Head

GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	tests/eiquadprog-rt.cpp	Lines:	251	251	100.0 %
Date:	2023-11-29 12:38:05	Branches:	666	1332	50.0 %


//
// Copyright (c) 2019 CNRS
//
// This file is part of eiquadprog.
//
// eiquadprog is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
//(at your option) any later version.

// eiquadprog is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Lesser General Public License for more details.

// You should have received a copy of the GNU Lesser General Public License
// along with eiquadprog.  If not, see <https://www.gnu.org/licenses/>.

#include "eiquadprog/eiquadprog-rt.hpp"

#include <Eigen/Core>
#include <boost/test/unit_test.hpp>
#include <iostream>

using namespace eiquadprog::solvers;

/**
 * solves the problem
 * min. 0.5 * x' Hess x + g0' x
 * s.t. CE x + ce0 = 0
 *      CI x + ci0 >= 0
 */

BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE)

// min ||x||^2

BOOST_AUTO_TEST_CASE(test_unbiased) {
  RtEiquadprog<2, 0, 0> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C.setZero();

  RtMatrixX<0, 2>::d Aeq;

  RtVectorX<0>::d Beq;

  RtMatrixX<0, 2>::d Aineq;

  RtVectorX<0>::d Bineq;

  RtVectorX<2>::d x;

  RtVectorX<2>::d solution;
  solution.setZero();

  double val = 0.0;

  RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_CHECK_EQUAL(status, expected);

  BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);

  BOOST_CHECK(x.isApprox(solution));
}

// min ||x-x_0||^2, x_0 = (1 1)^T

BOOST_AUTO_TEST_CASE(test_biased) {
  RtEiquadprog<2, 0, 0> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C(0) = -1.;
  C(1) = -1.;

  RtMatrixX<0, 2>::d Aeq;

  RtVectorX<0>::d Beq;

  RtMatrixX<0, 2>::d Aineq;

  RtVectorX<0>::d Bineq;

  RtVectorX<2>::d x;

  RtVectorX<2>::d solution;
  solution(0) = 1.;
  solution(1) = 1.;

  double val = -1.;

  RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_CHECK_EQUAL(status, expected);

  BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);

  BOOST_CHECK(x.isApprox(solution));
}

// min ||x||^2
//    s.t.
// x[1] = 1 - x[0]

BOOST_AUTO_TEST_CASE(test_equality_constraints) {
  RtEiquadprog<2, 1, 0> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C.setZero();

  RtMatrixX<1, 2>::d Aeq;
  Aeq(0, 0) = 1.;
  Aeq(0, 1) = 1.;

  RtVectorX<1>::d Beq;
  Beq(0) = -1.;

  RtMatrixX<0, 2>::d Aineq;

  RtVectorX<0>::d Bineq;

  RtVectorX<2>::d x;

  RtVectorX<2>::d solution;
  solution(0) = 0.5;
  solution(1) = 0.5;

  double val = 0.25;

  RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_CHECK_EQUAL(status, expected);

  BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);

  BOOST_CHECK(x.isApprox(solution));
}

// min ||x||^2
//    s.t.
// x[i] >= 1

BOOST_AUTO_TEST_CASE(test_inequality_constraints) {
  RtEiquadprog<2, 0, 2> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C.setZero();

  RtMatrixX<0, 2>::d Aeq;

  RtVectorX<0>::d Beq(0);

  RtMatrixX<2, 2>::d Aineq;
  Aineq.setZero();
  Aineq(0, 0) = 1.;
  Aineq(1, 1) = 1.;

  RtVectorX<2>::d Bineq;
  Bineq(0) = -1.;
  Bineq(1) = -1.;

  RtVectorX<2>::d x;

  RtVectorX<2>::d solution;
  solution(0) = 1.;
  solution(1) = 1.;

  double val = 1.;

  RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_CHECK_EQUAL(status, expected);

  BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);

