eiquadprog-rt.cpp

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//
// 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;

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()