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-rw-r--r--src/ml/dlib/dlib/test/optimization.cpp1231
1 files changed, 1231 insertions, 0 deletions
diff --git a/src/ml/dlib/dlib/test/optimization.cpp b/src/ml/dlib/dlib/test/optimization.cpp
new file mode 100644
index 000000000..b47449abe
--- /dev/null
+++ b/src/ml/dlib/dlib/test/optimization.cpp
@@ -0,0 +1,1231 @@
+// 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);
+
+ 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)
+ 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);
+
+ }
+
+// ----------------------------------------------------------------------------------------
+
+ 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();
+ }
+ } a;
+
+}
+
+
generated by cgit v1.2.3 (git 2.39.1) at 2024-07-01 08:19:42 +0000