mirror of
https://github.com/triqs/dft_tools
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109 lines
2.7 KiB
C++
109 lines
2.7 KiB
C++
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/*******************************************************************************
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*
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* TRIQS: a Toolbox for Research in Interacting Quantum Systems
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*
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* Copyright (C) 2011 by L. Boehnke, M. Ferrero, O. Parcollet
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*
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* TRIQS is free software: you can redistribute it and/or modify it under the
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* terms of the GNU General Public License as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option) any later
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* version.
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*
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* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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* details.
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*
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* You should have received a copy of the GNU General Public License along with
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* TRIQS. If not, see <http://www.gnu.org/licenses/>.
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*
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******************************************************************************/
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#ifndef LEGENDRE_asiowuer
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#define LEGENDRE_asiowuer
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#include <boost/math/special_functions/bessel.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <complex>
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#include <ostream>
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namespace triqs {
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namespace utility {
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const std::complex<double> i_c(0.0,1.0);
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const double pi = boost::math::constants::pi<double>();
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// This is T_{nl} following Eq.(E2) of our paper
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inline std::complex<double> legendre_T(int n, int l) {
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// we assume n positive. if we need n negative we can fix this here
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assert(n >= 0);
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// note: cyl_bessel_j(l,x) give the Bessel functions of the first kind J_l (x)
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// one then gets the spherical Bessel with j_l (x) = \sqrt{\pi / (2x)} J_{l+0.5} (x)
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return (sqrt(2*l+1)/sqrt(2*n+1)) * exp(i_c*(n+0.5)*pi) * pow(i_c,l) * boost::math::cyl_bessel_j(l+0.5,(n+0.5)*pi);
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}
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// This is t_l^p following Eq.(E8) of our paper
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inline double legendre_t(int l, int p) {
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// p is the 1/omega power, it can't be negative
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assert(p > 0);
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// in these two cases we can directly give back 0
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if ((l+p)%2 == 0 || p > l+1) return 0.0;
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// the factorials are done here
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double f = 1;
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for (int i = l+p-1; (i > l-p+1) && (i > 1); i--) f *= i;
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for (int i = p-1; i > 1; i--) f /= i;
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return pow( double(-1),double(p) ) * 2 * sqrt(2*l+1) * f;
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}
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/*
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Generates the Legendre polynomials
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P_0(x) = 1.0
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P_1(x) = x
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n P_{n} = (2n-1) x P_{n-1}(x) - (n-1) P_{n-2}(x)
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*/
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class legendre_generator {
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double _x;
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uint n;
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double cyclicArray[2];
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public:
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double next() {
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if (n>1)
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{
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uint eo=(n)%2;
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cyclicArray[eo]=((2*n-1)*_x*cyclicArray[1-eo]-(n-1)*cyclicArray[eo])/n;
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n++;
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return cyclicArray[eo];
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}
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else
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{
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n++;
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return cyclicArray[n-1];
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}
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}
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void reset (double x) {
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_x=x;
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n=0;
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cyclicArray[0]=1.0;
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cyclicArray[1]=x;
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}
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};
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}};
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#endif
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