Examples of PolynomialFunction

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

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        UnivariateInterpolator i = new SplineInterpolator();
        UnivariateFunction 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};
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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        UnivariateFunction 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], 1.5d, 0d, -2d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 0d, -3d, 2d};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
    }
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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         *     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, sineCoefficientTolerance);
        target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, sineCoefficientTolerance);
        target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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     * Verifies that interpolating polynomials satisfy consistency requirement:
     *    adjacent polynomials must agree through two derivatives at knot points
     */
    protected void verifyConsistency(PolynomialSplineFunction f, double x[])
        {
        PolynomialFunction polynomials[] = f.getPolynomials();
        for (int i = 1; i < x.length - 2; i++) {
            // evaluate polynomials and derivatives at x[i + 1]
            Assert.assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
            Assert.assertEquals(polynomials[i].derivative().value(x[i +1] - x[i]),
                                polynomials[i + 1].derivative().value(0), 0.5);
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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    public void testLinearFunction() {
        double min, max, expected, result, tolerance;

        // p(x) = 4x - 1
        double coefficients[] = { -1.0, 4.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        min = 0.0; max = 1.0; expected = 0.25;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
 
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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    public void testQuadraticFunction() {
        double min, max, expected, result, tolerance;

        // p(x) = 2x^2 + 5x - 3 = (x+3)(2x-1)
        double coefficients[] = { -3.0, 5.0, 2.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        min = 0.0; max = 2.0; expected = 0.5;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
 
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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    public void testQuinticFunction() {
        double min, max, expected, result, tolerance;

        // p(x) = x^5 - x^4 - 12x^3 + x^2 - x - 12 = (x+1)(x+3)(x-4)(x^2-x+1)
        double coefficients[] = { -12.0, -1.0, 1.0, -12.0, -1.0, 1.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        min = -2.0; max = 2.0; expected = -1.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
 
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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     * Test of parameters for the solver.
     */
    @Test
    public void testParameters() {
        double coefficients[] = { -3.0, 5.0, 2.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        LaguerreSolver solver = new LaguerreSolver();

        try {
            // bad interval
            solver.solve(100, f, 1, -1);
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Examples of org.apache.commons.math3.analysis.polynomials.PolynomialFunction

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

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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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