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/*!
* \file
* \brief Newton search test program
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2010 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ 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.
*
* IT++ 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 IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*/
#include <itpp/itoptim.h>
#include <iomanip>
using namespace std;
using namespace itpp;
double rosenbrock(const vec &x)
{
double f1 = x(1) - sqr(x(0)), f2 = 1 - x(0);
double F = 50 * sqr(f1) + 0.5 * sqr(f2) + 0.0;
return F;
}
vec rosenbrock_gradient(const vec &x)
{
double f1 = x(1) - sqr(x(0)), f2 = 1 - x(0);
vec g(2);
g(0) = -200.0 * x(0) * f1 - f2;
g(1) = 100.0 * f1;
return g;
}
int main(void)
{
cout << "=====================================" << endl;
cout << " Test of Numerical optimization " << endl;
cout << "=====================================" << endl;
cout << setprecision(6);
{
cout << " Line_Search " << endl;
cout << "--------------------" << endl;
vec x0 = "-1.2 1";
double F0 = rosenbrock(x0);
vec g0 = rosenbrock_gradient(x0);
vec h = -g0;
Line_Search line;
line.set_functions(rosenbrock, rosenbrock_gradient);
cout << "x0 = " << x0 << endl;
cout << "F0 = " << F0 << endl;
cout << "g0 = " << g0 << endl;
cout << "h = " << h << endl;
double Fn;
vec xn, gn;
line.enable_trace();
if (!line.search(x0, F0, g0, h, xn, Fn, gn))
cout << "Line search failed" << endl;
cout << "Soft: " << endl;
cout << "xn = " << xn << endl;
cout << "Fn = " << Fn << endl;
cout << "gn = " << gn << endl;
cout << "no_feval = " << line.get_no_function_evaluations() << endl;
vec alpha_values, F_values, dF_values;
line.get_trace(alpha_values, F_values, dF_values);
cout << endl << "trace:" << endl;
cout << "alpha = " << fixed << alpha_values << endl;
cout << "F = " << round_to_infty(F_values) << endl;
cout << "dF = " << round_to_infty(dF_values) << endl;
line.set_method(Exact);
if (!line.search(x0, F0, g0, h, xn, Fn, gn))
cout << "Line search failed" << endl;
cout << endl << "Exact: " << endl;
cout << "xn = " << xn << endl;
cout << "Fn = " << Fn << endl;
cout << "gn = " << gn << endl;
cout << "no_feval = " << line.get_no_function_evaluations() << endl;
line.get_trace(alpha_values, F_values, dF_values);
cout << endl << "trace:" << endl;
cout << "alpha = " << alpha_values << endl;
cout << "F = " << round_to_infty(F_values) << endl;
cout << "dF = " << round_to_infty(dF_values) << endl;
}
{
cout << endl << " Newton_Search " << endl;
cout << "--------------------" << endl;
vec x0 = "-1.2 1";
Newton_Search newton;
newton.set_functions(rosenbrock, rosenbrock_gradient);
newton.enable_trace();
cout << "x0 = " << x0 << endl;
vec xn, gn;
if (!newton.search(x0, xn))
cout << "Newton search failed" << endl;
cout << "xn = " << xn << endl;
cout << "F = " << newton.get_function_value() << endl;
cout << "norm(f') = " << newton.get_stop_1() << endl;
cout << "norm(dx) = " << newton.get_stop_2() << endl;
cout << "no_feval = " << newton.get_no_function_evaluations() << endl;
cout << "no_iter = " << newton.get_no_iterations() << endl;
Array<vec> xv;
vec Fv, ngv, dv;
newton.get_trace(xv, Fv, ngv, dv);
cout << endl << "trace:" << endl;
cout << "xv = " << xv << endl;
cout << "Fv = " << Fv << endl;
cout << "ngv = " << ngv << endl;
cout << "dv = " << dv << endl;
newton.disable_trace();
cout << endl << " fminunc " << endl;
cout << "--------------------" << endl;
xn = fminunc(rosenbrock, rosenbrock_gradient, x0);
cout << "x0 = " << x0 << endl;
cout << "xn = " << xn << endl;
}
return 0;
}
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