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| # ================================================================== | ||
| # codac / ellipsoid example - cmake configuration file | ||
| # ================================================================== | ||
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| cmake_minimum_required(VERSION 3.0.2) | ||
| project(ellipsoid_dev LANGUAGES CXX) | ||
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| set(CMAKE_CXX_STANDARD 20) | ||
| set(CMAKE_CXX_STANDARD_REQUIRED ON) | ||
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| # Adding IBEX | ||
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| # In case you installed IBEX in a local directory, you need | ||
| # to specify its path with the CMAKE_PREFIX_PATH option. | ||
| # set(CMAKE_PREFIX_PATH "~/ibex-lib/build_install") | ||
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| find_package(IBEX REQUIRED) | ||
| ibex_init_common() # IBEX should have installed this function | ||
| message(STATUS "Found IBEX version ${IBEX_VERSION}") | ||
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| # Adding Eigen3 | ||
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| # In case you installed Eigen3 in a local directory, you need | ||
| # to specify its path with the CMAKE_PREFIX_PATH option, e.g. | ||
| # set(CMAKE_PREFIX_PATH "~/eigen/build_install") | ||
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| find_package(Eigen3 3.4 REQUIRED NO_MODULE) | ||
| message(STATUS "Found Eigen3 version ${Eigen3_VERSION}") | ||
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| # Adding Codac | ||
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| # In case you installed Codac in a local directory, you need | ||
| # to specify its path with the CMAKE_PREFIX_PATH option. | ||
| set(CMAKE_PREFIX_PATH "~/Documents/Code_these/codac/build_install") | ||
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| find_package(CODAC REQUIRED) | ||
| message(STATUS "Found Codac version ${CODAC_VERSION}") | ||
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| # Compilation | ||
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| add_executable(${PROJECT_NAME} main.cpp) | ||
| target_compile_options(${PROJECT_NAME} PUBLIC ${CODAC_CXX_FLAGS}) | ||
| target_include_directories(${PROJECT_NAME} SYSTEM PUBLIC ${CODAC_INCLUDE_DIRS}) | ||
| target_link_libraries(${PROJECT_NAME} PUBLIC ${CODAC_LIBRARIES} Ibex::ibex Eigen3::Eigen) |
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| #include <codac> | ||
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| using namespace std; | ||
| using namespace codac2; | ||
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| int main() { | ||
| // ---------------------------------------------------------- | ||
| // ellipsoid projections | ||
| // ---------------------------------------------------------- | ||
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| Vector mu4({1., 0., 0.}); | ||
| Matrix G4({{1., 0.5, 0.}, | ||
| {0.5, 2., 0.2}, | ||
| {0., 0.2, 3.}}); | ||
| Ellipsoid e4(mu4, G4); | ||
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| Matrix G5 = 0.7 * G4; | ||
| Ellipsoid e5(mu4, G5); | ||
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| Matrix G6({{2., 0., 0.5}, | ||
| {0., 1., 0.2}, | ||
| {0., 0.2, 3.}}); | ||
| Ellipsoid e6(mu4, G6); | ||
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| Figure2D fig2("Projected ellipsoid xy", GraphicOutput::VIBES); | ||
| Figure2D fig3("Projected ellipsoid yz", GraphicOutput::VIBES); | ||
| Figure2D fig4("Projected ellipsoid xz", GraphicOutput::VIBES); | ||
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| fig2.set_window_properties({700, 100}, {500, 500}); | ||
| fig3.set_window_properties({1200, 100}, {500, 500}); | ||
| fig4.set_window_properties({0, 100}, {500, 500}); | ||
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| fig2.set_axes(axis(0, {-3, 3}), axis(1, {-3, 3})); | ||
| fig3.set_axes(axis(1, {-3, 3}), axis(2, {-3, 3})); | ||
| fig4.set_axes(axis(0, {-3, 3}), axis(2, {-3, 3})); | ||
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| fig2.draw_ellipsoid(e4, {Color::blue(), Color::blue(0.3)}); | ||
| fig3.draw_ellipsoid(e4, {Color::blue(), Color::blue(0.3)}); | ||
| fig4.draw_ellipsoid(e4, {Color::blue(), Color::blue(0.3)}); | ||
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| fig2.draw_ellipsoid(e5, {Color::red(), Color::red(0.3)}); | ||
| fig3.draw_ellipsoid(e5, {Color::red(), Color::red(0.3)}); | ||
| fig4.draw_ellipsoid(e5, {Color::red(), Color::red(0.3)}); | ||
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| fig2.draw_ellipsoid(e6, {Color::green(), Color::green(0.3)}); | ||
| fig3.draw_ellipsoid(e6, {Color::green(), Color::green(0.3)}); | ||
| fig4.draw_ellipsoid(e6, {Color::green(), Color::green(0.3)}); | ||
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| // ---------------------------------------------------------- | ||
| // inclusion tests | ||
| // ---------------------------------------------------------- | ||
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| cout << "\nInclusion test e5 in e4: " << e5.is_concentric_subset(e4) << endl; | ||
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| cout << "Inclusion test e4 in e5: " << e4.is_concentric_subset(e5) << endl; | ||
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| cout << "Inclusion test e4 in e6: " << e6.is_concentric_subset(e4) << endl; | ||
