org.apache.commons.math3.optim.PointValuePair Java Examples

@Test
public void testHalfBounded() {
    final BiQuadratic biQuadratic = new BiQuadratic(4.0, 4.0,
                                                    1.0, Double.POSITIVE_INFINITY,
                                                    Double.NEGATIVE_INFINITY, 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-10, 1.0e-20));
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[] { 1.0, 0.5 });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(400),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(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 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);
}
 

/**
 * @param maxIterations Maximal number of iterations.
 * @param stopFitness Whether to stop if objective function value is smaller than
 * {@code stopFitness}.
 * @param isActiveCMA Chooses the covariance matrix update method.
 * @param diagonalOnly Number of initial iterations, where the covariance matrix
 * remains diagonal.
 * @param checkFeasableCount Determines how often new random objective variables are
 * generated in case they are out of bounds.
 * @param random Random generator.
 * @param generateStatistics Whether statistic data is collected.
 * @param checker Convergence checker.
 *
 * @since 3.1
 */
public CMAESOptimizer(int maxIterations,
                      double stopFitness,
                      boolean isActiveCMA,
                      int diagonalOnly,
                      int checkFeasableCount,
                      RandomGenerator random,
                      boolean generateStatistics,
                      ConvergenceChecker<PointValuePair> checker) {
    super(checker);
    this.maxIterations = maxIterations;
    this.stopFitness = stopFitness;
    this.isActiveCMA = isActiveCMA;
    this.diagonalOnly = diagonalOnly;
    this.checkFeasableCount = checkFeasableCount;
    this.random = random;
    this.generateStatistics = generateStatistics;
}
 

@Test
public void testMinimize2() {
    SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
    final FourExtrema fourExtrema = new FourExtrema();

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(200),
                             new ObjectiveFunction(fourExtrema),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 1, 0 }),
                             new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
    Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
    Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
    Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 2e-12);
    Assert.assertTrue(optimizer.getEvaluations() > 120);
    Assert.assertTrue(optimizer.getEvaluations() < 150);

    // Check that the number of iterations is updated (MATH-949).
    Assert.assertTrue(optimizer.getIterations() > 0);
}
 

@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));
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[] { 1.0, 0.5 });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(600),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(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 testNonInversible() {
    LinearProblem problem = new LinearProblem(new double[][] {
            {  1, 2, -3 },
            {  2, 1,  3 },
            { -3, 0, -9 }
    }, new double[] { 1, 1, 1 });
    NonLinearConjugateGradientOptimizer optimizer
        = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                  new SimpleValueChecker(1e-6, 1e-6),
                                                  1e-3, 1e-3, 1);
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 0, 0, 0 }));
    Assert.assertTrue(optimum.getValue() > 0.5);
}
 

@Test
public void testMinimize1() {
    SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
    final FourExtrema fourExtrema = new FourExtrema();

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(200),
                             new ObjectiveFunction(fourExtrema),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { -3, 0 }),
                             new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
    Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 4e-6);
    Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
    Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 8e-13);
    Assert.assertTrue(optimizer.getEvaluations() > 120);
    Assert.assertTrue(optimizer.getEvaluations() < 150);

    // Check that the number of iterations is updated (MATH-949).
    Assert.assertTrue(optimizer.getIterations() > 0);
}
 

/** {@inheritDoc} */
@Override
protected PointValuePair doOptimize() {
    final double[] lowerBound = getLowerBound();
    final double[] upperBound = getUpperBound();

    // Validity checks.
    setup(lowerBound, upperBound);

    isMinimize = (getGoalType() == GoalType.MINIMIZE);
    currentBest = new ArrayRealVector(getStartPoint());

    final double value = bobyqa(lowerBound, upperBound);

    return new PointValuePair(currentBest.getDataRef(),
                              isMinimize ? value : -value);
}
 

@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 testStartSimplexInsideRange() {
    final BiQuadratic biQuadratic = new BiQuadratic(2.0, 2.5, 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);
    final AbstractSimplex simplex = 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(new MaxEval(300),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(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);
}
 

