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357 lines
17 KiB
C
357 lines
17 KiB
C
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/*
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* Copyright(C) 2017, Andrej Prochazka
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Affero General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Affero General Public License for more details.
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* You should have received a copy of the GNU Affero General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef GLQ_INTEGRATOR_H
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#define GLQ_INTEGRATOR_H
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#include <array>
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namespace integrators{
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template<int order>
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struct GL_data{
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};
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template<int order>
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class GaussLegendreIntegration{
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public:
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template<typename F>
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double integrate(F& f, double a, double b) const;
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template<typename F>
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double operator()(F& f, double a, double b) const {return integrate(f, a, b);}
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double w(int i) const {return GL_data<order>::w()[i];}
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double x(int i) const {return GL_data<order>::x()[i];}
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int n() const {return order;}
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std::array<double,order> get_points(double a = -1.0, double b = 1.0)const;
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};
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template<int order>
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template<typename F>
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double GaussLegendreIntegration<order>::integrate(F& f, double a, double b) const{
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double res=0.0;
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double p = 0.5*(b-a);
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double q = 0.5*(b+a);
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if(order%2){res+= w(0) * (f(p*x(0) + q));} // in case odd-order
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for(int i=order%2;i<order/2 + order%2;i++){
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res += w(i) * (f(p*x(i) + q) + f(-p*x(i) + q));
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}
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return p*res;
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}
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template<int order>
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std::array<double,order> GaussLegendreIntegration<order>::get_points(double a, double b)const{
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std::array<double,order> points;
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double p = 0.5*(b-a);
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double q = 0.5*(b+a);
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int num = (order/2);
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for(int i=0;i< num;i++){
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points[num-i-1] = -p*x(i) + q;
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points[num+i] = p*x(i) + q;
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}
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return points;
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}
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template<int order>
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class GaussLegendreIntegration2D{
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public:
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template<typename F>
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double integrate(F& f, double a, double b, double c, double d) const;
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template<typename F>
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double operator()(F& f, double a, double b, double c, double d) const {return integrate(f, a,b,c,d);}
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private:
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GaussLegendreIntegration<order> integrator;
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};
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template<int order>
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template<typename F>
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double GaussLegendreIntegration2D<order>::integrate(F& f, double a, double b, double c, double d) const{
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double res=0.0;
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double p = (b-a)/2.0;
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double q = (b+a)/2.0;
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double r = (d-c)/2.0;
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double s = (d+c)/2.0;
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double xx, yy, sum;
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for(int i=0;i<order/2;i++){
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xx = (p*integrator.x(i));
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for(int j=0;j<order/2;j++){
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yy = (r*integrator.x(j));
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sum = (f(xx + q, yy + s) + f(xx + q, -yy+s));
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sum += (f(-xx + q, yy + s) + f(-xx + q, -yy+s));
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res += integrator.w(i) * integrator.w(j) * sum;
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}
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}
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return p*r*res;
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}
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template<int order, int order2 = order>
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class GaussLegendreIntegration2DA{
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public:
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template<typename F>
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double integrate(F& f, double a, double b, double c, double d) const;
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template<typename F>
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double operator()(F& f, double a, double b, double c, double d) const {return integrate(f, a,b,c,d);}
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private:
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GaussLegendreIntegration<order> integrator;
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GaussLegendreIntegration<order2> integrator2;
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};
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template<int order, int order2>
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template<typename F>
