Examples of QuinticFunction

org.apache.commons.math.analysis.QuinticFunction
Auxillary class for testing solvers. @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
org.apache.commons.math3.analysis.QuinticFunction
Auxiliary class for testing solvers.

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


    /**
     * Test of solver for the quintic function.
     */
    public void testQuinticFunction() throws MathException {
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealSolver 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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Examples of org.apache.commons.math.analysis.QuinticFunction


    /**
     * Test of solver for the quintic function using solve2().
     */
    public void testQuinticFunction2() throws MathException {
        UnivariateRealFunction f = new QuinticFunction();
        MullerSolver 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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Examples of org.apache.commons.math.analysis.QuinticFunction


   /**
     *
     */
    public void testQuinticZero() throws MathException {
        DifferentiableUnivariateRealFunction f = new QuinticFunction();
        double result;


        UnivariateRealSolver solver = new NewtonSolver();
        result = solver.solve(f, -0.2, 0.2);
        assertEquals(result, 0, solver.getAbsoluteAccuracy());

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


    @Test
    public void testQuinticMin() throws MathException {
        // 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,
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealOptimizer underlying = new BrentOptimizer();
        underlying.setRelativeAccuracy(1e-15);
        JDKRandomGenerator g = new JDKRandomGenerator();
        g.setSeed(4312000053L);
        MultiStartUnivariateRealOptimizer minimizer =
            new MultiStartUnivariateRealOptimizer(underlying, 5, g);
        minimizer.setAbsoluteAccuracy(10 * minimizer.getAbsoluteAccuracy());
        minimizer.setRelativeAccuracy(10 * minimizer.getRelativeAccuracy());


        try {
            minimizer.getOptima();
            fail("an exception should have been thrown");
        } catch (IllegalStateException ise) {
            // expected
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            minimizer.getOptimaValues();
            fail("an exception should have been thrown");
        } catch (IllegalStateException ise) {
            // expected
        } catch (Exception e) {
            fail("wrong exception caught");
        }


        double result = minimizer.optimize(f, GoalType.MINIMIZE, -0.3, -0.2);
        assertEquals(-0.2719561270319131, result, 1.0e-13);
        assertEquals(-0.2719561270319131, minimizer.getResult(), 1.0e-13);
        assertEquals(-0.04433426954946637, minimizer.getFunctionValue(), 1.0e-13);


        double[] optima = minimizer.getOptima();
        double[] optimaValues = minimizer.getOptimaValues();
        for (int i = 0; i < optima.length; ++i) {
            assertEquals(f.value(optima[i]), optimaValues[i], 1.0e-10);
        }
        assertTrue(minimizer.getEvaluations()    >= 120);
        assertTrue(minimizer.getEvaluations()    <= 170);
        assertTrue(minimizer.getIterationCount() >= 120);
        assertTrue(minimizer.getIterationCount() <= 170);

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


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

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

    /**
     *
     */
    @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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Examples of org.apache.commons.math3.analysis.QuinticFunction


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

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

        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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