dlib C++ Library - optimization.cpp

// Copyright (C) 2008 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#include "optimization_test_functions.h"
#include <dlib/optimization.h>
#include <dlib/statistics.h>
#include <sstream>
#include <string>
#include <cstdlib>
#include <ctime>
#include <vector>
#include "../stl_checked.h"
#include "../array.h"
#include "../rand.h"
#include "tester.h"
namespace 
{
 using namespace test;
 using namespace dlib;
 using namespace std;
 logger dlog("test.optimization");
// ----------------------------------------------------------------------------------------
 bool approx_equal (
 double a,
 double b
 )
 {
 return std::abs(a - b) < 100*std::numeric_limits<double>::epsilon();
 }
// ----------------------------------------------------------------------------------------
 long total_count = 0;
 template <typename T>
 double apq ( const T& x)
 {
 DLIB_ASSERT(x.nr() > 1 && x.nc() == 1,"");
 COMPILE_TIME_ASSERT(is_matrix<T>::value);
 double temp = 0;
 for (long r = 0; r < x.nr(); ++r)
 {
 temp += (r+1)*x(r)*x(r);
 }
 ++total_count;
 return temp + 1/100.0*(x(0) + x(x.nr()-1))*(x(0) + x(x.nr()-1));
 }
 template <typename T>
 T der_apq ( const T& x)
 {
 DLIB_ASSERT(x.nr() > 1 && x.nc() == 1,"");
 COMPILE_TIME_ASSERT(is_matrix<T>::value);
 T temp(x.nr());
 for (long r = 0; r < x.nr(); ++r)
 {
 temp(r) = 2*(r+1)*x(r) ;
 }
 temp(0) += 1/50.0*(x(0) + x(x.nr()-1));
 temp(x.nr()-1) += 1/50.0*(x(0) + x(x.nr()-1));
 ++total_count;
 return temp;
 }
// ----------------------------------------------------------------------------------------
 // Rosenbrock's function. minimum at (1,1)
 double rosen ( const matrix<double,2,1>& x)
 {
 ++total_count;
 return 100*pow(x(1) - x(0)*x(0),2) + pow(1 - x(0),2);
 }
 matrix<double,2,1> der_rosen ( const matrix<double,2,1>& x)
 {
 ++total_count;
 matrix<double,2,1> res;
 res(0) = -400*x(0)*(x(1)-x(0)*x(0)) - 2*(1-x(0));
 res(1) = 200*(x(1)-x(0)*x(0));
 return res;
 }
// ----------------------------------------------------------------------------------------
 // negative of Rosenbrock's function. minimum at (1,1)
 double neg_rosen ( const matrix<double,2,1>& x)
 {
 ++total_count;
 return -(100*pow(x(1) - x(0)*x(0),2) + pow(1 - x(0),2));
 }
 matrix<double,2,1> der_neg_rosen ( const matrix<double,2,1>& x)
 {
 ++total_count;
 matrix<double,2,1> res;
 res(0) = -400*x(0)*(x(1)-x(0)*x(0)) - 2*(1-x(0));
 res(1) = 200*(x(1)-x(0)*x(0));
 return -res;
 }
// ----------------------------------------------------------------------------------------
 double simple ( const matrix<double,2,1>& x)
 {
 ++total_count;
 return 10*x(0)*x(0) + x(1)*x(1);
 }
 matrix<double,2,1> der_simple ( const matrix<double,2,1>& x)
 {
 ++total_count;
 matrix<double,2,1> res;
 res(0) = 20*x(0);
 res(1) = 2*x(1);
 return res;
 }
// ----------------------------------------------------------------------------------------
 double powell ( const matrix<double,4,1>& x)
 {
 ++total_count;
 return pow(x(0) + 10*x(1),2) +
 pow(std::sqrt(5.0)*(x(2) - x(3)),2) + 
 pow((x(1) - 2*x(2))*(x(1) - 2*x(2)),2) +
 pow(std::sqrt(10.0)*(x(0) - x(3))*(x(0) - x(3)),2);
 }
// ----------------------------------------------------------------------------------------
// a simple function with a minimum at zero
 double single_variable_function ( double x)
 {
 ++total_count;
 return 3*x*x + 5;
 }
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
 void test_apq (
 const matrix<double,0,1> p
 )
 {
 typedef matrix<double,0,1> T;
 const double eps = 1e-12;
 const double minf = -10;
 matrix<double,0,1> x(p.nr()), opt(p.nr());
 set_all_elements(opt, 0);
 double val = 0;
 if (p.size() < 20)
 dlog << LINFO << "testing with apq and the start point: " << trans(p);
 else
 dlog << LINFO << "testing with apq and a big vector with " << p.size() << " components.";
 // don't use bfgs on really large vectors
 if (p.size() < 20)
 {
 total_count = 0;
 x = p;
 val = find_min(bfgs_search_strategy(), 
 objective_delta_stop_strategy(eps),
 wrap_function(apq<T>), wrap_function(der_apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() bgfs: got apq in " << total_count;
 total_count = 0;
 x = p;
 find_min(bfgs_search_strategy(), 
 gradient_norm_stop_strategy(),
 wrap_function(apq<T>), wrap_function(der_apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 dlog << LINFO << "find_min() bgfs(gn): got apq in " << total_count;
 }
