/** * Gets the polynomials. * * @param n the n value * @param alpha the alpha value * @return the result */ public DoubleFunction1D[] getPolynomials(int n, double alpha) { 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[] {1 + alpha, -1}); } else { polynomials[i] = (polynomials[i - 1].multiply(2. * i + alpha - 1).subtract(polynomials[i - 1].multiply(getX())) .subtract(polynomials[i - 2].multiply((i - 1. + alpha))).divide(i)); } } return polynomials; }
/** * Gets the polynomials and derivative. * * @param n the n value * @param alpha the alpha value * @return the result */ public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(int n, double alpha) { ArgChecker.isTrue(n >= 0); @SuppressWarnings("unchecked") Pair<DoubleFunction1D, DoubleFunction1D>[] polynomials = new Pair[n + 1]; DoubleFunction1D p, dp, p1, p2; for (int i = 0; i <= n; i++) { if (i == 0) { polynomials[i] = Pair.of(getOne(), getZero()); } else if (i == 1) { polynomials[i] = Pair.of(F1, DF1); } else { p1 = polynomials[i - 1].getFirst(); p2 = polynomials[i - 2].getFirst(); p = (p1.multiply(2. * i + alpha - 1).subtract(p1.multiply(getX())).subtract(p2.multiply((i - 1. + alpha))).divide(i)); dp = (p.multiply(i).subtract(p1.multiply(i + alpha))).divide(getX()); polynomials[i] = Pair.of(p, dp); } } return polynomials; }