  BOOST_CHECK(x.isApprox(solution));
}

// min ||x-x_0||^2, x_0 = (1 1)^T
//    s.t.
// x[1] = 5 - x[0]
// x[1] >= 3

BOOST_AUTO_TEST_CASE(test_full) {
  RtEiquadprog<2, 1, 1> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C(0) = -1.;
  C(1) = -1.;

  RtMatrixX<1, 2>::d Aeq;
  Aeq(0, 0) = 1.;
  Aeq(0, 1) = 1.;

  RtVectorX<1>::d Beq;
  Beq(0) = -5.;

  RtMatrixX<1, 2>::d Aineq;
  Aineq.setZero();
  Aineq(0, 1) = 1.;

  RtVectorX<1>::d Bineq;
  Bineq(0) = -3.;

  RtVectorX<2>::d x;

  RtVectorX<2>::d solution;
  solution(0) = 2.;
  solution(1) = 3.;

  double val = 1.5;

  RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_CHECK_EQUAL(status, expected);

  BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);

  BOOST_CHECK(x.isApprox(solution));
}

// min ||x||^2
//    s.t.
// x[0] =  1
// x[0] = -1

BOOST_AUTO_TEST_CASE(test_unfeasible_equalities) {
  RtEiquadprog<2, 2, 0> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C.setZero();

  RtMatrixX<2, 2>::d Aeq;
  Aeq.setZero();
  Aeq(0, 0) = 1.;
  Aeq(1, 0) = 1.;

  RtVectorX<2>::d Beq;
  Beq(0) = -1.;
  Beq(1) = 1.;

  RtMatrixX<0, 2>::d Aineq;

  RtVectorX<0>::d Bineq;

  RtVectorX<2>::d x;

  RtEiquadprog_status expected = RT_EIQUADPROG_REDUNDANT_EQUALITIES;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_CHECK_EQUAL(status, expected);
}

// min ||x||^2
//    s.t.
// x[0] >=  1
// x[0] <= -1
//
// correctly fails, but returns wrong error code

BOOST_AUTO_TEST_CASE(test_unfeasible_inequalities) {
  RtEiquadprog<2, 0, 2> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C.setZero();

  RtMatrixX<0, 2>::d Aeq;

  RtVectorX<0>::d Beq;

  RtMatrixX<2, 2>::d Aineq;
  Aineq.setZero();
  Aineq(0, 0) = 1.;
  Aineq(1, 0) = -1.;

  RtVectorX<2>::d Bineq;
  Bineq(0) = -1;
  Bineq(1) = -1;

  RtVectorX<2>::d x;

  RtEiquadprog_status expected = RT_EIQUADPROG_INFEASIBLE;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_WARN_EQUAL(status, expected);
  BOOST_CHECK(status != RT_EIQUADPROG_OPTIMAL);
}

// min ||x-x_0||^2, x_0 = (1 1)^T
//    s.t.
// x[1] = 1 - x[0]
// x[0] <= 0
// x[1] <= 0
//
// correctly fails, but returns wrong error code

BOOST_AUTO_TEST_CASE(test_unfeasible_constraints) {
  RtEiquadprog<2, 1, 2> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = 1.0;
  Q(1, 1) = 1.0;

  RtVectorX<2>::d C;
  C(0) = -1.;
  C(1) = -1.;

  RtMatrixX<1, 2>::d Aeq;
  Aeq(0, 0) = 1.;
  Aeq(0, 1) = 1.;

  RtVectorX<1>::d Beq;
  Beq(0) = -1.;

  RtMatrixX<2, 2>::d Aineq;
  Aineq.setZero();
  Aineq(0, 0) = -1.;
  Aineq(1, 1) = -1.;

  RtVectorX<2>::d Bineq;
  Bineq.setZero();

  RtVectorX<2>::d x;

  RtEiquadprog_status expected = RT_EIQUADPROG_INFEASIBLE;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_WARN_EQUAL(status, expected);
  BOOST_CHECK(status != RT_EIQUADPROG_OPTIMAL);
}

// min -||x||^2
// DOES NOT WORK!