 if (p.size() < 100)
 {
 total_count = 0;
 x = p;
 val=find_min_bobyqa(wrap_function(apq<T>), x, 2*x.size()+1,
 uniform_matrix<double>(x.size(),1,-1e100),
 uniform_matrix<double>(x.size(),1,1e100),
 (max(abs(x))+1)/10,
 1e-6,
 10000);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min_bobyqa(): got apq in " << total_count;
 }
 total_count = 0;
 x = p;
 val=find_min(lbfgs_search_strategy(10), 
 objective_delta_stop_strategy(eps),
 wrap_function(apq<T>), wrap_function(der_apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() lbgfs-10: got apq in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(lbfgs_search_strategy(1), 
 objective_delta_stop_strategy(eps),
 wrap_function(apq<T>), wrap_function(der_apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() lbgfs-1: got apq in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 wrap_function(apq<T>), wrap_function(der_apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() cg: got apq in " << total_count;
 // don't do approximate derivative tests if the input point is really long
 if (p.size() < 20)
 {
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 wrap_function(apq<T>), derivative(wrap_function(apq<T>)), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() bfgs: got apq/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 wrap_function(apq<T>), derivative(wrap_function(apq<T>)), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() cg: got apq/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps), 
 wrap_function(apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() bfgs: got apq/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(lbfgs_search_strategy(10),
 objective_delta_stop_strategy(eps), 
 wrap_function(apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 dlog << LINFO << "find_min() lbfgs-10: got apq/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 wrap_function(apq<T>), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , apq(x)));
 dlog << LINFO << "find_min() cg: got apq/noder2 in " << total_count;
 }
 }
 void test_powell (
 const matrix<double,4,1> p
 )
 {
 const double eps = 1e-15;
 const double minf = -1;
 matrix<double,4,1> x, opt;
 opt(0) = 0;
 opt(1) = 0;
 opt(2) = 0;
 opt(3) = 0;
 double val = 0;
 dlog << LINFO << "testing with powell and the start point: " << trans(p);
 /*
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 powell, derivative(powell,1e-8), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-2),opt-x);
 DLIB_TEST(approx_equal(val , powell(x)));
 dlog << LINFO << "find_min() bfgs: got powell/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 powell, derivative(powell,1e-9), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-2),opt-x);
 DLIB_TEST(approx_equal(val , powell(x)));
 dlog << LINFO << "find_min() cg: got powell/noder in " << total_count;
 */
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 powell, x, minf, 1e-10);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-1),opt-x);
 DLIB_TEST(approx_equal(val , powell(x)));
 dlog << LINFO << "find_min() bfgs: got powell/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(lbfgs_search_strategy(4),
 objective_delta_stop_strategy(eps),
 powell, x, minf, 1e-10);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-1),opt-x);
 DLIB_TEST(approx_equal(val , powell(x)));
 dlog << LINFO << "find_min() lbfgs-4: got powell/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(lbfgs_search_strategy(4),
 gradient_norm_stop_strategy(),
 powell, x, minf, 1e-10);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-1),opt-x);
 DLIB_TEST(approx_equal(val , powell(x)));
 dlog << LINFO << "find_min() lbfgs-4(gn): got powell/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 powell, x, minf, 1e-10);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-1),opt-x);
 DLIB_TEST(approx_equal(val , powell(x)));
 dlog << LINFO << "find_min() cg: got powell/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_bobyqa(powell, x, 2*x.size()+1,
 uniform_matrix<double>(x.size(),1,-1e100),
 uniform_matrix<double>(x.size(),1,1e100),
 (max(abs(x))+1)/10,
 1e-8,
 10000);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-3),opt-x);
 DLIB_TEST(approx_equal(val , powell(x)));
 dlog << LINFO << "find_min_bobyqa(): got powell in " << total_count;
 }
 void test_simple (
 const matrix<double,2,1> p
 )
 {
 const double eps = 1e-12;