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double GaussLegendreIntegration2DA<order, order2>::integrate(F& f, double a, double b, double c, double d) const{
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double res=0.0;
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double p = (b-a)/2.0;
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double q = (b+a)/2.0;
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double r = (d-c)/2.0;
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double s = (d+c)/2.0;
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double xx, yy, sum;
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for(int i=0;i<order/2;i++){
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xx = (p*integrator.x(i));
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for(int j=0;j<order2/2;j++){
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yy = (r*integrator2.x(j));
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sum = (f(xx + q, yy + s) + f(xx + q, -yy+s));
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sum += (f(-xx + q, yy + s) + f(-xx + q, -yy+s));
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res += integrator.w(i) * integrator2.w(j) * sum;
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}
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}
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return p*r*res;
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}
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/// weights
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//order = 3
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template<>
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struct GL_data<3>{
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static const std::array<double,2>& x(){
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static const std::array<double,2> _x = {0.0,0.7745966692414833770359};
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return _x;
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}
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static const std::array<double,2>& w(){
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static const std::array<double,2> _w = {0.8888888888888888888889,0.555555555555555555556};
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return _w;
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}
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};
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// order = 4
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template<>
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struct GL_data<4>{
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static const std::array<double,2>& x(){
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static const std::array<double,2> _x =
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{0.3399810435848562648026658,0.8611363115940525752239465};
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return _x;
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}
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static const std::array<double,2>& w(){
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static const std::array<double,2> _w =
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{0.6521451548625461426269361,0.3478548451374538573730639};
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return _w;
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}
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};
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// order = 5
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template<>
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struct GL_data<5>{
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static const std::array<double,3>& x(){
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static const std::array<double,3> _x =
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{0.0, 0.5384693101056830910363, 0.9061798459386639927976};
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return _x;
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}
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static const std::array<double,3>& w(){
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static const std::array<double,3> _w =
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{0.568888888888888888888, 0.4786286704993664680413, 0.2369268850561890875143};
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return _w;
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}
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};
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// order = 6
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template<>
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struct GL_data<6>{
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static const std::array<double,3>& x(){
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static const std::array<double,3> _x =
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{0.2386191860831969086305017,0.6612093864662645136613996,0.9324695142031520278123016};
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return _x;
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}
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static const std::array<double,3>& w(){
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static const std::array<double,3> _w =
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{0.4679139345726910473898703,0.3607615730481386075698335,0.1713244923791703450402961};
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return _w;
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}
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};
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// order = 7
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template<>
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struct GL_data<7>{
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static const std::array<double,4>& x(){
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static const std::array<double,4> _x =
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{0.0, 0.4058451513773971669066, 0.7415311855993944398639,0.9491079123427585245262};
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return _x;
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}
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static const std::array<double,4>& w(){
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static const std::array<double,4> _w =
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{0.417959183673469387755, 0.38183005050511894495, 0.279705391489276667901, 0.129484966168869693271};
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return _w;
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}
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};
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// order = 8
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template<>
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struct GL_data<8>{
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static const std::array<double,4>& x(){
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static const std::array<double,4> _x =
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{0.1834346424956498049394761,0.5255324099163289858177390,0.7966664774136267395915539,0.9602898564975362316835609};
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return _x;