/**
 * Compute and evaluate a new simplex.
 *
 * @param evaluationFunction Evaluation function.
 * @param original Original simplex (to be preserved).
 * @param coeff Linear coefficient.
 * @param comparator Comparator to use to sort simplex vertices from best
 * to poorest.
 * @return the best point in the transformed simplex.
 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
 * if the maximal number of evaluations is exceeded.
 */
private PointValuePair evaluateNewSimplex(final MultivariateFunction evaluationFunction,
                                              final PointValuePair[] original,
                                              final double coeff,
                                              final Comparator<PointValuePair> comparator) {
    final double[] xSmallest = original[0].getPointRef();
    // Perform a linear transformation on all the simplex points,
    // except the first one.
    setPoint(0, original[0]);
    final int dim = getDimension();
    for (int i = 1; i < getSize(); i++) {
        final double[] xOriginal = original[i].getPointRef();
        final double[] xTransformed = new double[dim];
        for (int j = 0; j < dim; j++) {
            xTransformed[j] = xSmallest[j] + coeff * (xSmallest[j] - xOriginal[j]);
        }
        setPoint(i, new PointValuePair(xTransformed, Double.NaN, false));
    }

    // Evaluate the simplex.
    evaluate(evaluationFunction, comparator);

    return getPoint(0);
}
 

@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));
    Assert.assertEquals(1.0d, solution.getValue(), epsilon);
    Assert.assertTrue(validSolution(solution, constraints, epsilon));        
}
 

/**
 * @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 PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(func),
                                                 goal,
                                                 new InitialGuess(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);
    }
}
 

/**
 * Build an initial simplex.
 *
 * @param startPoint First point of the simplex.
 * @throws DimensionMismatchException if the start point does not match
 * simplex dimension.
 */
public void build(final double[] startPoint) {
    if (dimension != startPoint.length) {
        throw new DimensionMismatchException(dimension, startPoint.length);
    }

    // Set first vertex.
    simplex = new PointValuePair[dimension + 1];
    simplex[0] = new PointValuePair(startPoint, Double.NaN);

    // Set remaining vertices.
    for (int i = 0; i < dimension; i++) {
        final double[] confI = startConfiguration[i];
        final double[] vertexI = new double[dimension];
        for (int k = 0; k < dimension; k++) {
            vertexI[k] = startPoint[k] + confI[k];
        }
        simplex[i + 1] = new PointValuePair(vertexI, Double.NaN);
    }
}
 

@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));
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[] { 1.0, 0.5 });

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

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

/**
 * This constructor allows to specify a user-defined convergence checker,
 * in addition to the parameters that control the default convergence
 * checking procedure and the line search tolerances.
 *
 * @param rel Relative threshold for this optimizer.
 * @param abs Absolute threshold for this optimizer.
 * @param lineRel Relative threshold for the internal line search optimizer.
 * @param lineAbs Absolute threshold for the internal line search optimizer.
 * @param checker Convergence checker.
 * @throws NotStrictlyPositiveException if {@code abs <= 0}.
 * @throws NumberIsTooSmallException if {@code rel < 2 * Math.ulp(1d)}.
 */
public PowellOptimizer(double rel,
                       double abs,
                       double lineRel,
                       double lineAbs,
                       ConvergenceChecker<PointValuePair> checker) {
    super(checker);

    if (rel < MIN_RELATIVE_TOLERANCE) {
        throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);
    }
    if (abs <= 0) {
        throw new NotStrictlyPositiveException(abs);
    }
    relativeThreshold = rel;
    absoluteThreshold = abs;

    // Create the line search optimizer.
    line = new LineSearch(lineRel,
                          lineAbs);
}
 

@Test
public void testMinimize2() {
    SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
    final FourExtrema fourExtrema = new FourExtrema();

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(200),
                             new ObjectiveFunction(fourExtrema),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 1, 0 }),
                             new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
    Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
    Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
    Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 2e-12);
    Assert.assertTrue(optimizer.getEvaluations() > 120);
    Assert.assertTrue(optimizer.getEvaluations() < 150);

    // Check that the number of iterations is updated (MATH-949).
    Assert.assertTrue(optimizer.getIterations() > 0);
}
 

@Test
public void testUnbounded() {
    final BiQuadratic biQuadratic = new BiQuadratic(4.0, 0.0,
                                                    Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY,
                                                    Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);
    final MultivariateFunctionPenaltyAdapter wrapped
        = new MultivariateFunctionPenaltyAdapter(biQuadratic,
                                                 biQuadratic.getLower(),
                                                 biQuadratic.getUpper(),
                                                 1000.0, new double[] { 100.0, 100.0 });

