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

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

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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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        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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            xFitter.clearObservations();
            for (int i = 0; i < xLen; i++) {
                xFitter.addObservedPoint(1, xval[i], fval[i][j]);
            }

            yPolyX[j] = new PolynomialFunction(xFitter.fit());
        }

        // 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] = new PolynomialFunction(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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            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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        }
    }

    @Test
    public void testCompose() {
        PolynomialFunction poly =
                new PolynomialFunction(new double[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 });
        for (double x = 0.1; x < 1.2; x += 0.001) {
            SparseGradient sgX = SparseGradient.createVariable(0, x);
            SparseGradient sgY1 = sgX.getField().getZero();
            for (int i = poly.degree(); i >= 0; --i) {
                sgY1 = sgY1.multiply(sgX).add(poly.getCoefficients()[i]);
            }
            SparseGradient sgY2 = sgX.compose(poly.value(x), poly.derivative().value(x));
            SparseGradient zero = sgY1.subtract(sgY2);
            checkF0F1(zero, 0.0, 0.0);
        }
    }
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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(10000, p, -5.0, 15.0);
                    double reference = exactIntegration(p, -5.0, 15.0);
                    Assert.assertEquals(n + " " + degree + " " + i, reference, result, 1.0e-12 * (1.0 + FastMath.abs(reference)));
                }
            }
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  • org.apache.commons.math3.analysis.differentiation.DerivativeStructureTest
  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
  • 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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