BOOST_AUTO_TEST_CASE(test_unbounded) {
  RtEiquadprog<2, 0, 0> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = -1.0;
  Q(1, 1) = -1.0;

  RtVectorX<2>::d C;
  C.setZero();

  RtMatrixX<0, 2>::d Aeq;

  RtVectorX<0>::d Beq;

  RtMatrixX<0, 2>::d Aineq;

  RtVectorX<0>::d Bineq;

  RtVectorX<2>::d x;

  RtEiquadprog_status expected = RT_EIQUADPROG_UNBOUNDED;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_WARN_EQUAL(status, expected);
  BOOST_WARN(status != RT_EIQUADPROG_OPTIMAL);  // SHOULD pass!
}

// min -||x||^2
//    s.t.
// 0<= x[0] <= 1
// 0<= x[1] <= 1
// DOES NOT WORK!

BOOST_AUTO_TEST_CASE(test_nonconvex) {
  RtEiquadprog<2, 0, 4> qp;

  RtMatrixX<2, 2>::d Q;
  Q.setZero();
  Q(0, 0) = -1.0;
  Q(1, 1) = -1.0;

  RtVectorX<2>::d C;
  C.setZero();

  RtMatrixX<0, 2>::d Aeq;

  RtVectorX<0>::d Beq;

  RtMatrixX<4, 2>::d Aineq(4, 2);
  Aineq.setZero();
  Aineq(0, 0) = 1.;
  Aineq(1, 0) = -1.;
  Aineq(2, 1) = 1.;
  Aineq(3, 1) = -1.;

  RtVectorX<4>::d Bineq;
  Bineq(0) = 0.;
  Bineq(1) = 1.;
  Bineq(2) = 0.;
  Bineq(3) = 1.;

  RtVectorX<2>::d x;

  RtVectorX<2>::d solution;
  solution(0) = 1.;
  solution(1) = 1.;

  double val = -1.;

  RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;

  RtEiquadprog_status status =
      qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);

  BOOST_CHECK_EQUAL(status, expected);

  BOOST_WARN_CLOSE(qp.getObjValue(), val, 1e-6);

  BOOST_WARN(x.isApprox(solution));
}

BOOST_AUTO_TEST_SUITE_END()


Generated by: GCOVR (Version 4.2)

