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

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

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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 = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.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 = FastMath.max(solver.getAbsoluteAccuracy(),
                    FastMath.abs(expected * solver.getRelativeAccuracy()));
 
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    public void testQuadraticFunction() throws MathException {
        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);
        UnivariateRealSolver 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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    public void testQuinticFunction() throws MathException {
        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);
        UnivariateRealSolver 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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    /**
     * Test of parameters for the solver.
     */
    public void testParameters() throws Exception {
        double coefficients[] = { -3.0, 5.0, 2.0 };
        PolynomialFunction f = new PolynomialFunction(coefficients);
        UnivariateRealSolver solver = new LaguerreSolver();

        try {
            // bad interval
            solver.solve(f, 1, -1);
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    @Test
    public void testNoError() throws OptimizationException {
        Random randomizer = new Random(64925784252l);
        for (int degree = 1; degree < 10; ++degree) {
            PolynomialFunction p = buildRandomPolynomial(degree, randomizer);

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

            PolynomialFunction fitted = fitter.fit();

            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)));
                assertEquals(0.0, error, 1.0e-6);
            }

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

            PolynomialFitter fitter =
                new PolynomialFitter(degree, 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());
            }

            PolynomialFunction fitted = fitter.fit();

            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);
                assertTrue(FastMath.abs(error) < 0.1);
            }
        }
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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 + FastMath.abs(reference)));
                }
            }
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