 const double minf = -10000;
 matrix<double,2,1> x, opt;
 opt(0) = 0;
 opt(1) = 0;
 double val = 0;
 dlog << LINFO << "testing with simple and the start point: " << trans(p);
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 simple, der_simple, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() bfgs: got simple in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 gradient_norm_stop_strategy(),
 simple, der_simple, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() bfgs(gn): got simple in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(lbfgs_search_strategy(3),
 objective_delta_stop_strategy(eps),
 simple, der_simple, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() lbfgs-3: got simple in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 simple, der_simple, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() cg: got simple in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 simple, derivative(simple), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() bfgs: got simple/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(lbfgs_search_strategy(8),
 objective_delta_stop_strategy(eps),
 simple, derivative(simple), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() lbfgs-8: got simple/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 simple, derivative(simple), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() cg: got simple/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 simple, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() bfgs: got simple/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(lbfgs_search_strategy(6),
 objective_delta_stop_strategy(eps),
 simple, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() lbfgs-6: got simple/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 simple, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min() cg: got simple/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_bobyqa(simple, x, 2*x.size()+1,
 uniform_matrix<double>(x.size(),1,-1e100),
 uniform_matrix<double>(x.size(),1,1e100),
 (max(abs(x))+1)/10,
 1e-6,
 10000);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , simple(x)));
 dlog << LINFO << "find_min_bobyqa(): got simple in " << total_count;
 }
 void test_rosen (
 const matrix<double,2,1> p
 )
 {
 const double eps = 1e-15;
 const double minf = -10;
 matrix<double,2,1> x, opt;
 opt(0) = 1;
 opt(1) = 1;
 double val = 0;
 dlog << LINFO << "testing with rosen and the start point: " << trans(p);
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 rosen, der_rosen, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() bfgs: got rosen in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 gradient_norm_stop_strategy(),
 rosen, der_rosen, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() bfgs(gn): got rosen in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(lbfgs_search_strategy(20),
 objective_delta_stop_strategy(eps),
 rosen, der_rosen, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() lbfgs-20: got rosen in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 rosen, der_rosen, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() cg: got rosen in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(bfgs_search_strategy(),
 objective_delta_stop_strategy(eps),
 rosen, derivative(rosen,1e-5), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-4),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() bfgs: got rosen/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(lbfgs_search_strategy(5),
 objective_delta_stop_strategy(eps),
 rosen, derivative(rosen,1e-5), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-4),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() lbfgs-5: got rosen/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 rosen, derivative(rosen,1e-5), x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-4),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() cg: got rosen/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_min_using_approximate_derivatives(cg_search_strategy(),
 objective_delta_stop_strategy(eps),
 rosen, x, minf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-4),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min() cg: got rosen/noder2 in " << total_count;
 if (max(abs(p)) < 1000)
 {
 total_count = 0;
 x = p;
 val=find_min_bobyqa(rosen, x, 2*x.size()+1,
 uniform_matrix<double>(x.size(),1,-1e100),