Line	Branch	Exec	Source
1			//
2			// Copyright (c) 2019 CNRS
3			//
4			// This file is part of eiquadprog.
5			//
6			// eiquadprog is free software: you can redistribute it and/or modify
7			// it under the terms of the GNU Lesser General Public License as published by
8			// the Free Software Foundation, either version 3 of the License, or
9			//(at your option) any later version.
10
11			// eiquadprog is distributed in the hope that it will be useful,
12			// but WITHOUT ANY WARRANTY; without even the implied warranty of
13			// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14			// GNU Lesser General Public License for more details.
15
16			// You should have received a copy of the GNU Lesser General Public License
17			// along with eiquadprog. If not, see <https://www.gnu.org/licenses/>.
18
19			#include "eiquadprog/eiquadprog-rt.hpp"
20
21			#include <Eigen/Core>
22			#include <boost/test/unit_test.hpp>
23			#include <iostream>
24
25			using namespace eiquadprog::solvers;
26
27			/**
28			* solves the problem
29			* min. 0.5 * x' Hess x + g0' x
30			* s.t. CE x + ce0 = 0
31			* CI x + ci0 >= 0
32			*/
33
34			BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE)
35
36			// min \|\|x\|\|^2
37
38	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_unbiased) {
39	✓✗	4	RtEiquadprog<2, 0, 0> qp;
40
41	✓✗	2	RtMatrixX<2, 2>::d Q;
42	✓✗	2	Q.setZero();
43	✓✗	2	Q(0, 0) = 1.0;
44	✓✗	2	Q(1, 1) = 1.0;
45
46	✓✗	2	RtVectorX<2>::d C;
47	✓✗	2	C.setZero();
48
49	✓✗	2	RtMatrixX<0, 2>::d Aeq;
50
51	✓✗	2	RtVectorX<0>::d Beq;
52
53	✓✗	2	RtMatrixX<0, 2>::d Aineq;
54
55	✓✗	2	RtVectorX<0>::d Bineq;
56
57	✓✗	2	RtVectorX<2>::d x;
58
59	✓✗	2	RtVectorX<2>::d solution;
60	✓✗	2	solution.setZero();
61
62		2	double val = 0.0;
63
64		2	RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;
65
66			RtEiquadprog_status status =
67	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
68
69	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK_EQUAL(status, expected);
70
71	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);
72
73	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK(x.isApprox(solution));
74		2	}
75
76			// min \|\|x-x_0\|\|^2, x_0 = (1 1)^T
77
78	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_biased) {
79	✓✗	4	RtEiquadprog<2, 0, 0> qp;
80
81	✓✗	2	RtMatrixX<2, 2>::d Q;
82	✓✗	2	Q.setZero();
83	✓✗	2	Q(0, 0) = 1.0;
84	✓✗	2	Q(1, 1) = 1.0;
85
86	✓✗	2	RtVectorX<2>::d C;
87	✓✗	2	C(0) = -1.;
88	✓✗	2	C(1) = -1.;
89
90	✓✗	2	RtMatrixX<0, 2>::d Aeq;
91
92	✓✗	2	RtVectorX<0>::d Beq;
93
94	✓✗	2	RtMatrixX<0, 2>::d Aineq;
95
96	✓✗	2	RtVectorX<0>::d Bineq;
97
98	✓✗	2	RtVectorX<2>::d x;
99
100	✓✗	2	RtVectorX<2>::d solution;
101	✓✗	2	solution(0) = 1.;
102	✓✗	2	solution(1) = 1.;
103
104		2	double val = -1.;
105
106		2	RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;
107
108			RtEiquadprog_status status =
109	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
110
111	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK_EQUAL(status, expected);
112
113	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);
114
