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

#*****************************************************************************80
#
## BROYDEN computes the two dimensional modified Broyden function.
#
#  Discussion:
#
#    This function has a global minimizer:
#
#      X = ( -0.511547141775014, -0.398160951772036 )
#
#    for which
#
#      F(X) = 1.44E-04
#
#    Start the search at
#
#      X = ( -0.9, -1.0 )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Charles Broyden,
#    A class of methods for solving nonlinear simultaneous equations,
#    Mathematics of Computation,
#    Volume 19, 1965, pages 577-593.
#
#    Jorge More, Burton Garbow, Kenneth Hillstrom,
#    Testing unconstrained optimization software,
#    ACM Transactions on Mathematical Software,
#    Volume 7, Number 1, March 1981, pages 17-41. 
#
#  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 = abs ( ( 3.0 -       x[0] ) * x[0] - 2.0 * x[1] + 1.0 )
  f2 = abs ( ( 3.0 - 2.0 * x[1] ) * x[1] -       x[0] + 1.0 )

  p = 3.0 / 7.0

  f = f1 ** p + f2 ** p
 
  return f

def broyden_test ( ):

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

  x = np.array ( [ -0.9, -1.0 ] )
  r8vec_print ( m, x, '  Initial point X0:' )
  print ( '' )
  print ( '  F(X0) = %g' % ( broyden ( m, x ) ) )

  x, fx, k = compass_search ( broyden, 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 ( [ -0.511547141775014, -0.398160951772036 ] )
  r8vec_print ( m, x, '  Correct minimizer X*:' )
  print ( '' )
  print ( '  F(X*) = %g' % ( broyden ( m, x ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'BROYDEN_TEST' )
  print ( '  Normal end of execution.' )
  return

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