 uniform_matrix<double>(x.size(),1,1e100),
 (max(abs(x))+1)/10,
 1e-6,
 10000);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , rosen(x)));
 dlog << LINFO << "find_min_bobyqa(): got rosen in " << total_count;
 }
 }
 void test_neg_rosen (
 const matrix<double,2,1> p
 )
 {
 const double eps = 1e-15;
 const double maxf = 10;
 matrix<double,2,1> x, opt;
 opt(0) = 1;
 opt(1) = 1;
 double val = 0;
 dlog << LINFO << "testing with neg_rosen and the start point: " << trans(p);
 total_count = 0;
 x = p;
 val=find_max(
 bfgs_search_strategy(), 
 objective_delta_stop_strategy(eps), neg_rosen, der_neg_rosen, x, maxf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , neg_rosen(x)));
 dlog << LINFO << "find_max() bfgs: got neg_rosen in " << total_count;
 total_count = 0;
 x = p;
 val=find_max(
 lbfgs_search_strategy(5), 
 objective_delta_stop_strategy(eps), neg_rosen, der_neg_rosen, x, maxf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , neg_rosen(x)));
 dlog << LINFO << "find_max() lbfgs-5: got neg_rosen in " << total_count;
 total_count = 0;
 x = p;
 val=find_max(
 lbfgs_search_strategy(5), 
 objective_delta_stop_strategy(eps), neg_rosen, derivative(neg_rosen), x, maxf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , neg_rosen(x)));
 dlog << LINFO << "find_max() lbfgs-5: got neg_rosen/noder in " << total_count;
 total_count = 0;
 x = p;
 val=find_max_using_approximate_derivatives(
 cg_search_strategy(), 
 objective_delta_stop_strategy(eps), neg_rosen, x, maxf);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-7),opt-x);
 DLIB_TEST(approx_equal(val , neg_rosen(x)));
 dlog << LINFO << "find_max() cg: got neg_rosen/noder2 in " << total_count;
 total_count = 0;
 x = p;
 val=find_max_bobyqa(neg_rosen, x, 2*x.size()+1,
 uniform_matrix<double>(x.size(),1,-1e100),
 uniform_matrix<double>(x.size(),1,1e100),
 (max(abs(x))+1)/10,
 1e-6,
 10000);
 DLIB_TEST_MSG(dlib::equal(x,opt, 1e-5),opt-x);
 DLIB_TEST(approx_equal(val , neg_rosen(x)));
 dlog << LINFO << "find_max_bobyqa(): got neg_rosen in " << total_count;
 }
// ----------------------------------------------------------------------------------------
 void test_single_variable_function (
 const double p
 )
 {
 const double eps = 1e-7;
 dlog << LINFO << "testing with single_variable_function and the start point: " << p;
 double out, x;
 total_count = 0;
 x = p;
 out = find_min_single_variable(single_variable_function, x, -1e100, 1e100, eps, 1000);
 DLIB_TEST_MSG(std::abs(out-5) < 1e-6, out-5);
 DLIB_TEST_MSG(std::abs(x) < 1e-6, x);
 dlog << LINFO << "find_min_single_variable(): got single_variable_function in " << total_count;
 total_count = 0;
 x = p;
 out = -find_max_single_variable(negate_function(single_variable_function), x, -1e100, 1e100, eps, 1000);
 DLIB_TEST_MSG(std::abs(out-5) < 1e-6, out-5);
 DLIB_TEST_MSG(std::abs(x) < 1e-6, x);
 dlog << LINFO << "find_max_single_variable(): got single_variable_function in " << total_count;
 if (p > 0)
 {
 total_count = 0;
 x = p;
 out = find_min_single_variable(single_variable_function, x, -1e-4, 1e100, eps, 1000);
 DLIB_TEST_MSG(std::abs(out-5) < 1e-6, out-5);
 DLIB_TEST_MSG(std::abs(x) < 1e-6, x);
 dlog << LINFO << "find_min_single_variable(): got single_variable_function in " << total_count;
 if (p > 3)
 {
 total_count = 0;
 x = p;
 out = -find_max_single_variable(negate_function(single_variable_function), x, 3, 1e100, eps, 1000);
 DLIB_TEST_MSG(std::abs(out - (3*3*3+5)) < 1e-6, out-(3*3*3+5));
 DLIB_TEST_MSG(std::abs(x-3) < 1e-6, x);
 dlog << LINFO << "find_max_single_variable(): got single_variable_function in " << total_count;
 }
 }
 if (p < 0)
 {
 total_count = 0;
 x = p;
 out = find_min_single_variable(single_variable_function, x, -1e100, 1e-4, eps, 1000);
 DLIB_TEST_MSG(std::abs(out-5) < 1e-6, out-5);
 DLIB_TEST_MSG(std::abs(x) < 1e-6, x);
 dlog << LINFO << "find_min_single_variable(): got single_variable_function in " << total_count;
 if (p < -3)
 {
 total_count = 0;
 x = p;
 out = find_min_single_variable(single_variable_function, x, -1e100, -3, eps, 1000);
 DLIB_TEST_MSG(std::abs(out - (3*3*3+5)) < 1e-6, out-(3*3*3+5));
 DLIB_TEST_MSG(std::abs(x+3) < 1e-6, x);
 dlog << LINFO << "find_min_single_variable(): got single_variable_function in " << total_count;
 }
 }
 }
// ----------------------------------------------------------------------------------------
 void optimization_test (
 )
 /*!
