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/////////////////////////////////////////////////////////////////////////////// |
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// BSD 3-Clause License |
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// |
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// Copyright (C) 2019-2022, University of Edinburgh, Heriot-Watt University |
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// Copyright note valid unless otherwise stated in individual files. |
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// All rights reserved. |
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/////////////////////////////////////////////////////////////////////////////// |
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#define BOOST_TEST_NO_MAIN |
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#define BOOST_TEST_ALTERNATIVE_INIT_API |
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#include <boost/random.hpp> |
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#include "crocoddyl/core/solvers/box-qp.hpp" |
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#include "unittest_common.hpp" |
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using namespace boost::unit_test; |
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using namespace crocoddyl::unittest; |
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void test_constructor() { |
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// Setup the test |
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std::size_t nx = random_int_in_range(1, 100); |
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crocoddyl::BoxQP boxqp(nx); |
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// Test dimension of the decision vector |
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BOOST_CHECK(boxqp.get_nx() == nx); |
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} |
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void test_unconstrained_qp_with_identity_hessian() { |
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std::size_t nx = random_int_in_range(2, 5); |
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crocoddyl::BoxQP boxqp(nx); |
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boxqp.set_reg(0.); |
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Eigen::MatrixXd hessian = Eigen::MatrixXd::Identity(nx, nx); |
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Eigen::VectorXd gradient = Eigen::VectorXd::Random(nx); |
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Eigen::VectorXd lb = |
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-std::numeric_limits<double>::infinity() * Eigen::VectorXd::Ones(nx); |
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Eigen::VectorXd ub = |
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std::numeric_limits<double>::infinity() * Eigen::VectorXd::Ones(nx); |
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Eigen::VectorXd xinit = Eigen::VectorXd::Random(nx); |
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crocoddyl::BoxQPSolution sol = boxqp.solve(hessian, gradient, lb, ub, xinit); |
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// Checking the solution of the problem. Note that it the negative of the |
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// gradient since Hessian is identity matrix |
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BOOST_CHECK((sol.x + gradient).isZero(1e-9)); |
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// Checking the solution against a regularized case |
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double reg = random_real_in_range(1e-9, 1e2); |
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boxqp.set_reg(reg); |
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crocoddyl::BoxQPSolution sol_reg = |
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boxqp.solve(hessian, gradient, lb, ub, xinit); |
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BOOST_CHECK((sol_reg.x + gradient / (1 + reg)).isZero(1e-9)); |
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// Checking the all bounds are free and zero clamped |
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BOOST_CHECK(sol.free_idx.size() == nx); |
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BOOST_CHECK(sol.clamped_idx.size() == 0); |
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BOOST_CHECK(sol_reg.free_idx.size() == nx); |
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BOOST_CHECK(sol_reg.clamped_idx.size() == 0); |
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} |
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void test_unconstrained_qp() { |
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std::size_t nx = random_int_in_range(2, 5); |
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crocoddyl::BoxQP boxqp(nx); |
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boxqp.set_reg(0.); |
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Eigen::MatrixXd H = Eigen::MatrixXd::Random(nx, nx); |
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Eigen::MatrixXd hessian = |
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H.transpose() * H + nx * Eigen::MatrixXd::Identity(nx, nx); |
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hessian = 0.5 * (hessian + hessian.transpose()).eval(); |
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Eigen::VectorXd gradient = Eigen::VectorXd::Random(nx); |
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Eigen::VectorXd lb = |
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-std::numeric_limits<double>::infinity() * Eigen::VectorXd::Ones(nx); |
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Eigen::VectorXd ub = |
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std::numeric_limits<double>::infinity() * Eigen::VectorXd::Ones(nx); |
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Eigen::VectorXd xinit = Eigen::VectorXd::Random(nx); |
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crocoddyl::BoxQPSolution sol = boxqp.solve(hessian, gradient, lb, ub, xinit); |
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// Checking the solution against the KKT solution |
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Eigen::VectorXd xkkt = -hessian.inverse() * gradient; |
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BOOST_CHECK((sol.x - xkkt).isZero(1e-9)); |
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// Checking the solution against a regularized KKT problem |
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double reg = random_real_in_range(1e-9, 1e2); |
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boxqp.set_reg(reg); |
