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

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

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        // safety check
        checkInterpolation();

        // iteration initialization
        final PolynomialFunction zero = polynomial(0);
        PolynomialFunction[] polynomials = new PolynomialFunction[topDiagonal.get(0).length];
        for (int i = 0; i < polynomials.length; ++i) {
            polynomials[i] = zero;
        }
        PolynomialFunction coeff = polynomial(1);

        // build the polynomials by iterating on the top diagonal of the divided differences array
        for (int i = 0; i < topDiagonal.size(); ++i) {
            double[] tdi = topDiagonal.get(i);
            for (int k = 0; k < polynomials.length; ++k) {
                polynomials[k] = polynomials[k].add(coeff.multiply(polynomial(tdi[k])));
            }
            coeff = coeff.multiply(polynomial(-abscissae.get(i), 1.0));
        }

        return polynomials;

    }
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    /** Create a polynomial from its coefficients.
     * @param c polynomials coefficients
     * @return polynomial
     */
    private PolynomialFunction polynomial(double ... c) {
        return new PolynomialFunction(c);
    }
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    }

    @Test
    public void testCompose() {
        double[] epsilon = new double[] { 1.0e-20, 5.0e-14, 2.0e-13, 3.0e-13, 2.0e-13, 1.0e-20 };
        PolynomialFunction poly =
                new PolynomialFunction(new double[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 });
        for (int maxOrder = 0; maxOrder < 6; ++maxOrder) {
            PolynomialFunction[] p = new PolynomialFunction[maxOrder + 1];
            p[0] = poly;
            for (int i = 1; i <= maxOrder; ++i) {
                p[i] = p[i - 1].polynomialDerivative();
            }
            for (double x = 0.1; x < 1.2; x += 0.001) {
                DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);
                DerivativeStructure dsY1 = dsX.getField().getZero();
                for (int i = poly.degree(); i >= 0; --i) {
                    dsY1 = dsY1.multiply(dsX).add(poly.getCoefficients()[i]);
                }
                double[] f = new double[maxOrder + 1];
                for (int i = 0; i < f.length; ++i) {
                    f[i] = p[i].value(x);
                }
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        rng.reseedRandomGenerator(64925784252L);

        final LevenbergMarquardtOptimizer optim = new LevenbergMarquardtOptimizer();
        final PolynomialFitter fitter = new PolynomialFitter(optim);
        final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
        final PolynomialFunction f = new PolynomialFunction(coeff);

        // Collect data from a known polynomial.
        for (int i = 0; i < 100; i++) {
            final double x = rng.sample();
            fitter.addObservedPoint(x, f.value(x));
        }

        // Start fit from initial guesses that are far from the optimal values.
        final double[] best = fitter.fit(new double[] { -1e-20, 3e15, -5e25 });
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    @Test
    public void testNoError() {
        Random randomizer = new Random(64925784252l);
        for (int degree = 1; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(new LevenbergMarquardtOptimizer());
            for (int i = 0; i <= degree; ++i) {
                fitter.addObservedPoint(1.0, i, p.value(i));
            }

            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)));
                Assert.assertEquals(0.0, error, 1.0e-6);
            }
        }
    }
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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 testLargeSample() {
        Random randomizer = new Random(0x5551480dca5b369bl);
        double maxError = 0;
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(new LevenbergMarquardtOptimizer());
            for (int i = 0; i < 40000; ++i) {
                double x = -1.0 + i / 20000.0;
                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) < 0.01);
            }
        }
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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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    public void testFit() {
        final RealDistribution rng = new UniformRealDistribution(-100, 100);
        rng.reseedRandomGenerator(64925784252L);

        final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
        final PolynomialFunction f = new PolynomialFunction(coeff);

        // Collect data from a known polynomial.
        final WeightedObservedPoints obs = new WeightedObservedPoints();
        for (int i = 0; i < 100; i++) {
            final double x = rng.sample();
            obs.add(x, f.value(x));
        }

        // Start fit from initial guesses that are far from the optimal values.
        final PolynomialCurveFitter fitter
            = PolynomialCurveFitter.create(0).withStartPoint(new double[] { -1e-20, 3e15, -5e25 });
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Related Classes of org.apache.commons.math3.analysis.polynomials.PolynomialFunction$Parametric

  • 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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