org.apache.commons.math3.optimization.GoalType Java Examples

@Test
public void testRedundantEquations() {
    LinearProblem problem = new LinearProblem(new double[][] {
            { 1.0,  1.0 },
            { 1.0, -1.0 },
            { 1.0,  3.0 }
    }, new double[] { 3.0, 1.0, 5.0 });

    NonLinearConjugateGradientOptimizer optimizer =
        new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE,
                                                new SimpleValueChecker(1e-6, 1e-6));
    PointValuePair optimum =
        optimizer.optimize(100, problem, GoalType.MINIMIZE, new double[] { 1, 1 });
    Assert.assertEquals(2.0, optimum.getPoint()[0], 1.0e-8);
    Assert.assertEquals(1.0, optimum.getPoint()[1], 1.0e-8);

}
 

/** {@inheritDoc} */
public PointValuePair optimize(final LinearObjectiveFunction f,
                                   final Collection<LinearConstraint> constraints,
                                   final GoalType goalType, final boolean restrictToNonNegative)
     throws MathIllegalStateException {

    // store linear problem characteristics
    this.function          = f;
    this.linearConstraints = constraints;
    this.goal              = goalType;
    this.nonNegative       = restrictToNonNegative;

    iterations  = 0;

    // solve the problem
    return doOptimize();

}
 

@Test
public void testBadFunction() {
    UnivariateFunction f = new UnivariateFunction() {
            public double value(double x) {
                if (x < 0) {
                    throw new LocalException();
                }
                return 0;
            }
        };
    UnivariateOptimizer underlying = new BrentOptimizer(1e-9, 1e-14);
    JDKRandomGenerator g = new JDKRandomGenerator();
    g.setSeed(4312000053L);
    UnivariateMultiStartOptimizer<UnivariateFunction> optimizer =
        new UnivariateMultiStartOptimizer<UnivariateFunction>(underlying, 5, g);
 
    try {
        optimizer.optimize(300, f, GoalType.MINIMIZE, -0.3, -0.2);
        Assert.fail();
    } catch (LocalException e) {
        // Expected.
    }

    // Ensure that the exception was thrown because no optimum was found.
    Assert.assertTrue(optimizer.getOptima()[0] == null);
}
 

/**
 * Sort the optima from best to worst, followed by {@code null} elements.
 *
 * @param goal Goal type.
 */
private void sortPairs(final GoalType goal) {
    Arrays.sort(optima, new Comparator<UnivariatePointValuePair>() {
            public int compare(final UnivariatePointValuePair o1,
                               final UnivariatePointValuePair o2) {
                if (o1 == null) {
                    return (o2 == null) ? 0 : 1;
                } else if (o2 == null) {
                    return -1;
                }
                final double v1 = o1.getValue();
                final double v2 = o2.getValue();
                return (goal == GoalType.MINIMIZE) ?
                    Double.compare(v1, v2) : Double.compare(v2, v1);
            }
        });
}
 

@Ignore @Test
public void testConstrainedRosenWithMoreInterpolationPoints() {
    final double[] startPoint = point(DIM, 0.1);
    final double[][] boundaries = boundaries(DIM, -1, 2);
    final PointValuePair expected = new PointValuePair(point(DIM, 1.0), 0.0);

    // This should have been 78 because in the code the hard limit is
    // said to be
    //   ((DIM + 1) * (DIM + 2)) / 2 - (2 * DIM + 1)
    // i.e. 78 in this case, but the test fails for 48, 59, 62, 63, 64,
    // 65, 66, ...
    final int maxAdditionalPoints = 47;

    for (int num = 1; num <= maxAdditionalPoints; num++) {
        doTest(new Rosen(), startPoint, boundaries,
               GoalType.MINIMIZE,
               1e-12, 1e-6, 2000,
               num,
               expected,
               "num=" + num);
    }
}
 

@Test
public void testBadFunction() {
    UnivariateFunction f = new UnivariateFunction() {
            public double value(double x) {
                if (x < 0) {
                    throw new LocalException();
                }
                return 0;
            }
        };
    UnivariateOptimizer underlying = new BrentOptimizer(1e-9, 1e-14);
    JDKRandomGenerator g = new JDKRandomGenerator();
    g.setSeed(4312000053L);
    UnivariateMultiStartOptimizer<UnivariateFunction> optimizer =
        new UnivariateMultiStartOptimizer<UnivariateFunction>(underlying, 5, g);
 
    try {
        optimizer.optimize(300, f, GoalType.MINIMIZE, -0.3, -0.2);
        Assert.fail();
    } catch (LocalException e) {
        // Expected.
    }