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crocoddyl::BoxQPSolution sol_reg = |
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boxqp.solve(hessian, gradient, lb, ub, xinit); |
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Eigen::VectorXd xkkt_reg = |
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-(hessian + reg * Eigen::MatrixXd::Identity(nx, nx)).inverse() * gradient; |
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BOOST_CHECK((sol_reg.x - xkkt_reg).isZero(1e-9)); |
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// Checking the all bounds are free and zero clamped |
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BOOST_CHECK(sol.free_idx.size() == nx); |
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BOOST_CHECK(sol.clamped_idx.size() == 0); |
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BOOST_CHECK(sol_reg.free_idx.size() == nx); |
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BOOST_CHECK(sol_reg.clamped_idx.size() == 0); |
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} |
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void test_box_qp_with_identity_hessian() { |
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std::size_t nx = random_int_in_range(2, 5); |
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crocoddyl::BoxQP boxqp(nx); |
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boxqp.set_reg(0.); |
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Eigen::MatrixXd hessian = Eigen::MatrixXd::Identity(nx, nx); |
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Eigen::VectorXd gradient = Eigen::VectorXd::Ones(nx); |
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for (std::size_t i = 0; i < nx; ++i) { |
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gradient(i) *= random_real_in_range(-1., 1.); |
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} |
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Eigen::VectorXd lb = Eigen::VectorXd::Zero(nx); |
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Eigen::VectorXd ub = Eigen::VectorXd::Ones(nx); |
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Eigen::VectorXd xinit = Eigen::VectorXd::Random(nx); |
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crocoddyl::BoxQPSolution sol = boxqp.solve(hessian, gradient, lb, ub, xinit); |
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// The analytical solution is the a bounded, and negative, gradient |
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Eigen::VectorXd negbounded_gradient(nx), negbounded_gradient_reg(nx); |
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std::size_t nf = nx, nc = 0, nf_reg = nx, nc_reg = 0; |
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double reg = random_real_in_range(1e-9, 1e2); |
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for (std::size_t i = 0; i < nx; ++i) { |
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negbounded_gradient(i) = std::max(std::min(-gradient(i), ub(i)), lb(i)); |
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negbounded_gradient_reg(i) = |
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std::max(std::min(-gradient(i) / (1 + reg), ub(i)), lb(i)); |
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if (negbounded_gradient(i) != -gradient(i)) { |
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nc += 1; |
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nf -= 1; |
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} |
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if (negbounded_gradient_reg(i) != -gradient(i) / (1 + reg)) { |
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nc_reg += 1; |
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nf_reg -= 1; |
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} |
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} |
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// Checking the solution of the problem. Note that it the negative of the |
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// gradient since Hessian is identity matrix |
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BOOST_CHECK((sol.x - negbounded_gradient).isZero(1e-9)); |
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// Checking the solution against a regularized case |
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boxqp.set_reg(reg); |
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crocoddyl::BoxQPSolution sol_reg = |
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boxqp.solve(hessian, gradient, lb, ub, xinit); |
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BOOST_CHECK((sol_reg.x - negbounded_gradient_reg).isZero(1e-9)); |
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// Checking the all bounds are free and zero clamped |
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BOOST_CHECK(sol.free_idx.size() == nf); |
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BOOST_CHECK(sol.clamped_idx.size() == nc); |
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BOOST_CHECK(sol_reg.free_idx.size() == nf_reg); |
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BOOST_CHECK(sol_reg.clamped_idx.size() == nc_reg); |
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} |
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void register_unit_tests() { |
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framework::master_test_suite().add( |
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BOOST_TEST_CASE(boost::bind(&test_constructor))); |
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framework::master_test_suite().add(BOOST_TEST_CASE( |
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boost::bind(&test_unconstrained_qp_with_identity_hessian))); |
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framework::master_test_suite().add( |
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BOOST_TEST_CASE(boost::bind(&test_unconstrained_qp))); |
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framework::master_test_suite().add( |
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BOOST_TEST_CASE(boost::bind(&test_box_qp_with_identity_hessian))); |
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} |
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bool init_function() { |
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register_unit_tests(); |
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return true; |
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} |
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int main(int argc, char* argv[]) { |
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return ::boost::unit_test::unit_test_main(&init_function, argc, argv); |
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} |
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