 ensures
 - runs tests on the optimization stuff compliance with the specs
 !*/
 { 
 matrix<double,0,1> p;
 print_spinner();
 p.set_size(2);
 // test with single_variable_function
 test_single_variable_function(0);
 test_single_variable_function(1);
 test_single_variable_function(-10);
 test_single_variable_function(-100);
 test_single_variable_function(900.53);
 // test with the rosen function
 p(0) = 9;
 p(1) = -4.9;
 test_rosen(p);
 test_neg_rosen(p);
 p(0) = 0;
 p(1) = 0;
 test_rosen(p);
 p(0) = 5323;
 p(1) = 98248;
 test_rosen(p);
 // test with the simple function
 p(0) = 1;
 p(1) = 1;
 test_simple(p);
 p(0) = 0.5;
 p(1) = -9;
 test_simple(p);
 p(0) = 645;
 p(1) = 839485;
 test_simple(p);
 print_spinner();
 // test with the apq function
 p.set_size(5);
 p(0) = 1;
 p(1) = 1;
 p(2) = 1;
 p(3) = 1;
 p(4) = 1;
 test_apq(p);
 p(0) = 1;
 p(1) = 2;
 p(2) = 3;
 p(3) = 4;
 p(4) = 5;
 test_apq(p);
 p(0) = 1;
 p(1) = 2;
 p(2) = -3;
 p(3) = 4;
 p(4) = 5;
 test_apq(p);
 print_spinner();
 p(0) = 1;
 p(1) = 2324;
 p(2) = -3;
 p(3) = 4;
 p(4) = 534534;
 test_apq(p);
 p.set_size(10);
 p(0) = 1;
 p(1) = 2;
 p(2) = -3;
 p(3) = 4;
 p(4) = 5;
 p(5) = 1;
 p(6) = 2;
 p(7) = -3;
 p(8) = 4;
 p(9) = 5;
 test_apq(p);
 // test apq with a big vector
 p.set_size(500);
 dlib::rand rnd;
 for (long i = 0; i < p.size(); ++i)
 {
 p(i) = rnd.get_random_double()*20 - 10; 
 }
 test_apq(p);
 print_spinner();
 // test with the powell function
 p.set_size(4);
 p(0) = 3;
 p(1) = -1;
 p(2) = 0;
 p(3) = 1;
 test_powell(p);
 {
 matrix<double,2,1> m;
 m(0) = -0.43;
 m(1) = 0.919;
 DLIB_TEST(dlib::equal(der_rosen(m) , derivative(rosen)(m),1e-5));
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(0) - 
 make_line_search_function(derivative(rosen),m,m)(0)) < 1e-5,"");
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(1) - 
 make_line_search_function(derivative(rosen),m,m)(1)) < 1e-5,"");
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(0) - 
 make_line_search_function(der_rosen,m,m)(0)) < 1e-5,"");
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(1) - 
 make_line_search_function(der_rosen,m,m)(1)) < 1e-5,"");
 }
 {
 matrix<double,2,1> m;
 m(0) = 1;
 m(1) = 2;
 DLIB_TEST(dlib::equal(der_rosen(m) , derivative(rosen)(m),1e-5));
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(0) - 
 make_line_search_function(derivative(rosen),m,m)(0)) < 1e-5,"");
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(1) - 
 make_line_search_function(derivative(rosen),m,m)(1)) < 1e-5,"");
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(0) - 
 make_line_search_function(der_rosen,m,m)(0)) < 1e-5,"");
 DLIB_TEST_MSG(std::abs(derivative(make_line_search_function(rosen,m,m))(1) - 
 make_line_search_function(der_rosen,m,m)(1)) < 1e-5,"");
 }
 {
 matrix<double,2,1> m;
 m = 1,2;
