Package org.apache.commons.math.analysis

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

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public class MultiStartUnivariateRealOptimizerTest {

    @Test
    public void testSinMin() throws MathException {
        UnivariateRealFunction f = new SinFunction();
        UnivariateRealOptimizer underlying = new BrentOptimizer();
        JDKRandomGenerator g = new JDKRandomGenerator();
        g.setSeed(44428400075l);
        MultiStartUnivariateRealOptimizer minimizer =
            new MultiStartUnivariateRealOptimizer(underlying, 10, g);
        minimizer.optimize(f, GoalType.MINIMIZE, -100.0, 100.0);
        double[] optima = minimizer.getOptima();
        double[] optimaValues = minimizer.getOptimaValues();
        for (int i = 1; i < optima.length; ++i) {
            double d = (optima[i] - optima[i-1]) / (2 * FastMath.PI);
            assertTrue (FastMath.abs(d - FastMath.rint(d)) < 1.0e-8);
            assertEquals(-1.0, f.value(optima[i]), 1.0e-10);
            assertEquals(f.value(optima[i]), optimaValues[i], 1.0e-10);
        }
        assertTrue(minimizer.getEvaluations() > 150);
        assertTrue(minimizer.getEvaluations() < 250);
    }
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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 sine function.
     */
    public void testSinFunction() throws MathException {
        UnivariateRealFunction f = new SinFunction();
        UnivariateRealIntegrator integrator = new SimpsonIntegrator();
        double min, max, expected, result, tolerance;

        min = 0; max = FastMath.PI; expected = 2;
        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 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 parameters for the integrator.
     */
    public void testParameters() throws Exception {
        UnivariateRealFunction f = new SinFunction();
        UnivariateRealIntegrator integrator = new SimpsonIntegrator();

        try {
            // bad interval
            integrator.integrate(f, 1, -1);
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    }

    public void testValues() throws Exception {
        PolynomialSplineFunction spline =
            new PolynomialSplineFunction(knots, polynomials);
        UnivariateRealFunction dSpline = spline.derivative();

        /**
         * interior points -- spline value at x should equal p(x - knot)
         * where knot is the largest knot point less than or equal to x and p
         * is the polynomial defined over the knot segment to which x belongs.
         */
        double x = -1;
        int index = 0;
        for (int i = 0; i < 10; i++) {
           x+=0.25;
           index = findKnot(knots, x);
           assertEquals("spline function evaluation failed for x=" + x,
                   polynomials[index].value(x - knots[index]), spline.value(x), tolerance);
           assertEquals("spline derivative evaluation failed for x=" + x,
                   dp.value(x - knots[index]), dSpline.value(x), tolerance);
        }

        // knot points -- centering should zero arguments
        for (int i = 0; i < 3; i++) {
            assertEquals("spline function evaluation failed for knot=" + knots[i],
                    polynomials[i].value(0), spline.value(knots[i]), tolerance);
            assertEquals("spline function evaluation failed for knot=" + knots[i],
                    dp.value(0), dSpline.value(knots[i]), tolerance);
        }

        try { //outside of domain -- under min
            x = spline.value(-1.5);
            fail("Expecting ArgumentOutsideDomainException");
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    /**
     * Test of integrator for the sine function.
     */
    public void testSinFunction() throws MathException {
        UnivariateRealFunction f = new SinFunction();
        UnivariateRealIntegrator integrator = new RombergIntegrator();
        double min, max, expected, result, tolerance;

        min = 0; max = FastMath.PI; expected = 2;
        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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    /**
     * Test of parameters for the integrator.
     */
    public void testParameters() throws Exception {
        UnivariateRealFunction f = new SinFunction();
        UnivariateRealIntegrator integrator = new RombergIntegrator();

        try {
            // bad interval
            integrator.integrate(f, 1, -1);
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    public LegendreGaussIntegratorTest(String name) {
        super(name);
    }

    public void testSinFunction() throws MathException {
        UnivariateRealFunction f = new SinFunction();
        UnivariateRealIntegrator integrator = new LegendreGaussIntegrator(5, 64);
        integrator.setAbsoluteAccuracy(1.0e-10);
        integrator.setRelativeAccuracy(1.0e-14);
        integrator.setMinimalIterationCount(2);
        integrator.setMaximalIterationCount(15);
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