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

#*****************************************************************************80
#
## POWELL computes the Powell singular quartic function.
#
#  Discussion:
#
#    This function has a global minimizer:
#
#      X* = ( 0.0, 0.0, 0.0, 0.0 ), F(X*) = 0.
#
#    Start the search at
#
#      X = ( 3.0, -1.0, 0.0, 1.0 )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Michael Powell,
#    An Iterative Method for Finding Stationary Values of a Function
#    of Several Variables,
#    Computer Journal,
#    Volume 5, 1962, pages 147-151.
#
#  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 = x[0] + 10.0 * x[1]
  f2 =                            x[2] - x[3]
  f3 =               x[1] - 2.0 * x[2]
  f4 = x[0]                            - x[3]

  f = f1 * f1 + f2 * f2 + f3 * f3 + f4 * f4
 
  return f

def powell_test ( ):

#*****************************************************************************80
#
## POWELL_TEST works with the Powell 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 ( 'POWELL_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test COMPASS_SEARCH with the Powell function.' )
  m = 4
  delta_tol = 0.00001
  delta = 0.3
  k_max = 20000

  x = np.array ( [ 3.0, -1.0, 0.0, 1.0 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( powell ( m, x ) ) )

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

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