SimplexSolverTest

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 * this work for additional information regarding copyright ownership.
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 *
 *      https://www.apache.org/licenses/LICENSE-2.0
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/*
 * This is not the original file distributed by the Apache Software Foundation
 * It has been modified by the Hipparchus project
 */
package org.hipparchus.optim.linear;

import java.util.ArrayList;
import java.util.Collection;
import java.util.List;

import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathIllegalStateException;
import org.hipparchus.optim.MaxIter;
import org.hipparchus.optim.PointValuePair;
import org.hipparchus.optim.nonlinear.scalar.GoalType;
import org.hipparchus.util.Precision;
import org.junit.Assert;
import org.junit.Test;

public class SimplexSolverTest {
    private static final MaxIter DEFAULT_MAX_ITER = new MaxIter(100);

    @Test
    public void testMath842Cycle() {
        // from http://www.math.toronto.edu/mpugh/Teaching/APM236_04/bland
        //      maximize 10 x1 - 57 x2 - 9 x3 - 24 x4
        //      subject to
        //          1/2 x1 - 11/2 x2 - 5/2 x3 + 9 x4  <= 0
        //          1/2 x1 -  3/2 x2 - 1/2 x3 +   x4  <= 0
        //              x1                  <= 1
        //      x1,x2,x3,x4 >= 0

        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 10, -57, -9, -24}, 0);

        ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>();

        constraints.add(new LinearConstraint(new double[] {0.5, -5.5, -2.5, 9}, Relationship.LEQ, 0));
        constraints.add(new LinearConstraint(new double[] {0.5, -1.5, -0.5, 1}, Relationship.LEQ, 0));
        constraints.add(new LinearConstraint(new double[] {  1,    0,    0, 0}, Relationship.LEQ, 1));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE,
                                                  new NonNegativeConstraint(true),
                                                  PivotSelectionRule.BLAND);
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
        Assert.assertTrue(validSolution(solution, constraints, epsilon));
    }

    @Test
    public void testMath828() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(
                new double[] { 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, 0.0);

        ArrayList <LinearConstraint>constraints = new ArrayList<LinearConstraint>();

        constraints.add(new LinearConstraint(new double[] {0.0, 39.0, 23.0, 96.0, 15.0, 48.0, 9.0, 21.0, 48.0, 36.0, 76.0, 19.0, 88.0, 17.0, 16.0, 36.0,}, Relationship.GEQ, 15.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 59.0, 93.0, 12.0, 29.0, 78.0, 73.0, 87.0, 32.0, 70.0, 68.0, 24.0, 11.0, 26.0, 65.0, 25.0,}, Relationship.GEQ, 29.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 74.0, 5.0, 82.0, 6.0, 97.0, 55.0, 44.0, 52.0, 54.0, 5.0, 93.0, 91.0, 8.0, 20.0, 97.0,}, Relationship.GEQ, 6.0));
        constraints.add(new LinearConstraint(new double[] {8.0, -3.0, -28.0, -72.0, -8.0, -31.0, -31.0, -74.0, -47.0, -59.0, -24.0, -57.0, -56.0, -16.0, -92.0, -59.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {25.0, -7.0, -99.0, -78.0, -25.0, -14.0, -16.0, -89.0, -39.0, -56.0, -53.0, -9.0, -18.0, -26.0, -11.0, -61.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {33.0, -95.0, -15.0, -4.0, -33.0, -3.0, -20.0, -96.0, -27.0, -13.0, -80.0, -24.0, -3.0, -13.0, -57.0, -76.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {7.0, -95.0, -39.0, -93.0, -7.0, -94.0, -94.0, -62.0, -76.0, -26.0, -53.0, -57.0, -31.0, -76.0, -53.0, -52.0,}, Relationship.GEQ, 0.0));

        double epsilon = 1e-6;
        PointValuePair solution = new SimplexSolver().optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                               GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
        Assert.assertTrue(validSolution(solution, constraints, epsilon));
    }

    @Test
    public void testMath828Cycle() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(
                new double[] { 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, 0.0);

