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

#*****************************************************************************80
#
## BEALE computes the Beale function.
#
#  Discussion:
#
#    This function has a global minimizer:
#
#      X = ( 3.0, 0.5 )
#
#    for which
#
#      F(X) = 0.
#
#    For a relatively easy computation, start the search at
#
#      X = ( 1.0, 1.0 )
#
#    A harder computation starts at
#
#      X = ( 1.0, 4.0 )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Evelyn Beale,
#    On an Iterative Method for Finding a Local Minimum of a Function
#    of More than One Variable,
#    Technical Report 25, 
#    Statistical Techniques Research Group,
#    Princeton University, 1958.
#
#    Richard Brent,
#    Algorithms for Minimization with Derivatives,
#    Dover, 2002,
#    ISBN: 0-486-41998-3,
#    LC: QA402.5.B74.
#
#  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.
#
  f1 = 1.5   - x[0] * ( 1.0 - x[1]      )
  f2 = 2.25  - x[0] * ( 1.0 - x[1] ** 2 )
  f3 = 2.625 - x[0] * ( 1.0 - x[1] ** 3 )

  f = f1 ** 2 + f2 ** 2 + f3 ** 2
 
  return f

def beale_test ( ):

#*****************************************************************************80
#
#% BEALE_TEST works with the Beale 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 ( 'BEALE_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test COMPASS_SEARCH with the Beale function.' )
  m = 2
  delta_tol = 0.00001
  delta = 0.1
  k_max = 20000

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

  x, fx, k = compass_search ( beale, 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 ( [ 1.0, 4.0 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( beale ( m, x ) ) )

  x, fx, k = compass_search ( beale, 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 ( [ 3.0, 0.5 ] )
  r8vec_print ( m, x, '  Correct minimizer X*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( beale ( m, x ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'BEALE_TEST' )
  print ( '  Normal end of execution.' )
  return

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