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}
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static const std::array<double,4>& w(){
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static const std::array<double,4> _w =
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{0.3626837833783619829651504,0.3137066458778872873379622,0.2223810344533744705443560,0.1012285362903762591525314};
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return _w;
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}
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};
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// order = 10
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template<>
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struct GL_data<10>{
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static const std::array<double,5>& x(){
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static const std::array<double,5> _x =
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{0.1488743389816312108848260,0.4333953941292471907992659,0.6794095682990244062343274,0.8650633666889845107320967,0.9739065285171717200779640};
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return _x;
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}
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static const std::array<double,5>& w(){
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static const std::array<double,5> _w =
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{0.2955242247147528701738930,0.2692667193099963550912269,0.2190863625159820439955349,0.1494513491505805931457763,0.0666713443086881375935688};
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return _w;
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}
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};
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// order = 12
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template<>
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struct GL_data<12>{
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static const std::array<double,6>& x(){
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static const std::array<double,6> _x =
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{0.1252334085114689154724414,0.3678314989981801937526915,0.5873179542866174472967024,0.7699026741943046870368938,0.9041172563704748566784659,0.9815606342467192506905491};
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return _x;
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}
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static const std::array<double,6>& w(){
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static const std::array<double,6> _w =
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{0.2491470458134027850005624,0.2334925365383548087608499,0.2031674267230659217490645,0.1600783285433462263346525,0.1069393259953184309602547,0.0471753363865118271946160};
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return _w;
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}
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};
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// order = 14
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template<>
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struct GL_data<14>{
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static const std::array<double,7>& x(){
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static const std::array<double,7> _x =
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{0.1080549487073436620662447,0.3191123689278897604356718,0.5152486363581540919652907,0.6872929048116854701480198,0.8272013150697649931897947,0.9284348836635735173363911,0.9862838086968123388415973};
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return _x;
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}
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static const std::array<double,7>& w(){
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static const std::array<double,7> _w =
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{0.2152638534631577901958764,0.2051984637212956039659241,0.1855383974779378137417166,0.1572031671581935345696019,0.1215185706879031846894148,0.0801580871597602098056333,0.0351194603317518630318329};
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return _w;
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}
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};
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// order = 16
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template<>
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struct GL_data<16>{
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static const std::array<double,8>& x(){
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static const std::array<double,8> _x =
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{0.0950125098376374401853193,0.2816035507792589132304605,0.4580167776572273863424194,0.6178762444026437484466718,0.7554044083550030338951012,0.8656312023878317438804679,0.9445750230732325760779884,0.9894009349916499325961542};
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return _x;
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}
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static const std::array<double,8>& w(){
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static const std::array<double,8> _w =
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{0.1894506104550684962853967,0.1826034150449235888667637,0.1691565193950025381893121,0.1495959888165767320815017,0.1246289712555338720524763,0.0951585116824927848099251,0.0622535239386478928628438,0.0271524594117540948517806};
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return _w;
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}
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};
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// order = 20
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template<>
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struct GL_data<20>{
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static const std::array<double,10>& x(){
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static const std::array<double,10> _x =
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{0.0765265211334973337546404,0.2277858511416450780804962,0.3737060887154195606725482,0.5108670019508270980043641,0.6360536807265150254528367,0.7463319064601507926143051,0.8391169718222188233945291,0.9122344282513259058677524,0.9639719272779137912676661,0.9931285991850949247861224};
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return _x;
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}
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static const std::array<double,10>& w(){
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static const std::array<double,10> _w =
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{0.1527533871307258506980843,0.1491729864726037467878287,0.1420961093183820513292983,0.1316886384491766268984945,0.1181945319615184173123774,0.1019301198172404350367501,0.0832767415767047487247581,0.0626720483341090635695065,0.0406014298003869413310400,0.0176140071391521183118620};
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return _w;
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}
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};
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// order = 32
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template<>
