@Test(expectedExceptions = UnsupportedOperationException.class) public void testGetPolynomials() { JACOBI.getPolynomialsAndFirstDerivative(3); }
/** * Calculates polynomials. * @param n the n value * @param alpha the alpha value * @param beta the beta value * @return the result */ public DoubleFunction1D[] getPolynomials(int n, double alpha, double beta) { ArgChecker.isTrue(n >= 0); DoubleFunction1D[] polynomials = new DoubleFunction1D[n + 1]; for (int i = 0; i <= n; i++) { if (i == 0) { polynomials[i] = getOne(); } else if (i == 1) { polynomials[i] = new RealPolynomialFunction1D(new double[] {(alpha - beta) / 2, (alpha + beta + 2) / 2}); } else { int j = i - 1; polynomials[i] = (polynomials[j].multiply(getB(alpha, beta, j)).add(polynomials[j].multiply(getX()).multiply(getC(alpha, beta, j)) .add(polynomials[j - 1].multiply(getD(alpha, beta, j))))) .divide(getA(alpha, beta, j)); } } return polynomials; }
@Test(expectedExceptions = UnsupportedOperationException.class) public void testNoAlphaBeta() { JACOBI.getPolynomials(3); }
for (int i = 0; i <= n; i++) { if (i == 0) { polynomials[i] = Pair.of(getOne(), getZero()); } else if (i == 1) { double a1 = (alpha + beta + 2) / 2; p1 = polynomials[j].getFirst(); p2 = polynomials[j - 1].getFirst(); DoubleFunction1D temp1 = p1.multiply(getB(alpha, beta, j)); DoubleFunction1D temp2 = p1.multiply(getX()).multiply(getC(alpha, beta, j)); DoubleFunction1D temp3 = p2.multiply(getD(alpha, beta, j)); p = (temp1.add(temp2).add(temp3)).divide(getA(alpha, beta, j)); dp = p.derivative(); polynomials[i] = Pair.of(p, dp);
/** * {@inheritDoc} */ @Override public GaussianQuadratureData generate(int n) { ArgChecker.isTrue(n > 0, "n > 0"); Pair<DoubleFunction1D, DoubleFunction1D>[] polynomials = JACOBI.getPolynomialsAndFirstDerivative(n, _alpha, _beta); Pair<DoubleFunction1D, DoubleFunction1D> pair = polynomials[n]; DoubleFunction1D previous = polynomials[n - 1].getFirst(); DoubleFunction1D function = pair.getFirst(); DoubleFunction1D derivative = pair.getSecond(); double[] x = new double[n]; double[] w = new double[n]; double root = 0; for (int i = 0; i < n; i++) { double d = 2 * n + _c; root = getInitialRootGuess(root, i, n, x); root = ROOT_FINDER.getRoot(function, derivative, root); x[i] = root; w[i] = GAMMA_FUNCTION.applyAsDouble(_alpha + n) * GAMMA_FUNCTION.applyAsDouble(_beta + n) / CombinatoricsUtils.factorialDouble(n) / GAMMA_FUNCTION.applyAsDouble(n + _c + 1) * d * Math.pow(2, _c) / (derivative.applyAsDouble(root) * previous.applyAsDouble(root)); } return new GaussianQuadratureData(x, w); }
@Test(expectedExceptions = IllegalArgumentException.class) public void testNegativeN() { JACOBI.getPolynomials(-3, ALPHA, BETA); }
@Test public void test() { DoubleFunction1D[] p = JACOBI.getPolynomials(0, ALPHA, BETA); assertEquals(p.length, 1); final double x = 1.23; assertEquals(p[0].applyAsDouble(x), 1, EPS); for (int i = 0; i <= 2; i++) { p = JACOBI.getPolynomials(i, ALPHA, BETA); for (int j = 0; j <= i; j++) { assertEquals(P[j].applyAsDouble(x), p[j].applyAsDouble(x), EPS); } } } }