PS_Method_CCS_test/Pseudo_Spectral_Method/Legendre_functions/Dichotomy_LGR.cpp

// 输入：	Pos：1 * 2，两端点
//			n:阶数
// 输出：	tn：精确的零点
// 方法：	二分法(LGR)
// 编写：	李兆亭，2019 / 11 / 04

#include "GPM.h"

int Dichotomy_LGR(int* n, vec* Pos, double* tn) {

	double tol = 1e-12;
	int Iscontinue = 1;
	double fx1, fx2, fx;
	double fy1, fy2, fy;
	double fav1, fav2, fav;

	double x = (*Pos)(0);
	double y = (*Pos)(1);
	double av = (x + y) / 2;

	int n1 = (*n) + 1;
	Legendre(&n1, &x, &fx1);
	Legendre(n, &x, &fx2);
	fx = fx1 + fx2;
	// cout << fx << endl;
	Legendre(&n1, &y, &fy1);
	Legendre(n, &y, &fy2);
	fy = fy1 + fy2;
	
	Legendre(&n1, &av, &fav1);
	Legendre(n, &av, &fav2);
	fav = fav1 + fav2;
	
	while (Iscontinue == 1) {
	
		if (abs(fx) <= tol) {
			*tn = x;
			Iscontinue = 0;
		}	
		else if (abs(fy) <= tol) {
			*tn = y;
			Iscontinue = 0;
		}	
		else if (abs(fav) <= tol) {
			*tn = av;
			Iscontinue = 0;
		}		
		else {
			if (fx*fav < 0) {
				x = x; y = av; av = (x + y) / 2;
				Legendre(&n1, &y, &fy1);
				Legendre(n, &y, &fy2);
				fy = fy1 + fy2;

				Legendre(&n1, &av, &fav1);
				Legendre(n, &av, &fav2);
				fav = fav1 + fav2;
			}
			else if (fav*fy < 0) {
				x = av; y = y; av = (x + y) / 2;
				Legendre(&n1, &x, &fx1);
				Legendre(n, &x, &fx2);
				fx = fx1 + fx2;

				Legendre(&n1, &av, &fav1);
				Legendre(n, &av, &fav2);
				fav = fav1 + fav2;
			}
		}
	}

	return 1;
}