Examples of UnivariateRealFunction

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

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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 = Math.PI; expected = 2;
        tolerance = Math.abs(expected * integrator.getRelativeAccuracy());
 
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Examples of org.apache.commons.math.analysis.UnivariateRealFunction

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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 = Math.abs(expected * integrator.getRelativeAccuracy());
 
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Examples of org.apache.commons.math.analysis.UnivariateRealFunction

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

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

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

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    }

    public void testMap() throws Exception {
        double[] vec1Squared = { 1d, 4d, 9d, 16d, 25d };
        RealVector v = new TestVectorImpl(vec1.clone());
        RealVector w = v.map(new UnivariateRealFunction() { public double value(double x) { return x * x; } });
        assertEquals(vec1Squared, w.getData());
    }
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Examples of org.apache.commons.math.analysis.UnivariateRealFunction

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    public void testInterpolateLinearDegenerateTwoSegment()
        throws Exception {
        double x[] = { 0.0, 0.5, 1.0 };
        double y[] = { 0.0, 0.5, 1.0 };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);
        verifyConsistency((PolynomialSplineFunction) f, x);

        // Verify coefficients using analytical values
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
        double target[] = {y[0], 1d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 1d};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);

        // Check interpolation
        assertEquals(0.0,f.value(0.0), interpolationTolerance);
        assertEquals(0.4,f.value(0.4), interpolationTolerance);
        assertEquals(1.0,f.value(1.0), interpolationTolerance);
    }
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Examples of org.apache.commons.math.analysis.UnivariateRealFunction

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    public void testInterpolateLinearDegenerateThreeSegment()
        throws Exception {
        double x[] = { 0.0, 0.5, 1.0, 1.5 };
        double y[] = { 0.0, 0.5, 1.0, 1.5 };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);

        // Verify coefficients using analytical values
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
        double target[] = {y[0], 1d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 1d};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[2], 1d};
        TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);

        // Check interpolation
        assertEquals(0,f.value(0), interpolationTolerance);
        assertEquals(1.4,f.value(1.4), interpolationTolerance);
        assertEquals(1.5,f.value(1.5), interpolationTolerance);
    }
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Examples of org.apache.commons.math.analysis.UnivariateRealFunction

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    public void testInterpolateLinear() throws Exception {
        double x[] = { 0.0, 0.5, 1.0 };
        double y[] = { 0.0, 0.5, 0.0 };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);
        verifyConsistency((PolynomialSplineFunction) f, x);

        // Verify coefficients using analytical values
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
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Examples of org.apache.commons.math.analysis.UnivariateRealFunction

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                3d * Math.PI / 2d,
                11d * Math.PI / 6d,
                2.d * Math.PI };
        double y[] = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction f = i.interpolate(x, y);
        verifyInterpolation(f, x, y);
        verifyConsistency((PolynomialSplineFunction) f, x);

        /* Check coefficients against values computed using R (version 1.8.1, Red Hat Linux 9)
         *
         * To replicate in R:
         *     x[1] <- 0
         *     x[2] <- pi / 6, etc, same for y[] (could use y <- scan() for y values)
         *     g <- splinefun(x, y, "natural")
         *     splinecoef <- eval(expression(z), envir = environment(g))
         *     print(splinecoef)
         */
        PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
        double target[] = {y[0], 1.002676d, 0d, -0.17415829d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
        TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[3], -8.594367e-01, -2.735672e-01, 0.17415829};
        TestUtils.assertEquals(polynomials[3].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[4], -1.002676, 6.548562e-17, 0.17415829};
        TestUtils.assertEquals(polynomials[4].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[5], -8.594367e-01, 2.735672e-01, 0.08707914};
        TestUtils.assertEquals(polynomials[5].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[6], 3.466465e-16, 5.471344e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[6].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[7], 8.594367e-01, 2.735672e-01, -0.17415829};
        TestUtils.assertEquals(polynomials[7].getCoefficients(), target, coefficientTolerance);

        //Check interpolation
        assertEquals(Math.sqrt(2d) / 2d,f.value(Math.PI/4d),interpolationTolerance);
        assertEquals(Math.sqrt(2d) / 2d,f.value(3d*Math.PI/4d),interpolationTolerance);
    }
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