--- /dev/null
+## Copyright (C) 2004,2005,2006 Michael Creel <michael.creel@uab.es>
+##
+## 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/>.
+
+# usage: bfgsmin_example (to run) or edit bfgsmin_example (to examine)
+##
+# Shows how to call bfgsmin. There are two objective functions, the first
+# supplies the analytic gradient, and the second does not. The true minimizer
+# is at "location", a 50x1 vector (0.00, 0.02, 0.04 ..., 1.00).
+# Note that limited memory bfgs is faster when the dimension is high.
+# Also note that supplying analytic derivatives gives a speedup.
+##
+# Six examples are given:
+# Example 1: regular bfgs, analytic gradient
+# Example 2: same as Example 1, but verbose
+# Example 3: limited memory bfgs, analytic gradient
+# Example 4: regular bfgs, numeric gradient
+# Example 5: limited memory bfgs, numeric gradient
+# Example 6: regular bfgs, analytic gradient, minimize wrt second argument
+1;
+# example obj. fn.: supplies analytic gradient
+function [obj_value, gradient] = objective(theta, location)
+ x = theta - location + ones(rows(theta),1); # move minimizer to "location"
+ [obj_value, gradient] = rosenbrock(x);
+endfunction
+
+# example obj. fn.: no gradient
+function obj_value = objective2(theta, location)
+ x = theta - location + ones(rows(theta),1); # move minimizer to "location"
+ obj_value = rosenbrock(x);
+endfunction
+
+# initial values
+dim = 20; # dimension of Rosenbrock function
+theta0 = zeros(dim+1,1); # starting values
+location = (0:dim)/dim; # true values
+location = location';
+
+printf("EXAMPLE 1: Ordinary BFGS, using analytic gradient\n");
+t=cputime();
+control = {Inf,1}; # maxiters, verbosity
+[theta, obj_value, convergence] = bfgsmin("objective", {theta0, location}, control);
+fflush(1);
+t1 = cputime() - t;
+conv = norm(theta-location, 'inf');
+test1 = conv < 1e-5;
+
+printf("EXAMPLE 2: Same as Example 1, but verbose\n");
+t=cputime();
+control = {-1;3}; # maxiters, verbosity
+[theta, obj_value, convergence] = bfgsmin("objective", {theta0, location}, control);
+fflush(1);
+t2 = cputime() - t;
+conv = norm(theta-location, 'inf');
+test2 = conv < 1e-5;
+
+printf("EXAMPLE 3: Limited memory BFGS, using analytic gradient\n");
+t=cputime();
+control = {-1;1;1;1;3}; # maxiters, verbosity, conv. requirement., arg_to_min, lbfgs memory
+[theta, obj_value, convergence] = bfgsmin("objective", {theta0, location}, control);
+fflush(1);
+t3 = cputime() - t;
+conv = norm(theta-location, 'inf');
+test3 = conv < 1e-5;
+
+printf("EXAMPLE 4: Ordinary BFGS, using numeric gradient\n");
+t=cputime();
+control = {-1;1}; # maxiters, verbosity
+[theta, obj_value, convergence] = bfgsmin("objective2", {theta0, location}, control);
+fflush(1);
+t4 = cputime() - t;
+conv = norm(theta-location, 'inf');
+test4 = conv < 1e-5;
+
+printf("EXAMPLE 5: Limited memory BFGS, using numeric gradient\n");
+t=cputime();
+control = {-1;1;1;1;3}; # maxiters, verbosity, conv. reg., arg_to_min, lbfgs memory
+[theta, obj_value, convergence] = bfgsmin("objective2", {theta0, location}, control);
+fflush(1);
+t5 = cputime() - t;
+conv = norm(theta-location, 'inf');
+test5 = conv < 1e-5;
+
+
+printf("EXAMPLE 6: Funny case: minimize w.r.t. second argument, Ordinary BFGS, using numeric gradient\n");
+t=cputime();
+control = {-1;1;1;2}; # maxiters, verbosity, conv. reg., arg_to_min
+[theta, obj_value, convergence] = bfgsmin("objective2", {location, theta0}, control);
+fflush(1);
+t6 = cputime() - t;
+conv = norm(theta-location, 'inf');
+test6 = conv < 1e-5;
+
+printf("EXAMPLE 7: Ordinary BFGS, using numeric gradient, using non-default tolerances\n");
+t=cputime();
+control = {-1;1;1;1;0;1e-6;1e-2;1e-2}; # maxiters, verbosity, conv. reg., arg_to_min, lbfgs memory, fun. tol., param. tol., gradient tol.
+[theta, obj_value, convergence] = bfgsmin("objective2", {theta0, location}, control);
+fflush(1);
+t7 = cputime() - t;
+conv = norm(theta-location, 'inf');
+test7 = conv < 1e-2;
+
+
+printf("EXAMPLE 1: Ordinary BFGS, using analytic gradient\n");
+if test1
+ printf("Success!! :-)\n");
+else
+ printf("Failure?! :-(\n");
+endif
+printf("Elapsed time = %f\n\n\n\n",t1);
+
+printf("EXAMPLE 2: Same as Example 1, but verbose\n");
+if test2
+ printf("Success!! :-)\n");
+else
+ printf("Failure?! :-(\n");
+endif
+printf("Elapsed time = %f\n\n\n\n",t2);
+
+printf("EXAMPLE 3: Limited memory BFGS, using analytic gradient\n");
+if test3
+ printf("Success!! :-)\n");
+else
+ printf("Failure?! :-(\n");
+endif
+printf("Elapsed time = %f\n\n\n\n",t3);
+
+printf("EXAMPLE 4: Ordinary BFGS, using numeric gradient\n");
+if test4
+ printf("Success!! :-)\n");
+else
+ printf("Failure?! :-(\n");
+endif
+printf("Elapsed time = %f\n\n\n\n",t4);
+
+printf("EXAMPLE 5: Limited memory BFGS, using numeric gradient\n");
+if test5
+ printf("Success!! :-)\n");
+else
+ printf("Failure?! :-(\n");
+endif
+printf("Elapsed time = %f\n\n\n\n",t5);
+
+printf("EXAMPLE 6: Funny case: minimize w.r.t. second argument, Ordinary BFGS, using numeric gradient\n");
+if test6
+ printf("Success!! :-)\n");
+else
+ printf("Failure?! :-(\n");
+endif
+printf("Elapsed time = %f\n\n\n\n",t6);
+
+printf("EXAMPLE 7: Ordinary BFGS, using numeric gradient, using non-default tolerances\n");
+if test7
+ printf("Success!! :-)\n");
+else
+ printf("Failure?! :-(\n");
+endif
+printf("Elapsed time = %f\n\n\n\n",t7);
+
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