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[] { 1.0, 0.5 });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(300),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(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 testMoreEstimatedParametersSimple() {
    LinearProblem problem = new LinearProblem(new double[][] {
            { 3.0, 2.0,  0.0, 0.0 },
            { 0.0, 1.0, -1.0, 1.0 },
            { 2.0, 0.0,  1.0, 0.0 }
    }, new double[] { 7.0, 3.0, 5.0 });

    NonLinearConjugateGradientOptimizer optimizer
        = new NonLinearConjugateGradientOptimizer(NonLinearConjugateGradientOptimizer.Formula.POLAK_RIBIERE,
                                                  new SimpleValueChecker(1e-6, 1e-6));
    PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             problem.getObjectiveFunction(),
                             problem.getObjectiveFunctionGradient(),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 7, 6, 5, 4 }));
    Assert.assertEquals(0, optimum.getValue(), 1.0e-10);

}
 

@Test
public void testStartSimplexOutsideRange() {
    final BiQuadratic biQuadratic = new BiQuadratic(2.0, 2.5, 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(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[] { 1.0, 0.5 });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(300),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(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 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);
    final Gaussian2D function = new Gaussian2D(0, 0, 1);
    PointValuePair estimate = optimizer.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(function),
                                                 GoalType.MAXIMIZE,
                                                 new InitialGuess(function.getMaximumPosition()),
                                                 new MultiDirectionalSimplex(2));
    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 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 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 testUnbounded() {
    final BiQuadratic biQuadratic = new BiQuadratic(4.0, 0.0,
                                                    Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY,
                                                    Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);
    final MultivariateFunctionPenaltyAdapter wrapped
        = new MultivariateFunctionPenaltyAdapter(biQuadratic,
                                                 biQuadratic.getLower(),
                                                 biQuadratic.getUpper(),
                                                 1000.0, new double[] { 100.0, 100.0 });

    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final AbstractSimplex simplex = new NelderMeadSimplex(new double[] { 1.0, 0.5 });

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(300),
                             new ObjectiveFunction(wrapped),
                             simplex,
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { -1.5, 4.0 }));

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

/**
 * @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 PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

    final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                 new ObjectiveFunction(func),
                                                 goal,
                                                 new InitialGuess(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 testMaximize1() {
    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final FourExtrema fourExtrema = new FourExtrema();

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             new ObjectiveFunction(fourExtrema),
                             GoalType.MAXIMIZE,
                             new InitialGuess(new double[] { -3, 0 }),
                             new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
    Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 1e-5);
    Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
    Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 3e-12);
    Assert.assertTrue(optimizer.getEvaluations() > 60);
    Assert.assertTrue(optimizer.getEvaluations() < 90);

    // Check that the number of iterations is updated (MATH-949).
    Assert.assertTrue(optimizer.getIterations() > 0);
}
 

@Test
public void testMinimize2() {
    SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
    final FourExtrema fourExtrema = new FourExtrema();

    final PointValuePair optimum
        = optimizer.optimize(new MaxEval(100),
                             new ObjectiveFunction(fourExtrema),
                             GoalType.MINIMIZE,
                             new InitialGuess(new double[] { 1, 0 }),
                             new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
    Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 5e-6);
    Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 6e-6);
    Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 1e-11);
    Assert.assertTrue(optimizer.getEvaluations() > 60);
    Assert.assertTrue(optimizer.getEvaluations() < 90);

    // Check that the number of iterations is updated (MATH-949).
    Assert.assertTrue(optimizer.getIterations() > 0);
}
 

/**
 * Build an initial simplex.
 *
 * @param startPoint First point of the simplex.
 * @throws DimensionMismatchException if the start point does not match
 * simplex dimension.
 */
public void build(final double[] startPoint) {
    if (dimension != startPoint.length) {
        throw new DimensionMismatchException(dimension, startPoint.length);
    }

    // Set first vertex.
    simplex = new PointValuePair[dimension + 1];
    simplex[0] = new PointValuePair(startPoint, Double.NaN);

    // Set remaining vertices.
    for (int i = 0; i < dimension; i++) {
        final double[] confI = startConfiguration[i];
        final double[] vertexI = new double[dimension];
        for (int k = 0; k < dimension; k++) {
            vertexI[k] = startPoint[k] + confI[k];
        }
        simplex[i + 1] = new PointValuePair(vertexI, Double.NaN);
    }
}
 

@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);
}
 

/**
 * @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,
           "");
}