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

#*****************************************************************************80
#
## EXTENDED_ROSENBROCK computes the extended Rosenbrock function.
#
#  Discussion:
#
#    The number of dimensions is arbitrary, except that it must be even.
#
#    There is a global minimum at X* = (1,1,...), F(X*) = 0.
#
#    The contours are sharply twisted.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Howard Rosenbrock,
#    An Automatic Method for Finding the Greatest or Least Value of a Function,
#    Computer Journal,
#    Volume 3, 1960, pages 175-184.
#
#  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

  r = np.zeros ( m )

  for i in range ( 0, m, 2 ):
    r[i] = 1.0 - x[i]
    r[i+1] = 10.0 * ( x[i+1] - x[i] ** 2 )

  f = np.dot ( r, r )

  return f

def extended_rosenbrock_test ( ):

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

  x = np.array ( [ - 1.2, 1.0,  -1.5, 1.2 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( extended_rosenbrock ( m, x ) ) )

  x, fx, k = compass_search ( extended_rosenbrock, 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 ( [ 1.0, 1.0, 1.0, 1.0 ] )
  r8vec_print ( m, x, '  Correct minimizer X*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( extended_rosenbrock ( m, x ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'EXTENDED_ROSENBROCK_TEST' )
  print ( '  Normal end of execution.' )
  return

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