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

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

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    @Test
    public void testNoError() {
        final Random randomizer = new Random(64925784252l);
        for (int degree = 1; degree < 10; ++degree) {
            final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
            final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);

            final WeightedObservedPoints obs = new WeightedObservedPoints();
            for (int i = 0; i <= degree; ++i) {
                obs.add(1.0, i, p.value(i));
            }

            final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList()));

            for (double x = -1.0; x < 1.0; x += 0.01) {
                final 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() {
        final Random randomizer = new Random(53882150042l);
        double maxError = 0;
        for (int degree = 0; degree < 10; ++degree) {
            final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
            final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);

            final WeightedObservedPoints obs = new WeightedObservedPoints();
            for (double x = -1.0; x < 1.0; x += 0.01) {
                obs.add(1.0, x, p.value(x) + 0.1 * randomizer.nextGaussian());
            }

            final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList()));

            for (double x = -1.0; x < 1.0; x += 0.01) {
                final 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() {
        final Random randomizer = new Random(0x5551480dca5b369bl);
        double maxError = 0;
        for (int degree = 0; degree < 10; ++degree) {
            final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
            final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);
            final WeightedObservedPoints obs = new WeightedObservedPoints();
            for (int i = 0; i < 40000; ++i) {
                final double x = -1.0 + i / 20000.0;
                obs.add(1.0, x, p.value(x) + 0.1 * randomizer.nextGaussian());
            }

            final PolynomialFunction fitted = new PolynomialFunction(fitter.fit(obs.toList()));
            for (double x = -1.0; x < 1.0; x += 0.01) {
                final 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(boolean solvable) {
        final Random randomizer = new Random(1248788532l);

        for (int degree = 0; degree < 10; ++degree) {
            final PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
            final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);
            final WeightedObservedPoints obs = new WeightedObservedPoints();
            // 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) {
                obs.add(1.0, 0.0, p.value(0.0));
            }

            try {
                fitter.fit(obs.toList());
                Assert.assertTrue(solvable || (degree == 0));
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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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                xFitter.addObservedPoint(1, xval[i], fval[i][j]);
            }

            // Initial guess for the fit is zero for each coefficients (of which
            // there are "xDegree" + 1).
            yPolyX[j] = new PolynomialFunction(xFitter.fit(new double[xDegree + 1]));
        }

        // For every knot (xval[i], yval[j]) of the grid, calculate corrected
        // values fval_1
        final double[][] fval_1 = new double[xLen][yLen];
        for (int j = 0; j < yLen; j++) {
            final PolynomialFunction f = yPolyX[j];
            for (int i = 0; i < xLen; i++) {
                fval_1[i][j] = f.value(xval[i]);
            }
        }

        // For each line x[i] (0 <= i < xLen), construct a polynomial, with
        // respect to variable y, fitting array fval_1[i][]
        final PolynomialFunction[] xPolyY = new PolynomialFunction[xLen];
        for (int i = 0; i < xLen; i++) {
            yFitter.clearObservations();
            for (int j = 0; j < yLen; j++) {
                yFitter.addObservedPoint(1, yval[j], fval_1[i][j]);
            }

            // Initial guess for the fit is zero for each coefficients (of which
            // there are "yDegree" + 1).
            xPolyY[i] = new PolynomialFunction(yFitter.fit(new double[yDegree + 1]));
        }

        // For every knot (xval[i], yval[j]) of the grid, calculate corrected
        // values fval_2
        final double[][] fval_2 = new double[xLen][yLen];
        for (int i = 0; i < xLen; i++) {
            final PolynomialFunction f = xPolyY[i];
            for (int j = 0; j < yLen; j++) {
                fval_2[i][j] = f.value(yval[j]);
            }
        }

        return super.interpolate(xval, yval, fval_2);
    }
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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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Related Classes of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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  • org.apache.commons.math3.analysis.differentiation.DerivativeStructureTest
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  • 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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