239 lines
8.3 KiB
C++
239 lines
8.3 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file testQPSolver.cpp
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* @brief Test simple QP solver for a linear inequality constraint
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* @date Apr 10, 2014
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* @author Duy-Nguyen Ta
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*/
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#include <gtsam_unstable/linear/LPInitSolver.h>
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#include <gtsam_unstable/linear/LPSolver.h>
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#include <gtsam/base/Testable.h>
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#include <gtsam/inference/FactorGraph-inst.h>
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#include <gtsam/inference/Symbol.h>
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#include <gtsam/linear/GaussianFactorGraph.h>
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#include <gtsam/linear/VectorValues.h>
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#include <gtsam_unstable/linear/EqualityFactorGraph.h>
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#include <gtsam_unstable/linear/InequalityFactorGraph.h>
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#include <gtsam_unstable/linear/InfeasibleInitialValues.h>
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#include <CppUnitLite/TestHarness.h>
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using namespace std;
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using namespace gtsam;
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using namespace gtsam::symbol_shorthand;
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static const Vector kOne = Vector::Ones(1), kZero = Vector::Zero(1);
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/* ************************************************************************* */
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/**
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* min -x1-x2
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* s.t. x1 + 2x2 <= 4
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* 4x1 + 2x2 <= 12
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* -x1 + x2 <= 1
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* x1, x2 >= 0
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*/
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LP simpleLP1() {
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LP lp;
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lp.cost = LinearCost(1, Vector2(-1., -1.)); // min -x1-x2 (max x1+x2)
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lp.inequalities.add(1, Vector2(-1, 0), 0, 1); // x1 >= 0
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lp.inequalities.add(1, Vector2(0, -1), 0, 2); // x2 >= 0
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lp.inequalities.add(1, Vector2(1, 2), 4, 3); // x1 + 2*x2 <= 4
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lp.inequalities.add(1, Vector2(4, 2), 12, 4); // 4x1 + 2x2 <= 12
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lp.inequalities.add(1, Vector2(-1, 1), 1, 5); // -x1 + x2 <= 1
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return lp;
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}
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/* ************************************************************************* */
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namespace gtsam {
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TEST(LPInitSolver, InfiniteLoopSingleVar) {
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LP lp;
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lp.cost = LinearCost(1, Vector3(0, 0, 1)); // min alpha
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lp.inequalities.add(1, Vector3(-2, -1, -1), -2, 1); //-2x-y-a <= -2
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lp.inequalities.add(1, Vector3(-1, 2, -1), 6, 2); // -x+2y-a <= 6
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lp.inequalities.add(1, Vector3(-1, 0, -1), 0, 3); // -x - a <= 0
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lp.inequalities.add(1, Vector3(1, 0, -1), 20, 4); // x - a <= 20
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lp.inequalities.add(1, Vector3(0, -1, -1), 0, 5); // -y - a <= 0
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LPSolver solver(lp);
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VectorValues starter;
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starter.insert(1, Vector3(0, 0, 2));
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VectorValues results, duals;
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std::tie(results, duals) = solver.optimize(starter);
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VectorValues expected;
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expected.insert(1, Vector3(13.5, 6.5, -6.5));
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CHECK(assert_equal(results, expected, 1e-7));
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}
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TEST(LPInitSolver, InfiniteLoopMultiVar) {
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LP lp;
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Key X = symbol('X', 1);
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Key Y = symbol('Y', 1);
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Key Z = symbol('Z', 1);
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lp.cost = LinearCost(Z, kOne); // min alpha
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lp.inequalities.add(X, -2.0 * kOne, Y, -1.0 * kOne, Z, -1.0 * kOne, -2,
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1); //-2x-y-alpha <= -2
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lp.inequalities.add(X, -1.0 * kOne, Y, 2.0 * kOne, Z, -1.0 * kOne, 6,
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2); // -x+2y-alpha <= 6
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lp.inequalities.add(X, -1.0 * kOne, Z, -1.0 * kOne, 0,
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3); // -x - alpha <= 0
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lp.inequalities.add(X, 1.0 * kOne, Z, -1.0 * kOne, 20,
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4); // x - alpha <= 20
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lp.inequalities.add(Y, -1.0 * kOne, Z, -1.0 * kOne, 0,
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5); // -y - alpha <= 0
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LPSolver solver(lp);
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VectorValues starter;
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starter.insert(X, kZero);
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starter.insert(Y, kZero);
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starter.insert(Z, Vector::Constant(1, 2.0));
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VectorValues results, duals;
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std::tie(results, duals) = solver.optimize(starter);
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VectorValues expected;
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expected.insert(X, Vector::Constant(1, 13.5));
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expected.insert(Y, Vector::Constant(1, 6.5));
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expected.insert(Z, Vector::Constant(1, -6.5));
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CHECK(assert_equal(results, expected, 1e-7));
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}
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TEST(LPInitSolver, Initialization) {
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LP lp = simpleLP1();
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LPInitSolver initSolver(lp);
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GaussianFactorGraph::shared_ptr initOfInitGraph =
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initSolver.buildInitOfInitGraph();
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VectorValues x0 = initOfInitGraph->optimize();
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VectorValues expected_x0;
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expected_x0.insert(1, Vector::Zero(2));
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CHECK(assert_equal(expected_x0, x0, 1e-10));
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double y0 = initSolver.compute_y0(x0);
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double expected_y0 = 0.0;
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DOUBLES_EQUAL(expected_y0, y0, 1e-7);
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Key yKey = 2;
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LP::shared_ptr initLP = initSolver.buildInitialLP(yKey);
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LP expectedInitLP;