        ArrayList <LinearConstraint>constraints = new ArrayList<LinearConstraint>();

        constraints.add(new LinearConstraint(new double[] {0.0, 16.0, 14.0, 69.0, 1.0, 85.0, 52.0, 43.0, 64.0, 97.0, 14.0, 74.0, 89.0, 28.0, 94.0, 58.0, 13.0, 22.0, 21.0, 17.0, 30.0, 25.0, 1.0, 59.0, 91.0, 78.0, 12.0, 74.0, 56.0, 3.0, 88.0,}, Relationship.GEQ, 91.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 60.0, 40.0, 81.0, 71.0, 72.0, 46.0, 45.0, 38.0, 48.0, 40.0, 17.0, 33.0, 85.0, 64.0, 32.0, 84.0, 3.0, 54.0, 44.0, 71.0, 67.0, 90.0, 95.0, 54.0, 99.0, 99.0, 29.0, 52.0, 98.0, 9.0,}, Relationship.GEQ, 54.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 41.0, 12.0, 86.0, 90.0, 61.0, 31.0, 41.0, 23.0, 89.0, 17.0, 74.0, 44.0, 27.0, 16.0, 47.0, 80.0, 32.0, 11.0, 56.0, 68.0, 82.0, 11.0, 62.0, 62.0, 53.0, 39.0, 16.0, 48.0, 1.0, 63.0,}, Relationship.GEQ, 62.0));
        constraints.add(new LinearConstraint(new double[] {83.0, -76.0, -94.0, -19.0, -15.0, -70.0, -72.0, -57.0, -63.0, -65.0, -22.0, -94.0, -22.0, -88.0, -86.0, -89.0, -72.0, -16.0, -80.0, -49.0, -70.0, -93.0, -95.0, -17.0, -83.0, -97.0, -31.0, -47.0, -31.0, -13.0, -23.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {41.0, -96.0, -41.0, -48.0, -70.0, -43.0, -43.0, -43.0, -97.0, -37.0, -85.0, -70.0, -45.0, -67.0, -87.0, -69.0, -94.0, -54.0, -54.0, -92.0, -79.0, -10.0, -35.0, -20.0, -41.0, -41.0, -65.0, -25.0, -12.0, -8.0, -46.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {27.0, -42.0, -65.0, -49.0, -53.0, -42.0, -17.0, -2.0, -61.0, -31.0, -76.0, -47.0, -8.0, -93.0, -86.0, -62.0, -65.0, -63.0, -22.0, -43.0, -27.0, -23.0, -32.0, -74.0, -27.0, -63.0, -47.0, -78.0, -29.0, -95.0, -73.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {15.0, -46.0, -41.0, -83.0, -98.0, -99.0, -21.0, -35.0, -7.0, -14.0, -80.0, -63.0, -18.0, -42.0, -5.0, -34.0, -56.0, -70.0, -16.0, -18.0, -74.0, -61.0, -47.0, -41.0, -15.0, -79.0, -18.0, -47.0, -88.0, -68.0, -55.0,}, Relationship.GEQ, 0.0));

        double epsilon = 1e-6;
        PointValuePair solution = new SimplexSolver().optimize(DEFAULT_MAX_ITER, f,
                                                               new LinearConstraintSet(constraints),
                                                               GoalType.MINIMIZE, new NonNegativeConstraint(true),
                                                               PivotSelectionRule.BLAND);
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
        Assert.assertTrue(validSolution(solution, constraints, epsilon));
    }

    @Test
    public void testMath781() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 2, 6, 7 }, 0);

        ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 2, 1 }, Relationship.LEQ, 2));
        constraints.add(new LinearConstraint(new double[] { -1, 1, 1 }, Relationship.LEQ, -1));
        constraints.add(new LinearConstraint(new double[] { 2, -3, 1 }, Relationship.LEQ, -1));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0], 0.0d, epsilon) > 0);
        Assert.assertTrue(Precision.compareTo(solution.getPoint()[1], 0.0d, epsilon) > 0);
        Assert.assertTrue(Precision.compareTo(solution.getPoint()[2], 0.0d, epsilon) < 0);
        Assert.assertEquals(2.0d, solution.getValue(), epsilon);
    }

    @Test
    public void testMath713NegativeVariable() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {1.0, 1.0}, 0.0d);
        ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] {1, 0}, Relationship.EQ, 1));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0], 0.0d, epsilon) >= 0);
        Assert.assertTrue(Precision.compareTo(solution.getPoint()[1], 0.0d, epsilon) >= 0);
    }

    @Test
    public void testMath434NegativeVariable() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {0.0, 0.0, 1.0}, 0.0d);
        ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] {1, 1, 0}, Relationship.EQ, 5));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1}, Relationship.GEQ, -10));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(false));

        Assert.assertEquals(5.0, solution.getPoint()[0] + solution.getPoint()[1], epsilon);
        Assert.assertEquals(-10.0, solution.getPoint()[2], epsilon);
        Assert.assertEquals(-10.0, solution.getValue(), epsilon);

    }

    @Test(expected = MathIllegalStateException.class)
    public void testMath434UnfeasibleSolution() {
        double epsilon = 1e-6;

