--- /dev/null
+## Copyright (C) 2002 Etienne Grossmann <etienne@egdn.net>
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## Checks wether the function 'nelder_mead_min' works, by making it minimize a
+## quadratic function.
+
+ok = 1;
+cnt = 1;
+
+if ! exist ("verbose"), verbose = 0; end
+if verbose, printf (" test_nelder_mead : \n"); end
+
+if ! exist ("inspect"), inspect = 0; end
+
+tol = 100*sqrt (eps);
+
+R = 3 ;
+C = 2;
+
+if verbose,
+ printf (" optimization problem has dimension %i\n",R*C);
+end
+
+function c = my_quad_func (x,y,z)
+ c = 1 + sum (vec(x-y)'*z*(vec(x-y)));
+end
+
+function c = non_quad_func_1 (x,y,z)
+ tmp = sum (vec(x-y)'*z*(vec(x-y)));
+ c = 1 + 1.1*tmp + sin (sqrt(tmp));
+end
+
+function c = non_quad_func_2 (x,y,z)
+ tmp1 = sum (vec(x-y)'*z*(vec(x-y)));
+ tmp2 = max (abs (vec(x-y)))^2;
+ c = 1 + 1.1*tmp1 + tmp2 ;
+end
+
+## dt = mytic()
+##
+## Returns the cputime since last call to 'mytic'.
+
+function dt = mytic()
+ persistent last_mytic = 0 ;
+ [t,u,s] = cputime() ;
+ dt = t - last_mytic ;
+ last_mytic = t ;
+endfunction
+
+fnames = { "my_quad_func", "non_quad_func_1", "non_quad_func_2"};
+
+x0 = randn(R,C) ;
+x1 = x0 + randn(R,C) ;
+z = randn (R*C); z = z*z';
+
+for i = 1:length (fnames)
+ fname = fnames{i};
+ if verbose,
+ printf ("trying to minimize '%s'\n", fname);
+ end
+ ctl = nan*zeros (1,6);
+
+ mytic ();
+ [x2,v,nf] = nelder_mead_min (fname, {x1,x0,z}, ctl) ;
+ t0 = mytic ();
+
+ if any (abs (x2-x0)(:) > 100*tol),
+ if verbose || inspect, printf ("not ok %i\n",cnt); end
+ [max(abs (x2-x0)(:)), 100*tol]
+ if inspect, keyboard; end
+ ok = 0 ;
+ else
+ if verbose,
+ printf ("ok %i\n function evaluations = %i\n",cnt,nf);
+ end
+ end
+ cnt++;
+
+ # Use vanilla nelder_mead_min
+ mytic ();
+ [x2,v,nf] = nelder_mead_min (fname, {x1,x0,z}) ;
+ t1 = mytic ();
+
+ if any (abs (x2-x0)(:) > 100*tol),
+ if verbose || inspect, printf ("not ok %i\n",cnt); end
+ [max(abs (x2-x0)(:)), 100*tol]
+ if inspect, keyboard; end
+ ok = 0 ;
+ else
+ if verbose,
+ printf ("ok %i\n function evaluations = %i\n",cnt,nf);
+ end
+ end
+ cnt++;
+
+
+ # Optimize wrt 2nd arg.
+ ctl = nan * zeros (1,6);
+ ctl(6) = 0;
+ ctl(3) = 2;
+
+ mytic ();
+ [x2,v,nf] = nelder_mead_min (fname, {x1,x0,z}, ctl) ;
+ t0 = mytic ();
+
+ if any (abs (x2-x1)(:) > 100*tol),
+ if verbose || inspect, printf ("not ok %i\n",cnt); end
+ [max(abs (x2-x0)(:)), 100*tol]
+ if inspect, keyboard; end
+ ok = 0 ;
+ else
+ if verbose,
+ printf ("ok %i\n function evaluations = %i\n",cnt,nf);
+ end
+ end
+ cnt++;
+
+ # Optimize wrt 2nd arg.
+ ctl = nan * zeros (1,6);
+ ctl(3) = 2;
+
+ mytic ();
+ [x2,v,nf] = nelder_mead_min (fname, {x1,x0,z}, ctl) ;
+ t1 = mytic ();
+
+ if any (abs (x2-x1)(:) > tol),
+ if verbose || inspect, printf ("not ok %i\n",cnt); end
+ [max(abs (x2-x0)(:)), 100*tol]
+ if inspect, keyboard; end
+ ok = 0 ;
+ else
+ if verbose,
+ printf ("ok %i\n function evaluations = %i\n",cnt,nf);
+ end
+ end
+ cnt++;
+ if 0
+ # Check with struct control variable
+ ctls = struct ("narg", 2);
+ [x2bis,vbis,nfbis] = nelder_mead_min (fname, {x1,x0,z}, ctls) ;
+ t1 = mytic ();
+ ## [nf,nfbis]
+ if any ((x2-x2bis)(:))
+ if verbose || inspect, printf ("not ok %i\n",cnt); end
+ printf (" struct ctl : x2 - x2bis -> %g\n", max(abs (x2-x2bis)(:)));
+ if inspect, keyboard; end
+ ok = 0 ;
+ else
+ if verbose,
+ printf ("ok %i\n function evaluations = %i\n",cnt,nfbis);
+ end
+ end
+ cnt++;
+
+ # Check with named args
+ [x2bis,vbis,nfbis] = nelder_mead_min (fname, {x1,x0,z}, "narg", 2) ;
+ t1 = mytic ();
+ ## [nf,nfbis]
+ if any ((x2-x2bis)(:))
+ if verbose || inspect, printf ("not ok %i\n",cnt); end
+ printf (" named arg : x2 - x2bis -> %g\n", max(abs (x2-x2bis)(:)));
+ if inspect, keyboard; end
+ ok = 0 ;
+ else
+ if verbose,
+ printf ("ok %i\n function evaluations = %i\n",cnt,nfbis);
+ end
+ end
+ cnt++;
+ end
+end
+
+if verbose && ok
+ printf ("All tests ok\n");
+end
+
+