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| cout << "Inclusion test e5 in e6: " << e5.is_concentric_subset(e6) << endl; | ||
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| // ---------------------------------------------------------- | ||
| // test the non inclusion (e4 in e6) | ||
| // ---------------------------------------------------------- | ||
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| // step 1 identify the direction of non inclusion | ||
| Eigen::MatrixXd X = e4.G; | ||
| Eigen::MatrixXd Y = e6.G; | ||
| Eigen::MatrixXd Y_inv = Y.inverse(); | ||
| Eigen::MatrixXd D = Eigen::MatrixXd::Identity(3,3)- X.transpose()*Y_inv.transpose()*Y_inv*X; | ||
| cout << "D = " << D << endl; | ||
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| Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> es(D); | ||
| Eigen::VectorXd eigenvalues = es.eigenvalues(); | ||
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| Eigen::VectorXd v; | ||
| double min_eigenvalue = MAXFLOAT; | ||
| for (int i = 0; i < eigenvalues.size(); i++){ | ||
| if (eigenvalues(i) < min_eigenvalue){ | ||
| min_eigenvalue = eigenvalues(i); | ||
| v = es.eigenvectors().col(i); // the vector associated to the smallest eigenvalue | ||
| } | ||
| } | ||
| cout << " the min eigenvalue of D is " << min_eigenvalue << endl; | ||
| cout << " the vector associated to the min eigenvalue is " << v << endl; | ||
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| // select the less included point and draw it on the figures | ||
| Eigen::VectorXd x = e4.mu+e4.G*v; | ||
| cout << "the point " << x << " is the less included point" << endl; | ||
| fig2.draw_point(x, {Color::black()}); | ||
| fig3.draw_point(x, {Color::black()}); | ||
| fig4.draw_point(x, {Color::black()}); | ||
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| // IntervalVector x6(x); | ||
| // x6.inflate(0.001); | ||
| // fig2.draw_box(x6, {Color::black(), Color::black()}); | ||
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| // now let us prove by intervals that x is out of e6 | ||
| // by proving (x-mu6).T@G6^(-T)@G6^(-1)@(x-mu6) > 1 | ||
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| IntervalVector w(x); | ||
| w -= IntervalVector(e6.mu); | ||
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| IntervalMatrix Q(Y_inv); | ||
| Q = Q.transpose()*Q; | ||
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| IntervalMatrix res = w.transpose()*Q*w; | ||
| cout << "the result of the inclusion test is " << res << endl; | ||
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| if(res(0,0).lb() > 1.) { | ||
| cout << "the point is out of the ellipsoid" << endl; | ||
| cout << "the non inclusion is guaranteed" << endl; | ||
| } | ||
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| // can we also prove that x is in e4? -> we should take the point not on the boundary or | ||
| // have guaranteed operations previously | ||
| Eigen::MatrixXd X_inv = X.inverse(); | ||
| IntervalMatrix Qx(X_inv); | ||
| Qx = Qx.transpose()*Qx; | ||
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| IntervalMatrix res2 = w.transpose()*Qx*w; | ||
| cout << "the result of the inclusion test in e4 is " << res2 << endl; | ||
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| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,44 @@ | ||
| # ================================================================== | ||
| # codac / ellipsoid example - cmake configuration file | ||
| # ================================================================== | ||
|
|
||
| cmake_minimum_required(VERSION 3.0.2) | ||
| project(codac_example LANGUAGES CXX) | ||
|
|
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| set(CMAKE_CXX_STANDARD 20) | ||
| set(CMAKE_CXX_STANDARD_REQUIRED ON) | ||
|
|
||
| # Adding IBEX | ||
|
|
||
| # In case you installed IBEX in a local directory, you need | ||
| # to specify its path with the CMAKE_PREFIX_PATH option. | ||
| # set(CMAKE_PREFIX_PATH "~/ibex-lib/build_install") | ||
|
|
||
| find_package(IBEX REQUIRED) | ||
| ibex_init_common() # IBEX should have installed this function | ||
| message(STATUS "Found IBEX version ${IBEX_VERSION}") | ||
|
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| # Adding Eigen3 | ||
|
|
||
| # In case you installed Eigen3 in a local directory, you need | ||
| # to specify its path with the CMAKE_PREFIX_PATH option, e.g. | ||
| # set(CMAKE_PREFIX_PATH "~/eigen/build_install") | ||
|
|
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| find_package(Eigen3 3.4 REQUIRED NO_MODULE) | ||
| message(STATUS "Found Eigen3 version ${Eigen3_VERSION}") | ||
|
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| # Adding Codac | ||
|
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| # In case you installed Codac in a local directory, you need | ||
| # to specify its path with the CMAKE_PREFIX_PATH option. | ||
| set(CMAKE_PREFIX_PATH "~/Documents/Code_these/codac/build_install") | ||
|
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| find_package(CODAC REQUIRED) | ||
| message(STATUS "Found Codac version ${CODAC_VERSION}") | ||
|
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| # Compilation | ||
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| add_executable(${PROJECT_NAME} main.cpp) | ||
| target_compile_options(${PROJECT_NAME} PUBLIC ${CODAC_CXX_FLAGS}) | ||
| target_include_directories(${PROJECT_NAME} SYSTEM PUBLIC ${CODAC_INCLUDE_DIRS}) | ||
| target_link_libraries(${PROJECT_NAME} PUBLIC ${CODAC_LIBRARIES} Ibex::ibex Eigen3::Eigen) |
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