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expectedInitLP.cost = LinearCost(yKey, kOne);
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expectedInitLP.inequalities.add(1, Vector2(-1, 0), 2, Vector::Constant(1, -1),
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0, 1); // -x1 - y <= 0
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expectedInitLP.inequalities.add(1, Vector2(0, -1), 2, Vector::Constant(1, -1),
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0, 2); // -x2 - y <= 0
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expectedInitLP.inequalities.add(1, Vector2(1, 2), 2, Vector::Constant(1, -1),
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4,
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3); // x1 + 2*x2 - y <= 4
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expectedInitLP.inequalities.add(1, Vector2(4, 2), 2, Vector::Constant(1, -1),
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12,
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4); // 4x1 + 2x2 - y <= 12
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expectedInitLP.inequalities.add(1, Vector2(-1, 1), 2, Vector::Constant(1, -1),
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1,
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5); // -x1 + x2 - y <= 1
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CHECK(assert_equal(expectedInitLP, *initLP, 1e-10));
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LPSolver lpSolveInit(*initLP);
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VectorValues xy0(x0);
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xy0.insert(yKey, Vector::Constant(1, y0));
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VectorValues xyInit = lpSolveInit.optimize(xy0).first;
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VectorValues expected_init;
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expected_init.insert(1, Vector::Ones(2));
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expected_init.insert(2, Vector::Constant(1, -1));
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CHECK(assert_equal(expected_init, xyInit, 1e-10));
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VectorValues x = initSolver.solve();
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CHECK(lp.isFeasible(x));
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}
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} // namespace gtsam
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/* ************************************************************************* */
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/**
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* TEST gtsam solver with an over-constrained system
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* x + y = 1
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* x - y = 5
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* x + 2y = 6
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*/
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TEST(LPSolver, OverConstrainedLinearSystem) {
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GaussianFactorGraph graph;
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Matrix A1 = Vector3(1, 1, 1);
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Matrix A2 = Vector3(1, -1, 2);
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Vector b = Vector3(1, 5, 6);
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graph.add(1, A1, 2, A2, b, noiseModel::Constrained::All(3));
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VectorValues x = graph.optimize();
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// This check confirms that gtsam linear constraint solver can't handle
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// over-constrained system
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CHECK(graph[0]->error(x) != 0.0);
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}
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TEST(LPSolver, overConstrainedLinearSystem2) {
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GaussianFactorGraph graph;
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graph.add(1, I_1x1, 2, I_1x1, kOne, noiseModel::Constrained::All(1));
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graph.add(1, I_1x1, 2, -I_1x1, 5 * kOne, noiseModel::Constrained::All(1));
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graph.add(1, I_1x1, 2, 2 * I_1x1, 6 * kOne, noiseModel::Constrained::All(1));
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VectorValues x = graph.optimize();
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// This check confirms that gtsam linear constraint solver can't handle
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// over-constrained system
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CHECK(graph.error(x) != 0.0);
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}
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/* ************************************************************************* */
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TEST(LPSolver, SimpleTest1) {
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LP lp = simpleLP1();
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LPSolver lpSolver(lp);
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VectorValues init;
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init.insert(1, Vector::Zero(2));
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VectorValues x1 =
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lpSolver.buildWorkingGraph(InequalityFactorGraph(), init).optimize();
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VectorValues expected_x1;
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expected_x1.insert(1, Vector::Ones(2));
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CHECK(assert_equal(expected_x1, x1, 1e-10));
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VectorValues result, duals;
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std::tie(result, duals) = lpSolver.optimize(init);
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VectorValues expectedResult;
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expectedResult.insert(1, Vector2(8. / 3., 2. / 3.));
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CHECK(assert_equal(expectedResult, result, 1e-10));
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}
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/* ************************************************************************* */
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TEST(LPSolver, TestWithoutInitialValues) {
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LP lp = simpleLP1();
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LPSolver lpSolver(lp);
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VectorValues result, duals, expectedResult;
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expectedResult.insert(1, Vector2(8. / 3., 2. / 3.));
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std::tie(result, duals) = lpSolver.optimize();
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CHECK(assert_equal(expectedResult, result));
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}
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/**
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* TODO: More TEST cases:
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* - Infeasible
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* - Unbounded
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* - Underdetermined
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*/
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/* ************************************************************************* */
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TEST(LPSolver, LinearCost) {
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LinearCost cost(1, Vector3(2., 4., 6.));
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VectorValues x;
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x.insert(1, Vector3(1., 3., 5.));
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double error = cost.error(x);
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double expectedError = 44.0;
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DOUBLES_EQUAL(expectedError, error, 1e-100);
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}
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/* ************************************************************************* */
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int main() {
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TestResult tr;
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return TestRegistry::runAllTests(tr);
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}
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/* ************************************************************************* */
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