) )

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

  x, fx, k = compass_search ( himmelblau, 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 ) )

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

  x, fx, k = compass_search ( himmelblau, 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 ) )

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

  x, fx, k = compass_search ( himmelblau, 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 Himmelblau minimizers.
#
  x = np.array ( [ 3.0, 2.0 ] )
  r8vec_print ( m, x, '  Correct Himmelblau minimizer X1*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( himmelblau ( m, x ) ) )

  x = np.array ( [ 3.58439, -1.84813 ] )
  r8vec_print ( m, x, '  Correct Himmelblau minimizer X2*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( himmelblau ( m, x ) ) )

  x = np.array ( [ -3.77934, -3.28317 ] )
  r8vec_print ( m, x, '  Correct Himmelblau minimizer X3*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( himmelblau ( m, x ) ) )

  x = np.array ( [ -2.80512,  3.13134 ] )
  r8vec_print ( m, x, '  Correct Himmelblau minimizer X4*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( himmelblau ( m, x ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'HIMMELBLAU_TEST' )
  print ( '  Normal end of execution.' )
  return

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