115	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK(x.isApprox(solution));
116		2	}
117
118			// min \|\|x\|\|^2
119			// s.t.
120			// x[1] = 1 - x[0]
121
122	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_equality_constraints) {
123	✓✗	4	RtEiquadprog<2, 1, 0> qp;
124
125	✓✗	2	RtMatrixX<2, 2>::d Q;
126	✓✗	2	Q.setZero();
127	✓✗	2	Q(0, 0) = 1.0;
128	✓✗	2	Q(1, 1) = 1.0;
129
130	✓✗	2	RtVectorX<2>::d C;
131	✓✗	2	C.setZero();
132
133	✓✗	2	RtMatrixX<1, 2>::d Aeq;
134	✓✗	2	Aeq(0, 0) = 1.;
135	✓✗	2	Aeq(0, 1) = 1.;
136
137	✓✗	2	RtVectorX<1>::d Beq;
138	✓✗	2	Beq(0) = -1.;
139
140	✓✗	2	RtMatrixX<0, 2>::d Aineq;
141
142	✓✗	2	RtVectorX<0>::d Bineq;
143
144	✓✗	2	RtVectorX<2>::d x;
145
146	✓✗	2	RtVectorX<2>::d solution;
147	✓✗	2	solution(0) = 0.5;
148	✓✗	2	solution(1) = 0.5;
149
150		2	double val = 0.25;
151
152		2	RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;
153
154			RtEiquadprog_status status =
155	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
156
157	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK_EQUAL(status, expected);
158
159	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);
160
161	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK(x.isApprox(solution));
162		2	}
163
164			// min \|\|x\|\|^2
165			// s.t.
166			// x[i] >= 1
167
168	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_inequality_constraints) {
169	✓✗	4	RtEiquadprog<2, 0, 2> qp;
170
171	✓✗	2	RtMatrixX<2, 2>::d Q;
172	✓✗	2	Q.setZero();
173	✓✗	2	Q(0, 0) = 1.0;
174	✓✗	2	Q(1, 1) = 1.0;
175
176	✓✗	2	RtVectorX<2>::d C;
177	✓✗	2	C.setZero();
178
179	✓✗	2	RtMatrixX<0, 2>::d Aeq;
180
181	✓✗	2	RtVectorX<0>::d Beq(0);
182
183	✓✗	2	RtMatrixX<2, 2>::d Aineq;
184	✓✗	2	Aineq.setZero();
185	✓✗	2	Aineq(0, 0) = 1.;
186	✓✗	2	Aineq(1, 1) = 1.;
187
188	✓✗	2	RtVectorX<2>::d Bineq;
189	✓✗	2	Bineq(0) = -1.;
190	✓✗	2	Bineq(1) = -1.;
191
192	✓✗	2	RtVectorX<2>::d x;
193
194	✓✗	2	RtVectorX<2>::d solution;
195	✓✗	2	solution(0) = 1.;
196	✓✗	2	solution(1) = 1.;
197
198		2	double val = 1.;
199
200		2	RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;
201
202			RtEiquadprog_status status =
203	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
204
205	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK_EQUAL(status, expected);
206
207	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);
208
209	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK(x.isApprox(solution));
210		2	}
211
212			// min \|\|x-x_0\|\|^2, x_0 = (1 1)^T
213			// s.t.
214			// x[1] = 5 - x[0]
215			// x[1] >= 3
216
217	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_full) {
218	✓✗	4	RtEiquadprog<2, 1, 1> qp;
219
220	✓✗	2	RtMatrixX<2, 2>::d Q;
221	✓✗	2	Q.setZero();
222	✓✗	2	Q(0, 0) = 1.0;
223	✓✗	2	Q(1, 1) = 1.0;
224
225	✓✗	2	RtVectorX<2>::d C;
226	✓✗	2	C(0) = -1.;
227	✓✗	2	C(1) = -1.;
228
229	✓✗	2	RtMatrixX<1, 2>::d Aeq;
230	✓✗	2	Aeq(0, 0) = 1.;
231	✓✗	2	Aeq(0, 1) = 1.;
232
233	✓✗	2	RtVectorX<1>::d Beq;
234	✓✗	2	Beq(0) = -5.;
235
236	✓✗	2	RtMatrixX<1, 2>::d Aineq;
237	✓✗	2	Aineq.setZero();
238	✓✗	2	Aineq(0, 1) = 1.;
239
240	✓✗	2	RtVectorX<1>::d Bineq;
241	✓✗	2	Bineq(0) = -3.;
