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

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

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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 = Math.max(solver.getAbsoluteAccuracy(),
                    Math.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 = Math.max(solver.getAbsoluteAccuracy(),
                    Math.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 = Math.abs(p.value(x) - fitted.value(x)) /
                               (1.0 + Math.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 = Math.abs(p.value(x) - fitted.value(x)) /
                              (1.0 + Math.abs(p.value(x)));
                maxError = Math.max(maxError, error);
                assertTrue(Math.abs(error) < 0.1);
            }
        }
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        final double m[] = new double[n];
        for (int i = 0; i < n; i++) {
            m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
        }

        PolynomialFunction polynomials[] = new PolynomialFunction[n];
        final double coefficients[] = new double[2];
        for (int i = 0; i < n; i++) {
            coefficients[0] = y[i];
            coefficients[1] = m[i];
            polynomials[i] = new PolynomialFunction(coefficients);
        }

        return new PolynomialSplineFunction(x, polynomials);
    }
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        // 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]);
            }

            xPolyY[i] = yFitter.fit();
        }

        // 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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     * @return a fresh copy of the polynomial function
     * @deprecated as of 2.0 the function is not stored anymore within the instance.
     */
    @Deprecated
    public PolynomialFunction getPolynomialFunction() {
        return new PolynomialFunction(p.getCoefficients());
    }
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            c[j] = z[j] - mu[j] * c[j + 1];
            b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
            d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
        }

        PolynomialFunction polynomials[] = new PolynomialFunction[n];
        double coefficients[] = new double[4];
        for (int i = 0; i < n; i++) {
            coefficients[0] = y[i];
            coefficients[1] = b[i];
            coefficients[2] = c[i];
            coefficients[3] = d[i];
            polynomials[i] = new PolynomialFunction(coefficients);
        }

        return new PolynomialSplineFunction(x, polynomials);
    }
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     * @return polynomial function best fitting the observed points
     * @exception OptimizationException if the algorithm failed to converge
     */
    public PolynomialFunction fit() throws OptimizationException {
        try {
            return new PolynomialFunction(fitter.fit(new ParametricPolynomial(), new double[degree + 1]));
        } catch (FunctionEvaluationException fee) {
            // should never happen
            throw new RuntimeException(fee);
        }
    }
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