Examples of IterativeLegendreGaussIntegrator

org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator
orld.wolfram.com/Legendre-GaussQuadrature.html"> Legendre-Gauss quadrature. Because of its non-adaptive nature, this algorithm can converge to a wrong value for the integral (for example, if the function is significantly different from zero toward the ends of the integration interval). In particular, a change of variables aimed at estimating integrals over infinite intervals as proposed here should be avoided when using this class. @since 3.1

Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

     */
    @Test
    public void testDensityIntegrals() {
        final double tol = 1.0e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1.0e-12, 1.0e-10);
        final UnivariateFunction d = new UnivariateFunction() {
            public double value(double x) {
                return distribution.density(x);
            }
        };
        final ArrayList<Double> integrationTestPoints = new ArrayList<Double>();
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            if (Double.isNaN(cumulativeTestValues[i]) ||
                    cumulativeTestValues[i] < 1.0e-5 ||
                    cumulativeTestValues[i] > 1 - 1.0e-5) {
                continue; // exclude integrals outside domain.
            }
            integrationTestPoints.add(cumulativeTestPoints[i]);
        }
        Collections.sort(integrationTestPoints);
        for (int i = 1; i < integrationTestPoints.size(); i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability(  // FIXME @4.0 when rename happens
                            integrationTestPoints.get(0), integrationTestPoints.get(i)),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, integrationTestPoints.get(0),
                                    integrationTestPoints.get(i)), tol);
        }
    }

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Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

            public double value(double x) {
                return weight.value(x) * p1.value(x) * p2.value(x);
            }
        };
        double dotProduct =
                new IterativeLegendreGaussIntegrator(5, 1.0e-9, 1.0e-8, 2, 15).integrate(1000000, f, a, b);
        if (p1.degree() == p2.degree()) {
            // integral should be non-zero
            Assert.assertTrue("I(" + p1.degree() + ", " + p2.degree() + ") = "+ dotProduct,
                              FastMath.abs(dotProduct) > nonZeroThreshold);
        } else {

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Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

    @Test
    public void testDensityIntegrals() {
        final RealDistribution distribution = makeDistribution();
        final double tol = 1.0e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1.0e-12, 1.0e-10);
        final UnivariateFunction d = new UnivariateFunction() {
            public double value(double x) {
                return distribution.density(x);
            }
        };
        final double[] lower = {0, 5, 1000, 5001, 9995};
        final double[] upper = {5, 12, 1030, 5010, 10000};
        for (int i = 1; i < 5; i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability( 
                            lower[i], upper[i]),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, lower[i], upper[i]), tol);
        }
    }

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Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

     */
    @Test
    public void testDensityIntegrals() {
        final double tol = 1.0e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1.0e-12, 1.0e-10);
        final UnivariateFunction d = new UnivariateFunction() {
            public double value(double x) {
                return distribution.density(x);
            }
        };
        final ArrayList<Double> integrationTestPoints = new ArrayList<Double>();
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            if (Double.isNaN(cumulativeTestValues[i]) ||
                    cumulativeTestValues[i] < 1.0e-5 ||
                    cumulativeTestValues[i] > 1 - 1.0e-5) {
                continue; // exclude integrals outside domain.
            }
            integrationTestPoints.add(cumulativeTestPoints[i]);
        }
        Collections.sort(integrationTestPoints);
        for (int i = 1; i < integrationTestPoints.size(); i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability(  // FIXME @4.0 when rename happens
                            integrationTestPoints.get(0), integrationTestPoints.get(i)),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, integrationTestPoints.get(0),
                                    integrationTestPoints.get(i)), tol);
        }
    }

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Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

    @Test
    public void testDensityIntegrals() {
        final RealDistribution distribution = makeDistribution();
        final double tol = 1.0e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1.0e-12, 1.0e-10);
        final UnivariateFunction d = new UnivariateFunction() {
            public double value(double x) {
                return distribution.density(x);
            }
        };
        final double[] lower = {0, 5, 1000, 5001, 9995};
        final double[] upper = {5, 12, 1030, 5010, 10000};
        for (int i = 1; i < 5; i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability( 
                            lower[i], upper[i]),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, lower[i], upper[i]), tol);
        }
    }

