```// Copyright (C) 2008  Davis E. King (davis@dlib.net)

#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(),
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),
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(),
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(),
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>
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>
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;

}

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;

}

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);

x = starting_point;
double val = find_min_box_constrained(
search_strategy,
objective_delta_stop_strategy(1e-16, 500),
brown, brown_derivative, 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)
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)
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)
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;

}

```