%% TEST03 demonstrates the use of NELMIN on HELICAL.
%
%  Modified:
%
%    28 February 2008
%
%  Author:
%
%    John Burkardt
%
  clear

  n = 3;

  fprintf ( 1, '\n' );
  fprintf ( 1, 'TEST03\n' );
  fprintf ( 1, '  Apply NELMIN to the HELICAL function.\n' );

  start(1) = - 1.0;
  start(2) =   0.0;
  start(3) =   0.0;

  reqmin = 1.0E-08;

  step(1) = 1.0;
  step(2) = 1.0;
  step(3) = 1.0;

  konvge = 10;
  kcount = 500;

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Starting point X:\n' );
  fprintf ( 1, '\n' );
  for i = 1 : n
    fprintf ( 1, '  %f\n', start(i) );
  end

  ynewlo = helical ( start );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  F(X) = %f\n', ynewlo );

  [ xmin, ynewlo, icount, numres, ifault ] = nelmin ( @helical, n, start, ...
  reqmin, step, konvge, kcount );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Return code IFAULT = %d\n', ifault );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Estimate of minimizing value X*:\n' );
  fprintf ( 1, '\n' );
  for i = 1 : n
    fprintf ( 1, '  %f\n', xmin(i) );
  end

  fprintf ( 1, '\n' );
  fprintf ( 1, '  F(X*) = %f\n', ynewlo );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Number of iterations = %d\n', icount );
  fprintf ( 1, '  Number of restarts =   %d\n', numres );