        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {1.0, 0.0}, 0.0);
        ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] {epsilon/2, 0.5}, Relationship.EQ, 0));
        constraints.add(new LinearConstraint(new double[] {1e-3, 0.1}, Relationship.EQ, 10));

        SimplexSolver solver = new SimplexSolver();
        // allowing only non-negative values, no feasible solution shall be found
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MINIMIZE, new NonNegativeConstraint(true));
    }

    @Test
    public void testMath434PivotRowSelection() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {1.0}, 0.0);

        double epsilon = 1e-6;
        ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] {200}, Relationship.GEQ, 1));
        constraints.add(new LinearConstraint(new double[] {100}, Relationship.GEQ, 0.499900001));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(false));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0] * 200.d, 1.d, epsilon) >= 0);
        Assert.assertEquals(0.0050, solution.getValue(), epsilon);
    }

    @Test
    public void testMath434PivotRowSelection2() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {0.0d, 1.0d, 1.0d, 0.0d, 0.0d, 0.0d, 0.0d}, 0.0d);

        ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] {1.0d, -0.1d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d}, Relationship.EQ, -0.1d));
        constraints.add(new LinearConstraint(new double[] {1.0d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, -1e-18d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 1.0d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 1.0d, 0.0d, -0.0128588d, 1e-5d}, Relationship.EQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 0.0d, 1.0d, 1e-5d, -0.0128586d}, Relationship.EQ, 1e-10d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, -1.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 1.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d, -1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d, 1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));

        double epsilon = 1e-7;
        SimplexSolver simplex = new SimplexSolver();
        PointValuePair solution = simplex.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                   GoalType.MINIMIZE, new NonNegativeConstraint(false));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0], -1e-18d, epsilon) >= 0);
        Assert.assertEquals(1.0d, solution.getPoint()[1], epsilon);
        Assert.assertEquals(0.0d, solution.getPoint()[2], epsilon);
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
    }

    @Test
    public void testMath272() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 2, 2, 1 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 1, 0 }, Relationship.GEQ,  1));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 1 }, Relationship.GEQ,  1));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0 }, Relationship.GEQ,  1));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));

        Assert.assertEquals(0.0, solution.getPoint()[0], .0000001);
        Assert.assertEquals(1.0, solution.getPoint()[1], .0000001);
        Assert.assertEquals(1.0, solution.getPoint()[2], .0000001);
        Assert.assertEquals(3.0, solution.getValue(), .0000001);
    }

    @Test
    public void testMath286() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 0.8, 0.2, 0.7, 0.3, 0.6, 0.4 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 0, 1, 0, 1, 0 }, Relationship.EQ, 23.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 1, 0, 1 }, Relationship.EQ, 23.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 0, 0, 0, 0 }, Relationship.GEQ, 10.0));
        constraints.add(new LinearConstraint(new double[] { 0, 0, 1, 0, 0, 0 }, Relationship.GEQ, 8.0));
        constraints.add(new LinearConstraint(new double[] { 0, 0, 0, 0, 1, 0 }, Relationship.GEQ, 5.0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));

        Assert.assertEquals(25.8, solution.getValue(), .0000001);
        Assert.assertEquals(23.0, solution.getPoint()[0] + solution.getPoint()[2] + solution.getPoint()[4], 0.0000001);
        Assert.assertEquals(23.0, solution.getPoint()[1] + solution.getPoint()[3] + solution.getPoint()[5], 0.0000001);
        Assert.assertTrue(solution.getPoint()[0] >= 10.0 - 0.0000001);
        Assert.assertTrue(solution.getPoint()[2] >= 8.0 - 0.0000001);
        Assert.assertTrue(solution.getPoint()[4] >= 5.0 - 0.0000001);
    }

    @Test
    public void testDegeneracy() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 0.8, 0.7 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.LEQ, 18.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.GEQ, 10.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.GEQ, 8.0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(13.6, solution.getValue(), .0000001);
    }

    @Test
    public void testMath288() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 7, 3, 0, 0 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 3, 0, -5, 0 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 2, 0, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 0, 3, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 0, 0 }, Relationship.LEQ, 1.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 0 }, Relationship.LEQ, 1.0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(10.0, solution.getValue(), .0000001);
    }

    @Test
    public void testMath290GEQ() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 1, 5 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 2, 0 }, Relationship.GEQ, -1.0));
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(0, solution.getValue(), .0000001);
        Assert.assertEquals(0, solution.getPoint()[0], .0000001);
        Assert.assertEquals(0, solution.getPoint()[1], .0000001);
    }

