Package org.apache.commons.math3.analysis

Examples of org.apache.commons.math3.analysis.QuinticFunction

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        // of zero a 0.
        // The other roots are less well to find, in particular the root at 1, because
        // the function grows fast for x>1.
        // The function has extrema (first derivative is zero) at 0.27195613 and 0.82221643,
        // intervals containing these values are harder for the solvers.
        UnivariateFunction f = new QuinticFunction();
        double result;
        // Brent-Dekker solver.
        UnivariateSolver solver = new BrentSolver();
        // Symmetric bracket around 0. Test whether solvers can handle hitting
        // the root in the first iteration.
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        }
    }

    @Test
    public void testInitialGuess() {
        MonitoredFunction f = new MonitoredFunction(new QuinticFunction());
        BrentSolver solver = new BrentSolver();
        double result;

        // no guess
        result = solver.solve(100, f, 0.6, 7.0);
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    }

    @Test
    public void testQuinticMin() {
        // The function has local minima at -0.27195613 and 0.82221643.
        UnivariateFunction f = new QuinticFunction();
        UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-14);
        Assert.assertEquals(-0.27195613, optimizer.optimize(200, f, GoalType.MINIMIZE, -0.3, -0.2).getPoint(), 1.0e-8);
        Assert.assertEquals( 0.82221643, optimizer.optimize(200, f, GoalType.MINIMIZE,  0.3,  0.9).getPoint(), 1.0e-8);
        Assert.assertTrue(optimizer.getEvaluations() <= 50);
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    }

    @Test
    public void testQuinticMinStatistics() {
        // The function has local minima at -0.27195613 and 0.82221643.
        UnivariateFunction f = new QuinticFunction();
        UnivariateOptimizer optimizer = new BrentOptimizer(1e-11, 1e-14);

        final DescriptiveStatistics[] stat = new DescriptiveStatistics[2];
        for (int i = 0; i < stat.length; i++) {
            stat[i] = new DescriptiveStatistics();
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    @Test
    public void testQuinticMax() {
        // The quintic function has zeros at 0, +-0.5 and +-1.
        // The function has a local maximum at 0.27195613.
        UnivariateFunction f = new QuinticFunction();
        UnivariateOptimizer optimizer = new BrentOptimizer(1e-12, 1e-14);
        Assert.assertEquals(0.27195613, optimizer.optimize(100, f, GoalType.MAXIMIZE, 0.2, 0.3).getPoint(), 1e-8);
        try {
            optimizer.optimize(5, f, GoalType.MAXIMIZE, 0.2, 0.3);
            Assert.fail("an exception should have been thrown");
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    }

    @Test
    public void testQuinticMin() {
        // The function has local minima at -0.27195613 and 0.82221643.
        UnivariateFunction f = new QuinticFunction();
        UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-14);
        Assert.assertEquals(-0.27195613, optimizer.optimize(new MaxEval(200),
                                                            new UnivariateObjectiveFunction(f),
                                                            GoalType.MINIMIZE,
                                                            new SearchInterval(-0.3, -0.2)).getPoint(), 1.0e-8);
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    }

    @Test
    public void testQuinticMinStatistics() {
        // The function has local minima at -0.27195613 and 0.82221643.
        UnivariateFunction f = new QuinticFunction();
        UnivariateOptimizer optimizer = new BrentOptimizer(1e-11, 1e-14);

        final DescriptiveStatistics[] stat = new DescriptiveStatistics[2];
        for (int i = 0; i < stat.length; i++) {
            stat[i] = new DescriptiveStatistics();
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    @Test
    public void testQuinticMax() {
        // The quintic function has zeros at 0, +-0.5 and +-1.
        // The function has a local maximum at 0.27195613.
        UnivariateFunction f = new QuinticFunction();
        UnivariateOptimizer optimizer = new BrentOptimizer(1e-12, 1e-14);
        Assert.assertEquals(0.27195613, optimizer.optimize(new MaxEval(100),
                                                           new UnivariateObjectiveFunction(f),
                                                           GoalType.MAXIMIZE,
                                                           new SearchInterval(0.2, 0.3)).getPoint(), 1e-8);
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    /**
     * Test of integrator for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateIntegrator integrator = new TrapezoidIntegrator();
        double min, max, expected, result, tolerance;

        min = 0; max = 1; expected = -1.0/48;
        tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
 
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    /**
     * Test of integrator for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateIntegrator integrator = new SimpsonIntegrator();
        double min, max, expected, result, tolerance;

        min = 0; max = 1; expected = -1.0/48;
        tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
 
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Related Classes of org.apache.commons.math3.analysis.QuinticFunction

  • org.apache.commons.math3.analysis.differentiation.DerivativeStructure
  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
  • org.apache.commons.math3.analysis.function.HarmonicOscillator
  • org.apache.commons.math3.analysis.function.Sin
  • org.apache.commons.math3.analysis.function.Sinc
  • org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegratorTest
  • org.apache.commons.math3.analysis.integration.LegendreGaussIntegratorTest
  • org.apache.commons.math3.analysis.integration.MidPointIntegratorTest
  • org.apache.commons.math3.analysis.integration.RombergIntegratorTest
  • org.apache.commons.math3.analysis.integration.SimpsonIntegratorTest
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