    // Ensure that the exception was thrown because no optimum was found.
    Assert.assertTrue(optimizer.getOptima()[0] == null);
}
 

@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(f, constraints, GoalType.MINIMIZE, true);
    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(f, constraints, GoalType.MAXIMIZE, 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 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(f, constraints, GoalType.MINIMIZE, true);
    Assert.assertEquals(1.0d, solution.getValue(), epsilon);
    Assert.assertTrue(validSolution(solution, constraints, epsilon));
}
 

@Test
public void testLeastSquares3() {

    final RealMatrix factors =
        new Array2DRowRealMatrix(new double[][] {
                { 1, 0 },
                { 0, 1 }
            }, false);
    LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
            public double[] value(double[] variables) {
                return factors.operate(variables);
            }
        }, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
                { 1, 1.2 }, { 1.2, 2 }
            }));
    SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
    optimizer.setSimplex(new NelderMeadSimplex(2));
    PointValuePair optimum =
        optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
    Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
    Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
    Assert.assertTrue(optimizer.getEvaluations() > 60);
    Assert.assertTrue(optimizer.getEvaluations() < 80);
    Assert.assertTrue(optimum.getValue() < 1e-6);
}
 

@Test
public void testOptimumOutsideRange() {

    final BiQuadratic biQuadratic = new BiQuadratic(4.0, 0.0, 1.0, 3.0, 2.0, 3.0);
    final MultivariateFunctionMappingAdapter wrapped =
            new MultivariateFunctionMappingAdapter(biQuadratic,
                                                       biQuadratic.getLower(),
                                                       biQuadratic.getUpper());

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    optimizer.setSimplex(new NelderMeadSimplex(new double[][] {
        wrapped.boundedToUnbounded(new double[] { 1.5, 2.75 }),
        wrapped.boundedToUnbounded(new double[] { 1.5, 2.95 }),
        wrapped.boundedToUnbounded(new double[] { 1.7, 2.90 })
    }));

    final PointValuePair optimum
        = optimizer.optimize(100, wrapped, GoalType.MINIMIZE,
                             wrapped.boundedToUnbounded(new double[] { 1.5, 2.25 }));
    final double[] bounded = wrapped.unboundedToBounded(optimum.getPoint());

    Assert.assertEquals(biQuadratic.getBoundedXOptimum(), bounded[0], 2e-7);
    Assert.assertEquals(biQuadratic.getBoundedYOptimum(), bounded[1], 2e-7);

}
 

@Test
public void testLeastSquares3() {

    final RealMatrix factors =
        new Array2DRowRealMatrix(new double[][] {
                { 1, 0 },
                { 0, 1 }
            }, false);
    LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
            public double[] value(double[] variables) {
                return factors.operate(variables);
            }
        }, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
                { 1, 1.2 }, { 1.2, 2 }
            }));
    SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
    optimizer.setSimplex(new NelderMeadSimplex(2));
    PointValuePair optimum =
        optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
    Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
    Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
    Assert.assertTrue(optimizer.getEvaluations() > 60);
    Assert.assertTrue(optimizer.getEvaluations() < 80);
    Assert.assertTrue(optimum.getValue() < 1e-6);
}
 

/**
 * Build a tableau for a linear problem.
 * @param f linear objective function
 * @param constraints linear constraints
 * @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE}
 * or {@link GoalType#MINIMIZE}
 * @param restrictToNonNegative whether to restrict the variables to non-negative values
 * @param epsilon amount of error to accept when checking for optimality
 * @param maxUlps amount of error to accept in floating point comparisons
 */
SimplexTableau(final LinearObjectiveFunction f,
               final Collection<LinearConstraint> constraints,
               final GoalType goalType, final boolean restrictToNonNegative,
               final double epsilon,
               final int maxUlps) {
    this.f                      = f;
    this.constraints            = normalizeConstraints(constraints);
    this.restrictToNonNegative  = restrictToNonNegative;
    this.epsilon                = epsilon;
    this.maxUlps                = maxUlps;
    this.numDecisionVariables   = f.getCoefficients().getDimension() +
                                  (restrictToNonNegative ? 0 : 1);
    this.numSlackVariables      = getConstraintTypeCounts(Relationship.LEQ) +
                                  getConstraintTypeCounts(Relationship.GEQ);
    this.numArtificialVariables = getConstraintTypeCounts(Relationship.EQ) +
                                  getConstraintTypeCounts(Relationship.GEQ);
    this.tableau = createTableau(goalType == GoalType.MAXIMIZE);
    initializeColumnLabels();
}
 