    @Test(expected=MathIllegalStateException.class)
    public void testMath290LEQ() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 1, 5 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 2, 0 }, Relationship.LEQ, -1.0));
        SimplexSolver solver = new SimplexSolver();
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MINIMIZE, new NonNegativeConstraint(true));
    }

    @Test
    public void testMath293() {
      LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 0.8, 0.2, 0.7, 0.3, 0.4, 0.6}, 0 );
      Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
      constraints.add(new LinearConstraint(new double[] { 1, 0, 1, 0, 1, 0 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 1, 0, 1 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0.8, 0.2, 0.0, 0.0, 0.0, 0.0 }, Relationship.GEQ, 10.0));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.7, 0.3, 0.0, 0.0 }, Relationship.GEQ, 10.0));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.0, 0.0, 0.4, 0.6 }, Relationship.GEQ, 10.0));

      SimplexSolver solver = new SimplexSolver();
      PointValuePair solution1 = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                 GoalType.MAXIMIZE, new NonNegativeConstraint(true));

      Assert.assertEquals(15.7143, solution1.getPoint()[0], .0001);
      Assert.assertEquals(0.0, solution1.getPoint()[1], .0001);
      Assert.assertEquals(14.2857, solution1.getPoint()[2], .0001);
      Assert.assertEquals(0.0, solution1.getPoint()[3], .0001);
      Assert.assertEquals(0.0, solution1.getPoint()[4], .0001);
      Assert.assertEquals(30.0, solution1.getPoint()[5], .0001);
      Assert.assertEquals(40.57143, solution1.getValue(), .0001);

      double valA = 0.8 * solution1.getPoint()[0] + 0.2 * solution1.getPoint()[1];
      double valB = 0.7 * solution1.getPoint()[2] + 0.3 * solution1.getPoint()[3];
      double valC = 0.4 * solution1.getPoint()[4] + 0.6 * solution1.getPoint()[5];

      f = new LinearObjectiveFunction(new double[] { 0.8, 0.2, 0.7, 0.3, 0.4, 0.6}, 0 );
      constraints = new ArrayList<LinearConstraint>();
      constraints.add(new LinearConstraint(new double[] { 1, 0, 1, 0, 1, 0 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 1, 0, 1 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0.8, 0.2, 0.0, 0.0, 0.0, 0.0 }, Relationship.GEQ, valA));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.7, 0.3, 0.0, 0.0 }, Relationship.GEQ, valB));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.0, 0.0, 0.4, 0.6 }, Relationship.GEQ, valC));

      PointValuePair solution2 = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                 GoalType.MAXIMIZE, new NonNegativeConstraint(true));
      Assert.assertEquals(40.57143, solution2.getValue(), .0001);
    }

    @Test
    public void testMath930() {
        Collection<LinearConstraint> constraints = createMath930Constraints();

        double[] objFunctionCoeff = new double[33];
        objFunctionCoeff[3] = 1;
        LinearObjectiveFunction f = new LinearObjectiveFunction(objFunctionCoeff, 0);
        SimplexSolver solver = new SimplexSolver(1e-4, 10, 1e-6);

        PointValuePair solution = solver.optimize(new MaxIter(1000), f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(0.3752298, solution.getValue(), 1e-4);
    }

    private List<LinearConstraint> createMath930Constraints() {
        List<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] {1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.628803}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.676993}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1, -1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.136677}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.444434}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.254028}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.302218}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.653981}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.690437}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.423786}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.486717}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.049232}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.304747}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.129826}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.205625}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.621944}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.764385}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.432572}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.480762}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.055983}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.11378}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.009607}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.057797}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.407308}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.452749}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.269677}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.321806}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.049232}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.06902}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.028754}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.484254}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.524607}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.385492}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.430134}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.34983}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.375781}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.254028}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.281308}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.304995}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.345347}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.288899}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.332212}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.14351}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.17057}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -0.129826}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -0.157435}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -0.141071}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -0.232574}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -0.009607}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -0.057797}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -0.091644}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -0.203531}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -0.028754}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, Relationship.EQ, 1.0));
        return constraints;
    }

    @Test
    public void testSimplexSolver() {
        LinearObjectiveFunction f =
            new LinearObjectiveFunction(new double[] { 15, 10 }, 7);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.LEQ, 2));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.LEQ, 3));
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.EQ, 4));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(2.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(2.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(57.0, solution.getValue(), 0.0);
    }

    @Test
    public void testSingleVariableAndConstraint() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 3 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1 }, Relationship.LEQ, 10));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(10.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(30.0, solution.getValue(), 0.0);
    }

