Package org.apache.commons.math3.analysis

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

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        Assert.assertEquals(expected, result, tolerance);
    }

    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateIntegrator integrator =
                new IterativeLegendreGaussIntegrator(3,
                                                     BaseAbstractUnivariateIntegrator.DEFAULT_RELATIVE_ACCURACY,
                                                     BaseAbstractUnivariateIntegrator.DEFAULT_ABSOLUTE_ACCURACY,
                                                     BaseAbstractUnivariateIntegrator.DEFAULT_MIN_ITERATIONS_COUNT,
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        Assert.assertEquals(result, FastMath.PI, solver.getAbsoluteAccuracy());
    }

    @Test
    public void testQuinticZero() {
        UnivariateFunction f = new QuinticFunction();
        double result;

        BisectionSolver solver = new BisectionSolver();
        result = solver.solve(100, f, -0.2, 0.2);
        Assert.assertEquals(result, 0, solver.getAbsoluteAccuracy());
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        Assert.assertEquals(result, FastMath.PI, solver.getAbsoluteAccuracy());
    }

    @Test
    public void testQuinticZero() {
        UnivariateFunction f = new QuinticFunction();
        double result;

        BisectionSolver solver = new BisectionSolver();
        result = solver.solve(100, f, -0.2, 0.2);
        Assert.assertEquals(result, 0, solver.getAbsoluteAccuracy());
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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 quintic function has zeros at 0, +-0.5 and +-1.
        // The function has extrema (first derivative is zero) at 0.27195613 and 0.82221643,
        UnivariateFunction f = new QuinticFunction();
        UnivariateOptimizer underlying = new BrentOptimizer(1e-9, 1e-14);
        JDKRandomGenerator g = new JDKRandomGenerator();
        g.setSeed(4312000053L);
        UnivariateMultiStartOptimizer<UnivariateFunction> optimizer =
            new UnivariateMultiStartOptimizer<UnivariateFunction>(underlying, 5, g);

        UnivariatePointValuePair optimum
            = optimizer.optimize(300, f, GoalType.MINIMIZE, -0.3, -0.2);
        Assert.assertEquals(-0.2719561293, optimum.getPoint(), 1e-9);
        Assert.assertEquals(-0.0443342695, optimum.getValue(), 1e-9);

        UnivariatePointValuePair[] optima = optimizer.getOptima();
        for (int i = 0; i < optima.length; ++i) {
            Assert.assertEquals(f.value(optima[i].getPoint()), optima[i].getValue(), 1e-9);
        }
        Assert.assertTrue(optimizer.getEvaluations() >= 50);
        Assert.assertTrue(optimizer.getEvaluations() <= 100);
    }
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        UnivariateSolverUtils.bracket(sin, 1.5, 0, 2.0, 0);
    }

    @Test
    public void testMisc() {
        UnivariateFunction f = new QuinticFunction();
        double result;
        // Static solve method
        result = UnivariateSolverUtils.solve(f, -0.2, 0.2);
        Assert.assertEquals(result, 0, 1E-8);
        result = UnivariateSolverUtils.solve(f, -0.1, 0.3);
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    /**
     *
     */
    @Test
    public void testQuinticZero() {
        DifferentiableUnivariateFunction f = new QuinticFunction();
        double result;

        NewtonSolver solver = new NewtonSolver();
        result = solver.solve(100, f, -0.2, 0.2);
        Assert.assertEquals(result, 0, solver.getAbsoluteAccuracy());
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        // 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;
        UnivariateSolver solver = getSolver();
        double atol = solver.getAbsoluteAccuracy();
        int[] counts = getQuinticEvalCounts();
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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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