 DLIB_TEST(std::abs(neg_rosen(m) - negate_function(rosen)(m) ) < 1e-16);
 }
 }
 template <typename der_funct, typename T>
 double unconstrained_gradient_magnitude (
 const der_funct& grad,
 const T& x,
 const T& lower,
 const T& upper
 )
 {
 T g = grad(x);
 double unorm = 0;
 for (long i = 0; i < g.size(); ++i)
 {
 if (lower(i) < x(i) && x(i) < upper(i))
 unorm += g(i)*g(i);
 else if (x(i) == lower(i) && g(i) < 0)
 unorm += g(i)*g(i);
 else if (x(i) == upper(i) && g(i) > 0)
 unorm += g(i)*g(i);
 }
 return unorm;
 }
 template <typename der_funct, typename T>
 double unconstrained_gradient_magnitude_neg_funct (
 const der_funct& grad,
 const T& x,
 const T& lower,
 const T& upper
 )
 {
 T g = grad(x);
 double unorm = 0;
 for (long i = 0; i < g.size(); ++i)
 {
 if (lower(i) < x(i) && x(i) < upper(i))
 unorm += g(i)*g(i);
 else if (x(i) == lower(i) && g(i) > 0)
 unorm += g(i)*g(i);
 else if (x(i) == upper(i) && g(i) < 0)
 unorm += g(i)*g(i);
 }
 return unorm;
 }
 template <typename search_strategy_type>
 double test_bound_solver_neg_rosen (dlib::rand& rnd, search_strategy_type search_strategy)
 {
 using namespace dlib::test_functions;
 print_spinner();
 matrix<double,2,1> starting_point, lower, upper, x;
 // pick random bounds
 lower = rnd.get_random_gaussian()+1, rnd.get_random_gaussian()+1;
 upper = rnd.get_random_gaussian()+1, rnd.get_random_gaussian()+1;
 while (upper(0) < lower(0)) upper(0) = rnd.get_random_gaussian()+1;
 while (upper(1) < lower(1)) upper(1) = rnd.get_random_gaussian()+1;
 starting_point = rnd.get_random_double()*(upper(0)-lower(0))+lower(0), 
 rnd.get_random_double()*(upper(1)-lower(1))+lower(1);
 dlog << LINFO << "lower: "<< trans(lower);
 dlog << LINFO << "upper: "<< trans(upper);
 dlog << LINFO << "starting: "<< trans(starting_point);
 x = starting_point;
 double val = find_max_box_constrained( 
 search_strategy,
 objective_delta_stop_strategy(1e-16, 500), 
 neg_rosen, der_neg_rosen, x,
 lower, 
 upper 
 );
 DLIB_TEST_MSG(std::abs(val - neg_rosen(x)) < 1e-11, std::abs(val - neg_rosen(x)));
 dlog << LINFO << "neg_rosen solution:\n" << x;
 dlog << LINFO << "neg_rosen gradient: "<< trans(der_neg_rosen(x));
 const double gradient_residual = unconstrained_gradient_magnitude_neg_funct(der_neg_rosen, x, lower, upper);
 dlog << LINFO << "gradient_residual: "<< gradient_residual;
 return gradient_residual;
 }
 template <typename search_strategy_type>
 double test_bound_solver_rosen (dlib::rand& rnd, search_strategy_type search_strategy)
 {
 using namespace dlib::test_functions;
 print_spinner();
 matrix<double,2,1> starting_point, lower, upper, x;
 // pick random bounds and sometimes put the upper bound at zero so we can have
 // a test where the optimal value has a bound active at 0 so make sure this case
 // works properly.