    /**
     * With no artificial variables needed (no equals and no greater than
     * constraints) we can go straight to Phase 2.
     */
    @Test
    public void testModelWithNoArtificialVars() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 15, 10 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.LEQ, 2));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.LEQ, 3));
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.LEQ, 4));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(2.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(2.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(50.0, solution.getValue(), 0.0);
    }

    @Test
    public void testMinimization() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { -2, 1 }, -5);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 2 }, Relationship.LEQ, 6));
        constraints.add(new LinearConstraint(new double[] { 3, 2 }, Relationship.LEQ, 12));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.GEQ, 0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(4.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(0.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(-13.0, solution.getValue(), 0.0);
    }

    @Test
    public void testSolutionWithNegativeDecisionVariable() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { -2, 1 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.GEQ, 6));
        constraints.add(new LinearConstraint(new double[] { 1, 2 }, Relationship.LEQ, 14));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(-2.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(8.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(12.0, solution.getValue(), 0.0);
    }

    @Test(expected = MathIllegalStateException.class)
    public void testInfeasibleSolution() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 15 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1 }, Relationship.LEQ, 1));
        constraints.add(new LinearConstraint(new double[] { 1 }, Relationship.GEQ, 3));

        SimplexSolver solver = new SimplexSolver();
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MAXIMIZE, new NonNegativeConstraint(false));
    }

    @Test(expected = MathIllegalStateException.class)
    public void testUnboundedSolution() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 15, 10 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.EQ, 2));

        SimplexSolver solver = new SimplexSolver();
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MAXIMIZE, new NonNegativeConstraint(false));
    }

    @Test
    public void testRestrictVariablesToNonNegative() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 409, 523, 70, 204, 339 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] {    43,   56, 345,  56,    5 }, Relationship.LEQ,  4567456));
        constraints.add(new LinearConstraint(new double[] {    12,   45,   7,  56,   23 }, Relationship.LEQ,    56454));
        constraints.add(new LinearConstraint(new double[] {     8,  768,   0,  34, 7456 }, Relationship.LEQ,  1923421));
        constraints.add(new LinearConstraint(new double[] { 12342, 2342,  34, 678, 2342 }, Relationship.GEQ,     4356));
        constraints.add(new LinearConstraint(new double[] {    45,  678,  76,  52,   23 }, Relationship.EQ,    456356));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(2902.92783505155, solution.getPoint()[0], .0000001);
        Assert.assertEquals(480.419243986254, solution.getPoint()[1], .0000001);
        Assert.assertEquals(0.0, solution.getPoint()[2], .0000001);
        Assert.assertEquals(0.0, solution.getPoint()[3], .0000001);
        Assert.assertEquals(0.0, solution.getPoint()[4], .0000001);
        Assert.assertEquals(1438556.7491409, solution.getValue(), .0000001);
    }

    @Test
    public void testEpsilon() {
      LinearObjectiveFunction f =
          new LinearObjectiveFunction(new double[] { 10, 5, 1 }, 0);
      Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
      constraints.add(new LinearConstraint(new double[] {  9, 8, 0 }, Relationship.EQ,  17));
      constraints.add(new LinearConstraint(new double[] {  0, 7, 8 }, Relationship.LEQ,  7));
      constraints.add(new LinearConstraint(new double[] { 10, 0, 2 }, Relationship.LEQ, 10));

      SimplexSolver solver = new SimplexSolver();
      PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                GoalType.MAXIMIZE, new NonNegativeConstraint(false));
      Assert.assertEquals(1.0, solution.getPoint()[0], 0.0);
      Assert.assertEquals(1.0, solution.getPoint()[1], 0.0);
      Assert.assertEquals(0.0, solution.getPoint()[2], 0.0);
      Assert.assertEquals(15.0, solution.getValue(), 0.0);
  }

    @Test
    public void testTrivialModel() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 1, 1 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.EQ,  0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(0, solution.getValue(), .0000001);
    }

    @Test
    public void testLargeModel() {
        double[] objective = new double[] {
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 12, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           12, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 12, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 12, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 12, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 12, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1};