@Test
public void testSinMin() {
    UnivariateFunction f = new Sin();
    UnivariateOptimizer underlying = new BrentOptimizer(1e-10, 1e-14);
    JDKRandomGenerator g = new JDKRandomGenerator();
    g.setSeed(44428400075l);
    UnivariateMultiStartOptimizer<UnivariateFunction> optimizer =
        new UnivariateMultiStartOptimizer<UnivariateFunction>(underlying, 10, g);
    optimizer.optimize(300, f, GoalType.MINIMIZE, -100.0, 100.0);
    UnivariatePointValuePair[] optima = optimizer.getOptima();
    for (int i = 1; i < optima.length; ++i) {
        double d = (optima[i].getPoint() - optima[i-1].getPoint()) / (2 * FastMath.PI);
        Assert.assertTrue(FastMath.abs(d - FastMath.rint(d)) < 1.0e-8);
        Assert.assertEquals(-1.0, f.value(optima[i].getPoint()), 1.0e-10);
        Assert.assertEquals(f.value(optima[i].getPoint()), optima[i].getValue(), 1.0e-10);
    }
    Assert.assertTrue(optimizer.getEvaluations() > 200);
    Assert.assertTrue(optimizer.getEvaluations() < 300);
}
 

@Test
public void testOptimumOutsideRange() {

    final BiQuadratic biQuadratic = new BiQuadratic(4.0, 0.0, 1.0, 3.0, 2.0, 3.0);
    final MultivariateFunctionPenaltyAdapter wrapped =
            new MultivariateFunctionPenaltyAdapter(biQuadratic,
                                                       biQuadratic.getLower(),
                                                       biQuadratic.getUpper(),
                                                       1000.0, new double[] { 100.0, 100.0 });

    SimplexOptimizer optimizer = new SimplexOptimizer(new SimplePointChecker<PointValuePair>(1.0e-11, 1.0e-20));
    optimizer.setSimplex(new NelderMeadSimplex(new double[] { 1.0, 0.5 }));

    final PointValuePair optimum
        = optimizer.optimize(600, wrapped, GoalType.MINIMIZE, new double[] { -1.5, 4.0 });

    Assert.assertEquals(biQuadratic.getBoundedXOptimum(), optimum.getPoint()[0], 2e-7);
    Assert.assertEquals(biQuadratic.getBoundedYOptimum(), optimum.getPoint()[1], 2e-7);

}
 

@Test
public void testCircleFitting() {
    CircleScalar circle = new CircleScalar();
    circle.addPoint( 30.0,  68.0);
    circle.addPoint( 50.0,  -6.0);
    circle.addPoint(110.0, -20.0);
    circle.addPoint( 35.0,  15.0);
    circle.addPoint( 45.0,  97.0);
    NonLinearConjugateGradientOptimizer optimizer =
        new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE,
                                                new SimpleValueChecker(1e-30, 1e-30),
                                                new BrentSolver(1e-15, 1e-13));
    PointValuePair optimum =
        optimizer.optimize(100, circle, GoalType.MINIMIZE, new double[] { 98.680, 47.345 });
    Point2D.Double center = new Point2D.Double(optimum.getPointRef()[0], optimum.getPointRef()[1]);
    Assert.assertEquals(69.960161753, circle.getRadius(center), 1.0e-8);
    Assert.assertEquals(96.075902096, center.x, 1.0e-8);
    Assert.assertEquals(48.135167894, center.y, 1.0e-8);
}
 

/**
 * @param func Function to optimize.
 * @param startPoint Starting point.
 * @param boundaries Upper / lower point limit.
 * @param goal Minimization or maximization.
 * @param fTol Tolerance relative error on the objective function.
 * @param pointTol Tolerance for checking that the optimum is correct.
 * @param maxEvaluations Maximum number of evaluations.
 * @param expected Expected point / value.
 */
private void doTest(MultivariateFunction func,
                    double[] startPoint,
                    double[][] boundaries,
                    GoalType goal,
                    double fTol,
                    double pointTol,
                    int maxEvaluations,
                    PointValuePair expected) {
    doTest(func,
           startPoint,
           boundaries,
           goal,
           fTol,
           pointTol,
           maxEvaluations,
           0,
           expected,
           "");
}
 

