@Override public DoubleFunction1D[] getPolynomials(int n) { ArgChecker.isTrue(n >= 0); DoubleFunction1D[] polynomials = new DoubleFunction1D[n + 1]; for (int i = 0; i <= n; i++) { if (i == 0) { polynomials[i] = F0; } else if (i == 1) { polynomials[i] = polynomials[0].multiply(Math.sqrt(2)).multiply(getX()); } else { polynomials[i] = polynomials[i - 1].multiply(getX()).multiply(Math.sqrt(2. / i)) .subtract(polynomials[i - 2].multiply(Math.sqrt((i - 1.) / i))); } } return polynomials; }
@Test(expectedExceptions = IllegalArgumentException.class) public void testMultiplyNull() { F1.multiply(null); }
@Override public DoubleFunction1D[] getPolynomials(int n) { 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] = TWO_X; } else { polynomials[i] = polynomials[i - 1] .multiply(2) .multiply(getX()) .subtract(polynomials[i - 2].multiply(2 * i - 2)); } } return polynomials; }
@Override public DoubleFunction1D[] getPolynomials(int n) { 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] = getX(); } else { polynomials[i] = (polynomials[i - 1] .multiply(getX()) .multiply(2 * i - 1) .subtract(polynomials[i - 2].multiply(i - 1))).multiply(1. / i); } } return polynomials; }
@Override public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(int n) { ArgChecker.isTrue(n >= 0); @SuppressWarnings("unchecked") Pair<DoubleFunction1D, DoubleFunction1D>[] polynomials = new Pair[n + 1]; DoubleFunction1D p, dp, p1, p2; double sqrt2 = Math.sqrt(2); DoubleFunction1D x = getX(); for (int i = 0; i <= n; i++) { if (i == 0) { polynomials[i] = Pair.of((DoubleFunction1D) F0, getZero()); } else if (i == 1) { polynomials[i] = Pair.of(polynomials[0].getFirst().multiply(sqrt2).multiply(x), (DoubleFunction1D) DF1); } else { p1 = polynomials[i - 1].getFirst(); p2 = polynomials[i - 2].getFirst(); p = p1.multiply(x).multiply(Math.sqrt(2. / i)).subtract(p2.multiply(Math.sqrt((i - 1.) / i))); dp = p1.multiply(Math.sqrt(2 * i)); polynomials[i] = Pair.of(p, dp); } } return polynomials; }
/** * Multiplies the polynomial by a function. * If the function is not a {@link RealPolynomialFunction1D} then the multiplication takes * place as in {@link DoubleFunction1D}, otherwise the result will also be a polynomial. * * @param f the function by which to multiply * @return $P \dot f$ */ @Override public DoubleFunction1D multiply(DoubleFunction1D f) { ArgChecker.notNull(f, "function"); if (f instanceof RealPolynomialFunction1D) { RealPolynomialFunction1D p1 = (RealPolynomialFunction1D) f; double[] c = _coefficients; double[] c1 = p1.getCoefficients(); int m = c1.length; double[] newC = new double[_n + m - 1]; for (int i = 0; i < newC.length; i++) { newC[i] = 0; for (int j = Math.max(0, i + 1 - m); j < Math.min(_n, i + 1); j++) { newC[i] += c[j] * c1[i - j]; } } return new RealPolynomialFunction1D(newC); } return DoubleFunction1D.super.multiply(f); }
/** * 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; }
/** * 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; }
/** * 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; }
@Override public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(int n) { ArgChecker.isTrue(n >= 0); @SuppressWarnings("unchecked") Pair<DoubleFunction1D, DoubleFunction1D>[] polynomials = new Pair[n + 1]; DoubleFunction1D p, dp; for (int i = 0; i <= n; i++) { if (i == 0) { polynomials[i] = Pair.of(getOne(), getZero()); } else if (i == 1) { polynomials[i] = Pair.of(getX(), getOne()); } else { p = (polynomials[i - 1].getFirst() .multiply(getX()) .multiply(2 * i - 1) .subtract(polynomials[i - 2].getFirst().multiply(i - 1))).multiply(1. / i); dp = p.derivative(); polynomials[i] = Pair.of(p, dp); } } return polynomials; }
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();