        LinearObjectiveFunction f = new LinearObjectiveFunction(objective, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(equationFromString(objective.length, "x0 + x1 + x2 + x3 - x12 = 0"));
        constraints.add(equationFromString(objective.length, "x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 - x13 = 0"));
        constraints.add(equationFromString(objective.length, "x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 >= 49"));
        constraints.add(equationFromString(objective.length, "x0 + x1 + x2 + x3 >= 42"));
        constraints.add(equationFromString(objective.length, "x14 + x15 + x16 + x17 - x26 = 0"));
        constraints.add(equationFromString(objective.length, "x18 + x19 + x20 + x21 + x22 + x23 + x24 + x25 - x27 = 0"));
        constraints.add(equationFromString(objective.length, "x14 + x15 + x16 + x17 - x12 = 0"));
        constraints.add(equationFromString(objective.length, "x18 + x19 + x20 + x21 + x22 + x23 + x24 + x25 - x13 = 0"));
        constraints.add(equationFromString(objective.length, "x28 + x29 + x30 + x31 - x40 = 0"));
        constraints.add(equationFromString(objective.length, "x32 + x33 + x34 + x35 + x36 + x37 + x38 + x39 - x41 = 0"));
        constraints.add(equationFromString(objective.length, "x32 + x33 + x34 + x35 + x36 + x37 + x38 + x39 >= 49"));
        constraints.add(equationFromString(objective.length, "x28 + x29 + x30 + x31 >= 42"));
        constraints.add(equationFromString(objective.length, "x42 + x43 + x44 + x45 - x54 = 0"));
        constraints.add(equationFromString(objective.length, "x46 + x47 + x48 + x49 + x50 + x51 + x52 + x53 - x55 = 0"));
        constraints.add(equationFromString(objective.length, "x42 + x43 + x44 + x45 - x40 = 0"));
        constraints.add(equationFromString(objective.length, "x46 + x47 + x48 + x49 + x50 + x51 + x52 + x53 - x41 = 0"));
        constraints.add(equationFromString(objective.length, "x56 + x57 + x58 + x59 - x68 = 0"));
        constraints.add(equationFromString(objective.length, "x60 + x61 + x62 + x63 + x64 + x65 + x66 + x67 - x69 = 0"));
        constraints.add(equationFromString(objective.length, "x60 + x61 + x62 + x63 + x64 + x65 + x66 + x67 >= 51"));
        constraints.add(equationFromString(objective.length, "x56 + x57 + x58 + x59 >= 44"));
        constraints.add(equationFromString(objective.length, "x70 + x71 + x72 + x73 - x82 = 0"));
        constraints.add(equationFromString(objective.length, "x74 + x75 + x76 + x77 + x78 + x79 + x80 + x81 - x83 = 0"));
        constraints.add(equationFromString(objective.length, "x70 + x71 + x72 + x73 - x68 = 0"));
        constraints.add(equationFromString(objective.length, "x74 + x75 + x76 + x77 + x78 + x79 + x80 + x81 - x69 = 0"));
        constraints.add(equationFromString(objective.length, "x84 + x85 + x86 + x87 - x96 = 0"));
        constraints.add(equationFromString(objective.length, "x88 + x89 + x90 + x91 + x92 + x93 + x94 + x95 - x97 = 0"));
        constraints.add(equationFromString(objective.length, "x88 + x89 + x90 + x91 + x92 + x93 + x94 + x95 >= 51"));
        constraints.add(equationFromString(objective.length, "x84 + x85 + x86 + x87 >= 44"));
        constraints.add(equationFromString(objective.length, "x98 + x99 + x100 + x101 - x110 = 0"));
        constraints.add(equationFromString(objective.length, "x102 + x103 + x104 + x105 + x106 + x107 + x108 + x109 - x111 = 0"));
        constraints.add(equationFromString(objective.length, "x98 + x99 + x100 + x101 - x96 = 0"));
        constraints.add(equationFromString(objective.length, "x102 + x103 + x104 + x105 + x106 + x107 + x108 + x109 - x97 = 0"));
        constraints.add(equationFromString(objective.length, "x112 + x113 + x114 + x115 - x124 = 0"));
        constraints.add(equationFromString(objective.length, "x116 + x117 + x118 + x119 + x120 + x121 + x122 + x123 - x125 = 0"));
        constraints.add(equationFromString(objective.length, "x116 + x117 + x118 + x119 + x120 + x121 + x122 + x123 >= 49"));
        constraints.add(equationFromString(objective.length, "x112 + x113 + x114 + x115 >= 42"));
        constraints.add(equationFromString(objective.length, "x126 + x127 + x128 + x129 - x138 = 0"));
        constraints.add(equationFromString(objective.length, "x130 + x131 + x132 + x133 + x134 + x135 + x136 + x137 - x139 = 0"));
        constraints.add(equationFromString(objective.length, "x126 + x127 + x128 + x129 - x124 = 0"));
        constraints.add(equationFromString(objective.length, "x130 + x131 + x132 + x133 + x134 + x135 + x136 + x137 - x125 = 0"));
        constraints.add(equationFromString(objective.length, "x140 + x141 + x142 + x143 - x152 = 0"));