@Test
public void testMath283() {
    // fails because MultiDirectional.iterateSimplex is looping forever
    // the while(true) should be replaced with a convergence check
    SimplexOptimizer optimizer = new SimplexOptimizer(1e-14, 1e-14);
    optimizer.setSimplex(new MultiDirectionalSimplex(2));
    final Gaussian2D function = new Gaussian2D(0, 0, 1);
    PointValuePair estimate = optimizer.optimize(1000, function,
                                                     GoalType.MAXIMIZE, function.getMaximumPosition());
    final double EPSILON = 1e-5;
    final double expectedMaximum = function.getMaximum();
    final double actualMaximum = estimate.getValue();
    Assert.assertEquals(expectedMaximum, actualMaximum, EPSILON);

    final double[] expectedPosition = function.getMaximumPosition();
    final double[] actualPosition = estimate.getPoint();
    Assert.assertEquals(expectedPosition[0], actualPosition[0], EPSILON );
    Assert.assertEquals(expectedPosition[1], actualPosition[1], EPSILON );
}
 

@Test
public void testPowell() {
    MultivariateFunction powell =
        new MultivariateFunction() {
            public double value(double[] x) {
                ++count;
                double a = x[0] + 10 * x[1];
                double b = x[2] - x[3];
                double c = x[1] - 2 * x[2];
                double d = x[0] - x[3];
                return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d;
            }
        };

    count = 0;
    SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
    optimizer.setSimplex(new MultiDirectionalSimplex(4));
    PointValuePair optimum =
        optimizer.optimize(1000, powell, GoalType.MINIMIZE, new double[] { 3, -1, 0, 1 });
    Assert.assertEquals(count, optimizer.getEvaluations());
    Assert.assertTrue(optimizer.getEvaluations() > 800);
    Assert.assertTrue(optimizer.getEvaluations() < 900);
    Assert.assertTrue(optimum.getValue() > 1e-2);
}
 

@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(f, constraints, GoalType.MAXIMIZE, 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 testLeastSquares2() {

    final RealMatrix factors =
        new Array2DRowRealMatrix(new double[][] {
                { 1, 0 },
                { 0, 1 }
            }, false);
    LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
            public double[] value(double[] variables) {
                return factors.operate(variables);
            }
        }, new double[] { 2, -3 }, new double[] { 10, 0.1 });
    SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
    optimizer.setSimplex(new NelderMeadSimplex(2));
    PointValuePair optimum =
        optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
    Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
    Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
    Assert.assertTrue(optimizer.getEvaluations() > 60);
    Assert.assertTrue(optimizer.getEvaluations() < 80);
    Assert.assertTrue(optimum.getValue() < 1e-6);
}
 

@Test
public void testMinimumIsOnIntervalBoundary() {
    final UnivariateFunction func = new UnivariateFunction() {
            public double value(double x) {
                return x * x;
            }
        };

    final BracketFinder bFind = new BracketFinder();

    bFind.search(func, GoalType.MINIMIZE, 0, 1);
    Assert.assertTrue(bFind.getLo() <= 0);
    Assert.assertTrue(0 <= bFind.getHi());

    bFind.search(func, GoalType.MINIMIZE, -1, 0);
    Assert.assertTrue(bFind.getLo() <= 0);
    Assert.assertTrue(0 <= bFind.getHi());
}
 

/**
 * @param func Function to optimize.
 * @param optimum Expected optimum.
 * @param init Starting point.
 * @param goal Minimization or maximization.
 * @param fTol Tolerance (relative error on the objective function) for
 * "Powell" algorithm.
 * @param pointTol Tolerance for checking that the optimum is correct.
 */
private void doTest(MultivariateFunction func,
                    double[] optimum,
                    double[] init,
                    GoalType goal,
                    double fTol,
                    double pointTol) {
    final MultivariateOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(1000, func, goal, init);
    final double[] point = result.getPoint();

    for (int i = 0, dim = optimum.length; i < dim; i++) {
        Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                            optimum[i], point[i], pointTol);
    }
}
 

