Package org.apache.commons.math3.analysis

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

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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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        // 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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    /**
     *
     */
    @Test
    public void testQuinticZero() {
        final UnivariateDifferentiableFunction f = new QuinticFunction();
        double result;

        NewtonRaphsonSolver solver = new NewtonRaphsonSolver();
        result = solver.solve(100, f, -0.2, 0.2);
        Assert.assertEquals(result, 0, solver.getAbsoluteAccuracy());
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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 solver for the quintic function.
     */
    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateSolver solver = new MullerSolver();
        double min, max, expected, result, tolerance;

        min = -0.4; max = 0.2; expected = 0.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
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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() {
        final UnivariateDifferentiableFunction q = new QuinticFunction();
        DifferentiableUnivariateFunction f = new DifferentiableUnivariateFunction() {

            public double value(double x) {
                return q.value(x);
            }

            public UnivariateFunction derivative() {
                return new UnivariateFunction() {
                    public double value(double x) {
                        return q.value(new DerivativeStructure(1, 1, 0, x)).getPartialDerivative(1);
                    }
                };
            }

        };
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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 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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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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