        constraints.add(equationFromString(objective.length, "x144 + x145 + x146 + x147 + x148 + x149 + x150 + x151 - x153 = 0"));
        constraints.add(equationFromString(objective.length, "x144 + x145 + x146 + x147 + x148 + x149 + x150 + x151 >= 59"));
        constraints.add(equationFromString(objective.length, "x140 + x141 + x142 + x143 >= 42"));
        constraints.add(equationFromString(objective.length, "x154 + x155 + x156 + x157 - x166 = 0"));
        constraints.add(equationFromString(objective.length, "x158 + x159 + x160 + x161 + x162 + x163 + x164 + x165 - x167 = 0"));
        constraints.add(equationFromString(objective.length, "x154 + x155 + x156 + x157 - x152 = 0"));
        constraints.add(equationFromString(objective.length, "x158 + x159 + x160 + x161 + x162 + x163 + x164 + x165 - x153 = 0"));
        constraints.add(equationFromString(objective.length, "x83 + x82 - x168 = 0"));
        constraints.add(equationFromString(objective.length, "x111 + x110 - x169 = 0"));
        constraints.add(equationFromString(objective.length, "x170 - x182 = 0"));
        constraints.add(equationFromString(objective.length, "x171 - x183 = 0"));
        constraints.add(equationFromString(objective.length, "x172 - x184 = 0"));
        constraints.add(equationFromString(objective.length, "x173 - x185 = 0"));
        constraints.add(equationFromString(objective.length, "x174 - x186 = 0"));
        constraints.add(equationFromString(objective.length, "x175 + x176 - x187 = 0"));
        constraints.add(equationFromString(objective.length, "x177 - x188 = 0"));
        constraints.add(equationFromString(objective.length, "x178 - x189 = 0"));
        constraints.add(equationFromString(objective.length, "x179 - x190 = 0"));
        constraints.add(equationFromString(objective.length, "x180 - x191 = 0"));
        constraints.add(equationFromString(objective.length, "x181 - x192 = 0"));
        constraints.add(equationFromString(objective.length, "x170 - x26 = 0"));
        constraints.add(equationFromString(objective.length, "x171 - x27 = 0"));
        constraints.add(equationFromString(objective.length, "x172 - x54 = 0"));
        constraints.add(equationFromString(objective.length, "x173 - x55 = 0"));
        constraints.add(equationFromString(objective.length, "x174 - x168 = 0"));
        constraints.add(equationFromString(objective.length, "x177 - x169 = 0"));
        constraints.add(equationFromString(objective.length, "x178 - x138 = 0"));
        constraints.add(equationFromString(objective.length, "x179 - x139 = 0"));
        constraints.add(equationFromString(objective.length, "x180 - x166 = 0"));
        constraints.add(equationFromString(objective.length, "x181 - x167 = 0"));
        constraints.add(equationFromString(objective.length, "x193 - x205 = 0"));
        constraints.add(equationFromString(objective.length, "x194 - x206 = 0"));
        constraints.add(equationFromString(objective.length, "x195 - x207 = 0"));
        constraints.add(equationFromString(objective.length, "x196 - x208 = 0"));
        constraints.add(equationFromString(objective.length, "x197 - x209 = 0"));
        constraints.add(equationFromString(objective.length, "x198 + x199 - x210 = 0"));
        constraints.add(equationFromString(objective.length, "x200 - x211 = 0"));
        constraints.add(equationFromString(objective.length, "x201 - x212 = 0"));
        constraints.add(equationFromString(objective.length, "x202 - x213 = 0"));
        constraints.add(equationFromString(objective.length, "x203 - x214 = 0"));
        constraints.add(equationFromString(objective.length, "x204 - x215 = 0"));
        constraints.add(equationFromString(objective.length, "x193 - x182 = 0"));
        constraints.add(equationFromString(objective.length, "x194 - x183 = 0"));
        constraints.add(equationFromString(objective.length, "x195 - x184 = 0"));
        constraints.add(equationFromString(objective.length, "x196 - x185 = 0"));
        constraints.add(equationFromString(objective.length, "x197 - x186 = 0"));
        constraints.add(equationFromString(objective.length, "x198 + x199 - x187 = 0"));
        constraints.add(equationFromString(objective.length, "x200 - x188 = 0"));
        constraints.add(equationFromString(objective.length, "x201 - x189 = 0"));
        constraints.add(equationFromString(objective.length, "x202 - x190 = 0"));
        constraints.add(equationFromString(objective.length, "x203 - x191 = 0"));
        constraints.add(equationFromString(objective.length, "x204 - x192 = 0"));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(7518.0, solution.getValue(), .0000001);
    }