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struct GL_data<32>{
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static const std::array<double,16>& x(){
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static const std::array<double,16> _x =
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{0.0483076656877383162348126,0.1444719615827964934851864,0.2392873622521370745446032,0.3318686022821276497799168,0.4213512761306353453641194,0.5068999089322293900237475,0.5877157572407623290407455,0.6630442669302152009751152,0.7321821187402896803874267,0.7944837959679424069630973,0.8493676137325699701336930,0.8963211557660521239653072,0.9349060759377396891709191,0.9647622555875064307738119,0.9856115115452683354001750,0.9972638618494815635449811};
|
||
|
|
return _x;
|
||
|
|
}
|
||
|
|
|
||
|
|
static const std::array<double,16>& w(){
|
||
|
|
static const std::array<double,16> _w =
|
||
|
|
{0.0965400885147278005667648,0.0956387200792748594190820,0.0938443990808045656391802,0.0911738786957638847128686,0.0876520930044038111427715,0.0833119242269467552221991,0.0781938957870703064717409,0.0723457941088485062253994,0.0658222227763618468376501,0.0586840934785355471452836,0.0509980592623761761961632,0.0428358980222266806568786,0.0342738629130214331026877,0.0253920653092620594557526,0.0162743947309056706051706,0.0070186100094700966004071};
|
||
|
|
return _w;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
//order = 64
|
||
|
|
template<>
|
||
|
|
struct GL_data<64>{
|
||
|
|
static const std::array<double,32>& x(){
|
||
|
|
static const std::array<double,32> _x =
|
||
|
|
{0.0243502926634244325089558,0.0729931217877990394495429,0.1214628192961205544703765,0.1696444204239928180373136,0.2174236437400070841496487,0.2646871622087674163739642,0.3113228719902109561575127,0.3572201583376681159504426,0.4022701579639916036957668,0.4463660172534640879849477,0.4894031457070529574785263,0.5312794640198945456580139,0.5718956462026340342838781,0.6111553551723932502488530,0.6489654712546573398577612,0.6852363130542332425635584,0.7198818501716108268489402,0.7528199072605318966118638,0.7839723589433414076102205,0.8132653151227975597419233,0.8406292962525803627516915,0.8659993981540928197607834,0.8893154459951141058534040,0.9105221370785028057563807,0.9295691721319395758214902,0.9464113748584028160624815,0.9610087996520537189186141,0.9733268277899109637418535,0.9833362538846259569312993,0.9910133714767443207393824,0.9963401167719552793469245,0.9993050417357721394569056};
|
||
|
|
return _x;
|
||
|
|
}
|
||
|
|
|
||
|
|
static const std::array<double,32>& w(){
|
||
|
|
static const std::array<double,32> _w =
|
||
|
|
{0.0486909570091397203833654,0.0485754674415034269347991,0.0483447622348029571697695,0.0479993885964583077281262,0.0475401657148303086622822,0.0469681828162100173253263,0.0462847965813144172959532,0.0454916279274181444797710,0.0445905581637565630601347,0.0435837245293234533768279,0.0424735151236535890073398,0.0412625632426235286101563,0.0399537411327203413866569,0.0385501531786156291289625,0.0370551285402400460404151,0.0354722132568823838106931,0.0338051618371416093915655,0.0320579283548515535854675,0.0302346570724024788679741,0.0283396726142594832275113,0.0263774697150546586716918,0.0243527025687108733381776,0.0222701738083832541592983,0.0201348231535302093723403,0.0179517157756973430850453,0.0157260304760247193219660,0.0134630478967186425980608,0.0111681394601311288185905,0.0088467598263639477230309,0.0065044579689783628561174,0.0041470332605624676352875,0.0017832807216964329472961};
|
||
|
|
return _w;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
//order = 128
|
||
|
|
template<>
|
||
|
|
struct GL_data<128>{
|
||
|
|
static const std::array<double,64>& x(){
|
||
|
|
static const std::array<double,64> _x =
|
||
|
|
{0.0122236989606157641980521,0.0366637909687334933302153,0.0610819696041395681037870,0.0854636405045154986364980,0.1097942311276437466729747,0.1340591994611877851175753,0.1582440427142249339974755,0.1823343059853371824103826,0.2063155909020792171540580,0.2301735642266599864109866,0.2538939664226943208556180,0.2774626201779044028062316,0.3008654388776772026671541,0.3240884350244133751832523,0.3471177285976355084261628,0.3699395553498590266165917,0.3925402750332674427356482,0.4149063795522750154922739,0.4370245010371041629370429,0.4588814198335521954490891,0.4804640724041720258582757,0.5017595591361444642896063,0.5227551520511754784539479,0.5434383024128103634441936,0.5637966482266180839144308,0.5838180216287630895500389,0.6034904561585486242035732,0.6228021939105849107615396,0.6417416925623075571535249,0.6602976322726460521059468,0.6784589224477192593677557,0.6962147083695143323850866,0.7135543776835874133438599,0.7304675667419088064717369,0.7469441667970619811698824,0.7629743300440947227797691,0.7785484755064119668504941,0.7936572947621932902433329,0.8082917575079136601196422,0.8224431169556438424645942,0.8361029150609068471168753,0.8492629875779689691636001,0.8619154689395484605906323,0.8740527969580317986954180,0.8856677173453972174082924,0.8967532880491581843864474,0.9073028834017568139214859,0.9173101980809605370364836,0.9267692508789478433346245,0.9356743882779163757831268,0.9440202878302201821211114,0.9518019613412643862177963,0.9590147578536999280989185,0.9656543664319652686458290,0.9717168187471365809043384,0.9771984914639073871653744,0.9820961084357185360247656,0.9864067427245862088712355,0.9901278184917343833379303,0.9932571129002129353034372,0.9957927585349811868641612,0.9977332486255140198821574,0.9990774599773758950119878,0.9998248879471319144736081};
|
||
|
|
return _x;
|
||
|
|
}
|
||
|
|
|
||
|
|
static const std::array<double,64>& w(){
|
||
|
|
static const std::array<double,64> _w =
|
||
|
|
{0.0244461801962625182113259,0.0244315690978500450548486,0.0244023556338495820932980,0.0243585572646906258532685,0.0243002001679718653234426,0.0242273192228152481200933,0.0241399579890192849977167,0.0240381686810240526375873,0.0239220121367034556724504,0.0237915577810034006387807,0.0236468835844476151436514,0.0234880760165359131530253,0.0233152299940627601224157,0.0231284488243870278792979,0.0229278441436868469204110,0.0227135358502364613097126,0.0224856520327449668718246,0.0222443288937997651046291,0.0219897106684604914341221,0.0217219495380520753752610,0.0214412055392084601371119,0.0211476464682213485370195,0.0208414477807511491135839,0.0205227924869600694322850,0.0201918710421300411806732,0.0198488812328308622199444,0.0194940280587066028230219,0.0191275236099509454865185,0.0187495869405447086509195,0.0183604439373313432212893,0.0179603271850086859401969,0.0175494758271177046487069,0.0171281354231113768306810,0.0166965578015892045890915,0.0162550009097851870516575,0.0158037286593993468589656,0.0153430107688651440859909,0.0148731226021473142523855,0.0143943450041668461768239,0.0139069641329519852442880,0.0134112712886163323144890,0.0129075627392673472204428,0.0123961395439509229688217,0.0118773073727402795758911,0.0113513763240804166932817,0.0108186607395030762476596,0.0102794790158321571332153,0.0097341534150068058635483,0.0091830098716608743344787,0.0086263777986167497049788,0.0080645898904860579729286,0.0074979819256347286876720,0.0069268925668988135634267,0.0063516631617071887872143,0.0057726375428656985893346,0.0051901618326763302050708,0.0046045842567029551182905,0.0040162549837386423131943,0.0034255260409102157743378,0.0028327514714579910952857,0.0022382884309626187436221,0.0016425030186690295387909,0.0010458126793403487793129,0.0004493809602920903763943};
|
||
|
|
return _w;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
} // end of namespace
|
||
|
|
#endif
|