Package org.apache.commons.math3.analysis

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

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    /**
     * Test of solver for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateSolver solver = new RiddersSolver();
        double min, max, expected, result, tolerance;

        min = -0.4; max = 0.2; expected = 0.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
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    /**
     * Test of solver for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateSolver solver = new MullerSolver2();
        double min, max, expected, result, tolerance;

        min = -0.4; max = 0.2; expected = 0.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
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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 testConvergenceOnFunctionAccuracy() {
        BracketingNthOrderBrentSolver solver =
                new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-10, 0.001, 3);
        QuinticFunction f = new QuinticFunction();
        double result = solver.solve(20, f, 0.2, 0.9, 0.4, AllowedSolution.BELOW_SIDE);
        Assert.assertEquals(0, f.value(result), solver.getFunctionValueAccuracy());
        Assert.assertTrue(f.value(result) <= 0);
        Assert.assertTrue(result - 0.5 > solver.getAbsoluteAccuracy());
        result = solver.solve(20, f, -0.9, -0.2,  -0.4, AllowedSolution.ABOVE_SIDE);
        Assert.assertEquals(0, f.value(result), solver.getFunctionValueAccuracy());
        Assert.assertTrue(f.value(result) >= 0);
        Assert.assertTrue(result + 0.5 < -solver.getAbsoluteAccuracy());
    }
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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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    /**
     * Test of integrator for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateIntegrator integrator = new RombergIntegrator();
        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
    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);
        MultiStartUnivariateOptimizer optimizer = new MultiStartUnivariateOptimizer(underlying, 5, g);

        UnivariatePointValuePair optimum
            = optimizer.optimize(new MaxEval(300),
                                 new UnivariateObjectiveFunction(f),
                                 GoalType.MINIMIZE,
                                 new SearchInterval(-0.3, -0.2));
        Assert.assertEquals(-0.27195613, 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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        Assert.assertEquals(expected, result, tolerance);
    }

    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateIntegrator integrator =
                new LegendreGaussIntegrator(3,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_RELATIVE_ACCURACY,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_ABSOLUTE_ACCURACY,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_MIN_ITERATIONS_COUNT,
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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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