Package org.apache.commons.math.analysis.polynomials

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

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    private void checkUnsolvableProblem(DifferentiableMultivariateVectorialOptimizer optimizer,
                                        boolean solvable) {
        Random randomizer = new Random(1248788532l);
        for (int degree = 0; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

            PolynomialFitter fitter = new PolynomialFitter(degree, 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 {
                fitter.fit();
                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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                for (int i = 0; i < 10; ++i) {
                    double[] coeff = new double[degree + 1];
                    for (int k = 0; k < coeff.length; ++k) {
                        coeff[k] = 2 * random.nextDouble() - 1;
                    }
                    PolynomialFunction p = new PolynomialFunction(coeff);
                    double result    = integrator.integrate(p, -5.0, 15.0);
                    double reference = exactIntegration(p, -5.0, 15.0);
                    assertEquals(n + " " + degree + " " + i, reference, result, 1.0e-12 * (1.0 + Math.abs(reference)));
                }
            }
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        UnivariateRealFunction 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], 1d};
        TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[1], 1d};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
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        UnivariateRealInterpolator i = new SplineInterpolator();
        UnivariateRealFunction 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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        UnivariateRealFunction 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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         *     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, coefficientTolerance);
        target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
        TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
        target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
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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[])
        throws Exception {
        PolynomialFunction polynomials[] = f.getPolynomials();
        for (int i = 1; i < x.length - 2; i++) {
            // evaluate polynomials and derivatives at x[i + 1]
            assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
            assertEquals(polynomials[i].derivative().value(x[i +1] - x[i]),
                    polynomials[i + 1].derivative().value(0), 0.5);
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    public void testDeprecated() throws MathException {
        double min, max, expected, result, tolerance;

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

        min = 0.0; max = 1.0; expected = 0.25;
        tolerance = Math.max(solver.getAbsoluteAccuracy(),
                    Math.abs(expected * solver.getRelativeAccuracy()));
 
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    public void testLinearFunction() throws MathException {
        double min, max, expected, result, tolerance;

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

        min = 0.0; max = 1.0; expected = 0.25;
        tolerance = Math.max(solver.getAbsoluteAccuracy(),
                    Math.abs(expected * solver.getRelativeAccuracy()));
 
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