 if (rnd.get_random_double() > 0.2)
 {
 lower = rnd.get_random_gaussian()+1, rnd.get_random_gaussian()+1;
 upper = rnd.get_random_gaussian()+1, rnd.get_random_gaussian()+1;
 while (upper(0) < lower(0)) upper(0) = rnd.get_random_gaussian()+1;
 while (upper(1) < lower(1)) upper(1) = rnd.get_random_gaussian()+1;
 }
 else
 {
 upper = 0,0;
 if (rnd.get_random_double() > 0.5)
 upper(0) = -rnd.get_random_double();
 if (rnd.get_random_double() > 0.5)
 upper(1) = -rnd.get_random_double();
 lower = rnd.get_random_double()+1, rnd.get_random_double()+1;
 lower = upper - lower;
 }
 const bool pick_uniform_bounds = rnd.get_random_double() > 0.9;
 if (pick_uniform_bounds)
 {
 double x = rnd.get_random_gaussian()*2;
 double y = rnd.get_random_gaussian()*2;
 lower = min(x,y);
 upper = max(x,y);
 }
 starting_point = rnd.get_random_double()*(upper(0)-lower(0))+lower(0), 
 rnd.get_random_double()*(upper(1)-lower(1))+lower(1);
 dlog << LINFO << "lower: "<< trans(lower);
 dlog << LINFO << "upper: "<< trans(upper);
 dlog << LINFO << "starting: "<< trans(starting_point);
 x = starting_point;
 double val;
 if (!pick_uniform_bounds)
 {
 val = find_min_box_constrained( 
 search_strategy,
 objective_delta_stop_strategy(1e-16, 500), 
 rosen, der_rosen, x,
 lower, 
 upper 
 );
 }
 else
 {
 val = find_min_box_constrained( 
 search_strategy,
 objective_delta_stop_strategy(1e-16, 500), 
 rosen, der_rosen, x,
 lower(0), 
 upper(0) 
 );
 }
 DLIB_TEST_MSG(std::abs(val - rosen(x)) < 1e-11, std::abs(val - rosen(x)));
 dlog << LINFO << "rosen solution:\n" << x;
 dlog << LINFO << "rosen gradient: "<< trans(der_rosen(x));
 const double gradient_residual = unconstrained_gradient_magnitude(der_rosen, x, lower, upper);
 dlog << LINFO << "gradient_residual: "<< gradient_residual;
 return gradient_residual;
 }
 template <typename search_strategy_type>
 double test_bound_solver_brown (dlib::rand& rnd, search_strategy_type search_strategy)
 {
 using namespace dlib::test_functions;
 print_spinner();
 matrix<double,4,1> starting_point(4), lower(4), upper(4), x;
 const matrix<double,0,1> solution = brown_solution();
 // pick random bounds
 lower = rnd.get_random_gaussian(), rnd.get_random_gaussian(), rnd.get_random_gaussian(), rnd.get_random_gaussian();
 lower = lower*10 + solution;
 upper = rnd.get_random_gaussian(), rnd.get_random_gaussian(), rnd.get_random_gaussian(), rnd.get_random_gaussian();
 upper = upper*10 + solution;
 for (int i = 0; i < lower.size(); ++i)
 {
 if (upper(i) < lower(i)) 
 swap(upper(i),lower(i));
 }
 starting_point = rnd.get_random_double()*(upper(0)-lower(0))+lower(0), 
 rnd.get_random_double()*(upper(1)-lower(1))+lower(1),
 rnd.get_random_double()*(upper(2)-lower(2))+lower(2),
 rnd.get_random_double()*(upper(3)-lower(3))+lower(3);
 dlog << LINFO << "lower: "<< trans(lower);
 dlog << LINFO << "upper: "<< trans(upper);
 dlog << LINFO << "starting: "<< trans(starting_point);
 // The contract for find_min_box_constrained() says we always call obj() before der(). So
 // these lambdas verify that this is so.
 dlib::matrix<double,0,1> last_x;
 auto obj = [&](const dlib::matrix<double,0,1> &x) { last_x = x; return brown(x); };
 auto der = [&](const dlib::matrix<double,0,1> &x) { 
 // check that obj(x) was called before der(x).