242
243	✓✗	2	RtVectorX<2>::d x;
244
245	✓✗	2	RtVectorX<2>::d solution;
246	✓✗	2	solution(0) = 2.;
247	✓✗	2	solution(1) = 3.;
248
249		2	double val = 1.5;
250
251		2	RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;
252
253			RtEiquadprog_status status =
254	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
255
256	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK_EQUAL(status, expected);
257
258	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_CHECK_CLOSE(qp.getObjValue(), val, 1e-6);
259
260	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK(x.isApprox(solution));
261		2	}
262
263			// min \|\|x\|\|^2
264			// s.t.
265			// x[0] = 1
266			// x[0] = -1
267
268	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_unfeasible_equalities) {
269	✓✗	4	RtEiquadprog<2, 2, 0> qp;
270
271	✓✗	2	RtMatrixX<2, 2>::d Q;
272	✓✗	2	Q.setZero();
273	✓✗	2	Q(0, 0) = 1.0;
274	✓✗	2	Q(1, 1) = 1.0;
275
276	✓✗	2	RtVectorX<2>::d C;
277	✓✗	2	C.setZero();
278
279	✓✗	2	RtMatrixX<2, 2>::d Aeq;
280	✓✗	2	Aeq.setZero();
281	✓✗	2	Aeq(0, 0) = 1.;
282	✓✗	2	Aeq(1, 0) = 1.;
283
284	✓✗	2	RtVectorX<2>::d Beq;
285	✓✗	2	Beq(0) = -1.;
286	✓✗	2	Beq(1) = 1.;
287
288	✓✗	2	RtMatrixX<0, 2>::d Aineq;
289
290	✓✗	2	RtVectorX<0>::d Bineq;
291
292	✓✗	2	RtVectorX<2>::d x;
293
294		2	RtEiquadprog_status expected = RT_EIQUADPROG_REDUNDANT_EQUALITIES;
295
296			RtEiquadprog_status status =
297	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
298
299	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK_EQUAL(status, expected);
300		2	}
301
302			// min \|\|x\|\|^2
303			// s.t.
304			// x[0] >= 1
305			// x[0] <= -1
306			//
307			// correctly fails, but returns wrong error code
308
309	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_unfeasible_inequalities) {
310	✓✗	4	RtEiquadprog<2, 0, 2> qp;
311
312	✓✗	2	RtMatrixX<2, 2>::d Q;
313	✓✗	2	Q.setZero();
314	✓✗	2	Q(0, 0) = 1.0;
315	✓✗	2	Q(1, 1) = 1.0;
316
317	✓✗	2	RtVectorX<2>::d C;
318	✓✗	2	C.setZero();
319
320	✓✗	2	RtMatrixX<0, 2>::d Aeq;
321
322	✓✗	2	RtVectorX<0>::d Beq;
323
324	✓✗	2	RtMatrixX<2, 2>::d Aineq;
325	✓✗	2	Aineq.setZero();
326	✓✗	2	Aineq(0, 0) = 1.;
327	✓✗	2	Aineq(1, 0) = -1.;
328
329	✓✗	2	RtVectorX<2>::d Bineq;
330	✓✗	2	Bineq(0) = -1;
331	✓✗	2	Bineq(1) = -1;
332
333	✓✗	2	RtVectorX<2>::d x;
334
335		2	RtEiquadprog_status expected = RT_EIQUADPROG_INFEASIBLE;
336
337			RtEiquadprog_status status =
338	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
339
340	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_WARN_EQUAL(status, expected);
341	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_CHECK(status != RT_EIQUADPROG_OPTIMAL);
342		2	}
343
344			// min \|\|x-x_0\|\|^2, x_0 = (1 1)^T
345			// s.t.
346			// x[1] = 1 - x[0]
347			// x[0] <= 0
348			// x[1] <= 0
349			//
350			// correctly fails, but returns wrong error code
351
352	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_unfeasible_constraints) {
353	✓✗	4	RtEiquadprog<2, 1, 2> qp;
354
355	✓✗	2	RtMatrixX<2, 2>::d Q;
356	✓✗	2	Q.setZero();
357	✓✗	2	Q(0, 0) = 1.0;
358	✓✗	2	Q(1, 1) = 1.0;
359
360	✓✗	2	RtVectorX<2>::d C;
