Package org.apache.commons.math.analysis

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

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    /**
     * 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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    /**
     * 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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   /**
     *
     */
    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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    @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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    /**
     * Test of integrator for the quintic function.
     */
    public void testQuinticFunction() throws MathException {
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealIntegrator 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.
     */
    public void testQuinticFunction() throws MathException {
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealIntegrator 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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        result = integrator.integrate(f, min, max);
        assertEquals(expected, result, tolerance);
    }

    public void testQuinticFunction() throws MathException {
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealIntegrator integrator = new LegendreGaussIntegrator(3, 64);
        double min, max, expected, result;

        min = 0; max = 1; expected = -1.0/48;
        result = integrator.integrate(f, min, max);
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    }

    @Test
    public void testQuinticMin() throws MathException {
        // The function has local minima at -0.27195613 and 0.82221643.
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealOptimizer minimizer = new BrentOptimizer();
        assertEquals(-0.27195613, minimizer.optimize(f, GoalType.MINIMIZE, -0.3, -0.2), 1.0e-8);
        assertEquals( 0.82221643, minimizer.optimize(f, GoalType.MINIMIZE,  0.3,  0.9), 1.0e-8);
        assertTrue(minimizer.getIterationCount() <= 50);
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    }

    @Test
    public void testQuinticMinStatistics() throws MathException {
        // The function has local minima at -0.27195613 and 0.82221643.
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealOptimizer minimizer = new BrentOptimizer();
        minimizer.setRelativeAccuracy(1e-10);
        minimizer.setAbsoluteAccuracy(1e-11);

        final DescriptiveStatistics[] stat = new DescriptiveStatistics[3];
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    @Test
    public void testQuinticMax() throws MathException {
        // The quintic function has zeros at 0, +-0.5 and +-1.
        // The function has a local maximum at 0.27195613.
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealOptimizer minimizer = new BrentOptimizer();
        assertEquals(0.27195613, minimizer.optimize(f, GoalType.MAXIMIZE, 0.2, 0.3), 1.0e-8);
        minimizer.setMaximalIterationCount(5);
        try {
            minimizer.optimize(f, GoalType.MAXIMIZE, 0.2, 0.3);
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Related Classes of org.apache.commons.math.analysis.QuinticFunction

  • org.apache.commons.math.analysis.integration.LegendreGaussIntegratorTest
  • org.apache.commons.math.analysis.integration.RombergIntegratorTest
  • org.apache.commons.math.analysis.integration.SimpsonIntegratorTest
  • org.apache.commons.math.analysis.integration.TrapezoidIntegratorTest
  • org.apache.commons.math.analysis.solvers.BisectionSolverTest
  • org.apache.commons.math.analysis.solvers.BrentSolverTest
  • org.apache.commons.math.analysis.solvers.MullerSolverTest
  • org.apache.commons.math.analysis.solvers.NewtonSolverTest
  • org.apache.commons.math.analysis.solvers.RiddersSolverTest
  • org.apache.commons.math.optimization.MultiStartUnivariateRealOptimizerTest
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