 DLIB_TEST_MSG(max(abs(x - last_x)) == 0, max(abs(x - last_x)));
 return brown_derivative(x); 
 };
 x = starting_point;
 double val = find_min_box_constrained( 
 search_strategy,
 objective_delta_stop_strategy(1e-16, 500), 
 obj, der, x,
 lower, 
 upper 
 );
 DLIB_TEST(std::abs(val - brown(x)) < 1e-14);
 dlog << LINFO << "brown solution:\n" << x;
 return unconstrained_gradient_magnitude(brown_derivative, x, lower, upper);
 }
 template <typename search_strategy_type>
 void test_box_constrained_optimizers(search_strategy_type search_strategy)
 {
 dlib::rand rnd;
 running_stats<double> rs;
 dlog << LINFO << "test find_min_box_constrained() on rosen";
 for (int i = 0; i < 10000; ++i)
 rs.add(test_bound_solver_rosen(rnd, search_strategy));
 dlog << LINFO << "mean rosen gradient: " << rs.mean();
 dlog << LINFO << "max rosen gradient: " << rs.max();
 DLIB_TEST(rs.mean() < 1e-12);
 DLIB_TEST(rs.max() < 1e-9);
 dlog << LINFO << "test find_min_box_constrained() on brown";
 rs.clear();
 for (int i = 0; i < 1000; ++i)
 rs.add(test_bound_solver_brown(rnd, search_strategy));
 dlog << LINFO << "mean brown gradient: " << rs.mean();
 dlog << LINFO << "max brown gradient: " << rs.max();
 dlog << LINFO << "min brown gradient: " << rs.min();
 DLIB_TEST(rs.mean() < 4e-5);
 DLIB_TEST_MSG(rs.max() < 3e-2, rs.max());
 DLIB_TEST(rs.min() < 1e-10);
 dlog << LINFO << "test find_max_box_constrained() on neg_rosen";
 rs.clear();
 for (int i = 0; i < 1000; ++i)
 rs.add(test_bound_solver_neg_rosen(rnd, search_strategy));
 dlog << LINFO << "mean neg_rosen gradient: " << rs.mean();
 dlog << LINFO << "max neg_rosen gradient: " << rs.max();
 DLIB_TEST(rs.mean() < 1e-12);
 DLIB_TEST(rs.max() < 1e-9);
 }
 void test_poly_min_extract_2nd()
 {
 double off;
 off = 0.0; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.1; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.2; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.3; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.4; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.5; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.6; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.8; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 0.9; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 off = 1.0; DLIB_TEST(std::abs( poly_min_extrap(off*off, -2*off, (1-off)*(1-off)) - off) < 1e-13); 
 }
 void test_solve_trust_region_subproblem_bounded()
 {
 print_spinner();
 matrix<double> H(2,2);
 H = 1, 0,
 0, 1;
 matrix<double,0,1> g, lower, upper, p, true_p;
 g = {0, 0};
 double radius = 0.5;
 lower = {0.5, 0};
 upper = {10, 10};
 solve_trust_region_subproblem_bounded(H,g, radius, p, 0.001, 500, lower, upper);
 true_p = { 0.5, 0};
 DLIB_TEST_MSG(length(p-true_p) < 1e-12, p);
 }
// ----------------------------------------------------------------------------------------
 void test_find_min_single_variable()
 {
 auto f = [](double x) { return (x-0.2)*(x-0.2); };
 double x = 0.8;
 try
 {
 find_min_single_variable(f, x, 0, 1, 1e-9);
 DLIB_TEST(std::abs(x-0.2) < 1e-7);
 }
 catch(optimize_single_variable_failure&)
 {
 DLIB_TEST(false);
 }
 }
// ----------------------------------------------------------------------------------------
 class optimization_tester : public tester
 {
 public:
 optimization_tester (
 ) :
 tester ("test_optimization",
 "Runs tests on the optimization component.")
 {}
 void perform_test (
 )
 {
 dlog << LINFO << "test_box_constrained_optimizers(bfgs_search_strategy())";
 test_box_constrained_optimizers(bfgs_search_strategy());
 dlog << LINFO << "test_box_constrained_optimizers(lbfgs_search_strategy(5))";
 test_box_constrained_optimizers(lbfgs_search_strategy(5));
 test_poly_min_extract_2nd();
 optimization_test();
 test_solve_trust_region_subproblem_bounded();
 test_find_min_single_variable();
 }
 } a;
}