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Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

            public double value(double x) {
                return weight.value(x) * p1.value(x) * p2.value(x);
            }
        };
        double dotProduct =
                new IterativeLegendreGaussIntegrator(5, 1.0e-9, 1.0e-8, 2, 15).integrate(1000000, f, a, b);
        if (p1.degree() == p2.degree()) {
            // integral should be non-zero
            Assert.assertTrue("I(" + p1.degree() + ", " + p2.degree() + ") = "+ dotProduct,
                              FastMath.abs(dotProduct) > nonZeroThreshold);
        } else {

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Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

     */
    @Test
    public void testDensityIntegrals() {
        final double tol = 1.0e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1.0e-12, 1.0e-10);
        final UnivariateFunction d = new UnivariateFunction() {
            public double value(double x) {
                return distribution.density(x);
            }
        };
        final ArrayList<Double> integrationTestPoints = new ArrayList<Double>();
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            if (Double.isNaN(cumulativeTestValues[i]) ||
                    cumulativeTestValues[i] < 1.0e-5 ||
                    cumulativeTestValues[i] > 1 - 1.0e-5) {
                continue; // exclude integrals outside domain.
            }
            integrationTestPoints.add(cumulativeTestPoints[i]);
        }
        Collections.sort(integrationTestPoints);
        for (int i = 1; i < integrationTestPoints.size(); i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability(  // FIXME @4.0 when rename happens
                            integrationTestPoints.get(0), integrationTestPoints.get(i)),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, integrationTestPoints.get(0),
                                    integrationTestPoints.get(i)), tol);
        }
    }

View Full Code Here

Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

    @Test
    public void testDensityIntegrals() {
        final RealDistribution distribution = makeDistribution();
        final double tol = 1.0e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1.0e-12, 1.0e-10);
        final UnivariateFunction d = new UnivariateFunction() {
            public double value(double x) {
                return distribution.density(x);
            }
        };
        final double[] lower = {0, 5, 1000, 5001, 9995};
        final double[] upper = {5, 12, 1030, 5010, 10000};
        for (int i = 1; i < 5; i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability( 
                            lower[i], upper[i]),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, lower[i], upper[i]), tol);
        }
    }

View Full Code Here

Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

            public double value(double x) {
                return weight.value(x) * p1.value(x) * p2.value(x);
            }
        };
        double dotProduct =
                new IterativeLegendreGaussIntegrator(5, 1.0e-9, 1.0e-8, 2, 15).integrate(1000000, f, a, b);
        if (p1.degree() == p2.degree()) {
            // integral should be non-zero
            Assert.assertTrue("I(" + p1.degree() + ", " + p2.degree() + ") = "+ dotProduct,
                              FastMath.abs(dotProduct) > nonZeroThreshold);
        } else {

View Full Code Here

Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator

     */
    @Test
    public void testDensityIntegrals() {
        final double tol = 1.0e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1.0e-12, 1.0e-10);
        final UnivariateFunction d = new UnivariateFunction() {
            public double value(double x) {
                return distribution.density(x);
            }
        };
        final ArrayList<Double> integrationTestPoints = new ArrayList<Double>();
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            if (Double.isNaN(cumulativeTestValues[i]) ||
                    cumulativeTestValues[i] < 1.0e-5 ||
                    cumulativeTestValues[i] > 1 - 1.0e-5) {
                continue; // exclude integrals outside domain.
            }
            integrationTestPoints.add(cumulativeTestPoints[i]);
        }
        Collections.sort(integrationTestPoints);
        for (int i = 1; i < integrationTestPoints.size(); i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability(  // FIXME @4.0 when rename happens
                            integrationTestPoints.get(0), integrationTestPoints.get(i)),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, integrationTestPoints.get(0),
                                    integrationTestPoints.get(i)), tol);
        }
    }

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