Package org.apache.commons.math3.analysis.polynomials

Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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    @Test
    public void testSmallError() {
        Random randomizer = new Random(53882150042l);
        double maxError = 0;
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(new LevenbergMarquardtOptimizer());
            for (double x = -1.0; x < 1.0; x += 0.01) {
                fitter.addObservedPoint(1.0, x,
                                        p.value(x) + 0.1 * randomizer.nextGaussian());
            }

            final double[] init = new double[degree + 1];
            PolynomialFunction fitted = new PolynomialFunction(fitter.fit(init));

            for (double x = -1.0; x < 1.0; x += 0.01) {
                double error = FastMath.abs(p.value(x) - fitted.value(x)) /
                              (1.0 + FastMath.abs(p.value(x)));
                maxError = FastMath.max(maxError, error);
                Assert.assertTrue(FastMath.abs(error) < 0.1);
            }
        }
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    @Test
    public void testSmallError() {
        Random randomizer = new Random(53882150042l);
        double maxError = 0;
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(new LevenbergMarquardtOptimizer());
            for (double x = -1.0; x < 1.0; x += 0.01) {
                fitter.addObservedPoint(1.0, x,
                                        p.value(x) + 0.1 * randomizer.nextGaussian());
            }

            final double[] init = new double[degree + 1];
            PolynomialFunction fitted = new PolynomialFunction(fitter.fit(init));

            for (double x = -1.0; x < 1.0; x += 0.01) {
                double error = FastMath.abs(p.value(x) - fitted.value(x)) /
                              (1.0 + FastMath.abs(p.value(x)));
                maxError = FastMath.max(maxError, error);
                Assert.assertTrue(FastMath.abs(error) < 0.1);
            }
        }
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    private void checkUnsolvableProblem(DifferentiableMultivariateVectorOptimizer optimizer,
                                        boolean solvable) {
        Random randomizer = new Random(1248788532l);
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(optimizer);

            // reusing the same point over and over again does not bring
            // information, the problem cannot be solved in this case for
            // degrees greater than 1 (but one point is sufficient for
            // degree 0)
            for (double x = -1.0; x < 1.0; x += 0.01) {
                fitter.addObservedPoint(1.0, 0.0, p.value(0.0));
            }

            try {
                final double[] init = new double[degree + 1];
                fitter.fit(init);
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    private void checkUnsolvableProblem(MultivariateVectorOptimizer optimizer,
                                        boolean solvable) {
        Random randomizer = new Random(1248788532l);
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(optimizer);

            // reusing the same point over and over again does not bring
            // information, the problem cannot be solved in this case for
            // degrees greater than 1 (but one point is sufficient for
            // degree 0)
            for (double x = -1.0; x < 1.0; x += 0.01) {
                fitter.addObservedPoint(1.0, 0.0, p.value(0.0));
            }

            try {
                final double[] init = new double[degree + 1];
                fitter.fit(init);
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    private PolynomialFunction buildRandomPolynomial(int degree, Random randomizer) {
        final double[] coefficients = new double[degree + 1];
        for (int i = 0; i <= degree; ++i) {
            coefficients[i] = randomizer.nextGaussian();
        }
        return new PolynomialFunction(coefficients);
    }
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    private PolynomialFunction buildRandomPolynomial(int degree, Random randomizer) {
        final double[] coefficients = new double[degree + 1];
        for (int i = 0; i <= degree; ++i) {
            coefficients[i] = randomizer.nextGaussian();
        }
        return new PolynomialFunction(coefficients);
    }
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        for (double x = -10; x < 10; x += 1.0) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
            Assert.assertEquals(0.0, y.getValue(), 1.0e-15);
            Assert.assertEquals(0.0, y.getPartialDerivative(1), 1.0e-15);
        }
        checkPolynomial(new PolynomialFunction(new double[] { 0.0 }),
                        interpolator.getPolynomials()[0]);
    }
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        for (double x = -10; x < 10; x += 1.0) {
            DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
            Assert.assertEquals((x - 1.0) * (x - 2.0), y.getValue(), 1.0e-15);
            Assert.assertEquals(2 * x - 3.0, y.getPartialDerivative(1), 1.0e-15);
        }
        checkPolynomial(new PolynomialFunction(new double[] { 2.0, -3.0, 1.0 }),
                        interpolator.getPolynomials()[0]);
    }
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        Assert.assertEquals(2.0, y0.getPartialDerivative(1), 1.0e-15);
        Assert.assertEquals(4.0, interpolator.value(1.0)[0], 1.0e-15);
        DerivativeStructure y2 = interpolator.value(new DerivativeStructure(1, 1, 0, 2.0))[0];
        Assert.assertEquals(5.0, y2.getValue(), 1.0e-15);
        Assert.assertEquals(2.0, y2.getPartialDerivative(1), 1.0e-15);
        checkPolynomial(new PolynomialFunction(new double[] { 1.0, 2.0, 4.0, -4.0, 1.0 }),
                        interpolator.getPolynomials()[0]);
    }
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            double x4 = x2 * x2;
            double x8 = x4 * x4;
            Assert.assertEquals(x8 + 1, y.getValue(), 1.0e-15);
            Assert.assertEquals(8 * x4 * x2 * x, y.getPartialDerivative(1), 1.0e-15);
        }
        checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 0, 0, 0, 0, 0, 0, 1 }),
                        interpolator.getPolynomials()[0]);
    }
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Related Classes of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

  • org.apache.commons.math3.analysis.differentiation.DerivativeStructure
  • org.apache.commons.math3.analysis.differentiation.DerivativeStructureTest
  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
  • org.apache.commons.math3.analysis.function.HarmonicOscillator
  • org.apache.commons.math3.analysis.function.Sin
  • org.apache.commons.math3.analysis.function.Sinc
  • org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegratorTest
  • org.apache.commons.math3.analysis.integration.LegendreGaussIntegratorTest
  • org.apache.commons.math3.analysis.interpolation.HermiteInterpolator
  • org.apache.commons.math3.analysis.interpolation.HermiteInterpolatorTest
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