361	✓✗	2	C(0) = -1.;
362	✓✗	2	C(1) = -1.;
363
364	✓✗	2	RtMatrixX<1, 2>::d Aeq;
365	✓✗	2	Aeq(0, 0) = 1.;
366	✓✗	2	Aeq(0, 1) = 1.;
367
368	✓✗	2	RtVectorX<1>::d Beq;
369	✓✗	2	Beq(0) = -1.;
370
371	✓✗	2	RtMatrixX<2, 2>::d Aineq;
372	✓✗	2	Aineq.setZero();
373	✓✗	2	Aineq(0, 0) = -1.;
374	✓✗	2	Aineq(1, 1) = -1.;
375
376	✓✗	2	RtVectorX<2>::d Bineq;
377	✓✗	2	Bineq.setZero();
378
379	✓✗	2	RtVectorX<2>::d x;
380
381		2	RtEiquadprog_status expected = RT_EIQUADPROG_INFEASIBLE;
382
383			RtEiquadprog_status status =
384	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
385
386	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_WARN_EQUAL(status, expected);
387	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_CHECK(status != RT_EIQUADPROG_OPTIMAL);
388		2	}
389
390			// min -\|\|x\|\|^2
391			// DOES NOT WORK!
392
393	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_unbounded) {
394	✓✗	4	RtEiquadprog<2, 0, 0> qp;
395
396	✓✗	2	RtMatrixX<2, 2>::d Q;
397	✓✗	2	Q.setZero();
398	✓✗	2	Q(0, 0) = -1.0;
399	✓✗	2	Q(1, 1) = -1.0;
400
401	✓✗	2	RtVectorX<2>::d C;
402	✓✗	2	C.setZero();
403
404	✓✗	2	RtMatrixX<0, 2>::d Aeq;
405
406	✓✗	2	RtVectorX<0>::d Beq;
407
408	✓✗	2	RtMatrixX<0, 2>::d Aineq;
409
410	✓✗	2	RtVectorX<0>::d Bineq;
411
412	✓✗	2	RtVectorX<2>::d x;
413
414		2	RtEiquadprog_status expected = RT_EIQUADPROG_UNBOUNDED;
415
416			RtEiquadprog_status status =
417	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
418
419	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_WARN_EQUAL(status, expected);
420	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_WARN(status != RT_EIQUADPROG_OPTIMAL); // SHOULD pass!
421		2	}
422
423			// min -\|\|x\|\|^2
424			// s.t.
425			// 0<= x[0] <= 1
426			// 0<= x[1] <= 1
427			// DOES NOT WORK!
428
429	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗	4	BOOST_AUTO_TEST_CASE(test_nonconvex) {
430	✓✗	4	RtEiquadprog<2, 0, 4> qp;
431
432	✓✗	2	RtMatrixX<2, 2>::d Q;
433	✓✗	2	Q.setZero();
434	✓✗	2	Q(0, 0) = -1.0;
435	✓✗	2	Q(1, 1) = -1.0;
436
437	✓✗	2	RtVectorX<2>::d C;
438	✓✗	2	C.setZero();
439
440	✓✗	2	RtMatrixX<0, 2>::d Aeq;
441
442	✓✗	2	RtVectorX<0>::d Beq;
443
444	✓✗	2	RtMatrixX<4, 2>::d Aineq(4, 2);
445	✓✗	2	Aineq.setZero();
446	✓✗	2	Aineq(0, 0) = 1.;
447	✓✗	2	Aineq(1, 0) = -1.;
448	✓✗	2	Aineq(2, 1) = 1.;
449	✓✗	2	Aineq(3, 1) = -1.;
450
451	✓✗	2	RtVectorX<4>::d Bineq;
452	✓✗	2	Bineq(0) = 0.;
453	✓✗	2	Bineq(1) = 1.;
454	✓✗	2	Bineq(2) = 0.;
455	✓✗	2	Bineq(3) = 1.;
456
457	✓✗	2	RtVectorX<2>::d x;
458
459	✓✗	2	RtVectorX<2>::d solution;
460	✓✗	2	solution(0) = 1.;
461	✓✗	2	solution(1) = 1.;
462
463		2	double val = -1.;
464
465		2	RtEiquadprog_status expected = RT_EIQUADPROG_OPTIMAL;
466
467			RtEiquadprog_status status =
468	✓✗	2	qp.solve_quadprog(Q, C, Aeq, Beq, Aineq, Bineq, x);
469
470	✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_CHECK_EQUAL(status, expected);
471
472	✓✗✓✗ ✓✗✓✗ ✓✗✗✓	2	BOOST_WARN_CLOSE(qp.getObjValue(), val, 1e-6);
473
474	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✗✓	2	BOOST_WARN(x.isApprox(solution));
475		2	}
476
477			BOOST_AUTO_TEST_SUITE_END()