@Test
public void testMath864() {
    final CMAESOptimizer optimizer = new CMAESOptimizer();
    final MultivariateFunction fitnessFunction = new MultivariateFunction() {
            public double value(double[] parameters) {
                final double target = 1;
                final double error = target - parameters[0];
                return error * error;
            }
        };

    final double[] start = { 0 };
    final double[] lower = { -1e6 };
    final double[] upper = { 1.5 };
    final double[] result = optimizer.optimize(10000, fitnessFunction, GoalType.MINIMIZE,
                                               start, lower, upper).getPoint();
    Assert.assertTrue("Out of bounds (" + result[0] + " > " + upper[0] + ")",
                      result[0] <= upper[0]);
}
 

/** {@inheritDoc} */
public PointValuePair optimize(final LinearObjectiveFunction f,
                               final Collection<LinearConstraint> constraints,
                               final GoalType goalType, final boolean restrictToNonNegative)
    throws MathIllegalStateException {

    // store linear problem characteristics
    this.function          = f;
    this.linearConstraints = constraints;
    this.goal              = goalType;
    this.nonNegative       = restrictToNonNegative;

    iterations  = 0;

    // solve the problem
    return doOptimize();

}
 

@Test
public void testInconsistentEquations() {
    LinearProblem problem = new LinearProblem(new double[][] {
            { 1.0,  1.0 },
            { 1.0, -1.0 },
            { 1.0,  3.0 }
    }, new double[] { 3.0, 1.0, 4.0 });

    NonLinearConjugateGradientOptimizer optimizer =
        new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE,
                                                new SimpleValueChecker(1e-6, 1e-6));
    PointValuePair optimum =
        optimizer.optimize(100, problem, GoalType.MINIMIZE, new double[] { 1, 1 });
    Assert.assertTrue(optimum.getValue() > 0.1);

}
 

/**
 * Build a tableau for a linear problem.
 * @param f linear objective function
 * @param constraints linear constraints
 * @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE} or {@link GoalType#MINIMIZE}
 * @param restrictToNonNegative whether to restrict the variables to non-negative values
 * @param epsilon amount of error to accept when checking for optimality
 * @param maxUlps amount of error to accept in floating point comparisons
 */
SimplexTableau(final LinearObjectiveFunction f,
               final Collection<LinearConstraint> constraints,
               final GoalType goalType, final boolean restrictToNonNegative,
               final double epsilon,
               final int maxUlps) {
    this.f                      = f;
    this.constraints            = normalizeConstraints(constraints);
    this.restrictToNonNegative  = restrictToNonNegative;
    this.epsilon                = epsilon;
    this.maxUlps                = maxUlps;
    this.numDecisionVariables   = f.getCoefficients().getDimension() +
                                  (restrictToNonNegative ? 0 : 1);
    this.numSlackVariables      = getConstraintTypeCounts(Relationship.LEQ) +
                                  getConstraintTypeCounts(Relationship.GEQ);
    this.numArtificialVariables = getConstraintTypeCounts(Relationship.EQ) +
                                  getConstraintTypeCounts(Relationship.GEQ);
    this.tableau = createTableau(goalType == GoalType.MAXIMIZE);
    initializeColumnLabels();
}
 

@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(f, constraints, GoalType.MAXIMIZE, 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 testNoDependency() {
    LinearProblem problem = new LinearProblem(new double[][] {
            { 2, 0, 0, 0, 0, 0 },
            { 0, 2, 0, 0, 0, 0 },
            { 0, 0, 2, 0, 0, 0 },
            { 0, 0, 0, 2, 0, 0 },
            { 0, 0, 0, 0, 2, 0 },
            { 0, 0, 0, 0, 0, 2 }
    }, new double[] { 0.0, 1.1, 2.2, 3.3, 4.4, 5.5 });
    NonLinearConjugateGradientOptimizer optimizer =
        new NonLinearConjugateGradientOptimizer(ConjugateGradientFormula.POLAK_RIBIERE,
                                                new SimpleValueChecker(1e-6, 1e-6));
    PointValuePair optimum =
        optimizer.optimize(100, problem, GoalType.MINIMIZE, new double[] { 0, 0, 0, 0, 0, 0 });
    for (int i = 0; i < problem.target.length; ++i) {
        Assert.assertEquals(0.55 * i, optimum.getPoint()[i], 1.0e-10);
    }
}
 

@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(f, constraints, GoalType.MAXIMIZE, 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);
}