    @Test
    public void testSolutionCallback() {
        // re-use the problem from testcase for MATH-288
        // it normally requires 5 iterations

        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 7, 3, 0, 0 }, 0 );

        List<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        constraints.add(new LinearConstraint(new double[] { 3, 0, -5, 0 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 2, 0, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 0, 3, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 0, 0 }, Relationship.LEQ, 1.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 0 }, Relationship.LEQ, 1.0));

        final SimplexSolver solver = new SimplexSolver();
        final SolutionCallback callback = new SolutionCallback();

        Assert.assertNull(callback.getSolution());
        Assert.assertFalse(callback.isSolutionOptimal());

        try {
            solver.optimize(new MaxIter(3), f, new LinearConstraintSet(constraints),
                            GoalType.MAXIMIZE, new NonNegativeConstraint(true), callback);
            Assert.fail("expected MathIllegalStateException");
        } catch (MathIllegalStateException ex) {
            // expected
        }

        final PointValuePair solution = callback.getSolution();
        Assert.assertNotNull(solution);
        Assert.assertTrue(validSolution(solution, constraints, 1e-4));
        Assert.assertFalse(callback.isSolutionOptimal());
        // the solution is clearly not optimal: optimal = 10.0
        Assert.assertEquals(7.0, solution.getValue(), 1e-4);
    }

    @Test(expected=MathIllegalArgumentException.class)
    public void testDimensionMatch() {
        // min 2x1 +15x2 +18x3
        // Subject to
        //   -x1 +2x2 -6x3  <=-10
        //         x2 +2x3  <= 6
        //   2x1      +10x3 <= 19
        //   -x1  +x2       <= -2
        // x1,x2,x3 >= 0

        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 2, 15, 18 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
        // this constraint is wrong, the dimension is less than expected one
        constraints.add(new LinearConstraint(new double[] { -1, 2 - 6 }, Relationship.LEQ, -10));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 2 }, Relationship.LEQ, 6));
        constraints.add(new LinearConstraint(new double[] { 2, 0, 10 }, Relationship.LEQ, 19));
        constraints.add(new LinearConstraint(new double[] { -1, 1, 0 }, Relationship.LEQ, -2));

        SimplexSolver solver = new SimplexSolver();
        solver.optimize(f,
                        new LinearConstraintSet(constraints),
                        new NonNegativeConstraint(true),
                        PivotSelectionRule.BLAND);
    }

    /**
     * Converts a test string to a {@link LinearConstraint}.
     * Ex: x0 + x1 + x2 + x3 - x12 = 0
     */
    private LinearConstraint equationFromString(int numCoefficients, String s) {
        Relationship relationship;
        if (s.contains(">=")) {
            relationship = Relationship.GEQ;
        } else if (s.contains("<=")) {
            relationship = Relationship.LEQ;
        } else if (s.contains("=")) {
            relationship = Relationship.EQ;
        } else {
            throw new IllegalArgumentException();
        }

        String[] equationParts = s.split("[>|<]?=");
        double rhs = Double.parseDouble(equationParts[1].trim());

        double[] lhs = new double[numCoefficients];
        String left = equationParts[0].replaceAll(" ?x", "");
        String[] coefficients = left.split(" ");
        for (String coefficient : coefficients) {
            double value = coefficient.charAt(0) == '-' ? -1 : 1;
            int index = Integer.parseInt(coefficient.replaceFirst("[+|-]", "").trim());
            lhs[index] = value;
        }
        return new LinearConstraint(lhs, relationship, rhs);
    }

    private static boolean validSolution(PointValuePair solution, List<LinearConstraint> constraints, double epsilon) {
        double[] vals = solution.getPoint();
        for (LinearConstraint c : constraints) {
            double[] coeffs = c.getCoefficients().toArray();
            double result = 0.0d;
            for (int i = 0; i < vals.length; i++) {
                result += vals[i] * coeffs[i];
            }

            switch (c.getRelationship()) {
            case EQ:
                if (!Precision.equals(result, c.getValue(), epsilon)) {
                    return false;
                }
                break;

            case GEQ:
                if (Precision.compareTo(result, c.getValue(), epsilon) < 0) {
                    return false;
                }
                break;

            case LEQ:
                if (Precision.compareTo(result, c.getValue(), epsilon) > 0) {
                    return false;
                }
                break;
            }
        }

        return true;
    }

}