// mo3.cpp : This file contains the 'main' function. Program execution begins and ends there.
//

#include "pch.h"
#include <iostream>
#include <cmath>
#include <tuple>
#include <iomanip>

const int MAX_IT = 30;				// maksymalna ilosc iteracji
const double TOL_X = 10e-10;		//kryterium dokladnosci wyznaczenia Xn
const double TOL_F = 10e-10;		//kryterium wiarygodnosci Xn jako przyblizenia pierwiastka


double fun1(double x) {
	return sin(x / 4) * sin(x / 4) - x;
}
double fun1pic(double x) {
	return sin(x / 4) * sin(x / 4);
}
double fun1prim(double x) {
	// 1/2*sin(x/4)*cos(x/4)-1
	return sin(x / 2) / 4 - 1;
}

double fun2(double x) {
	return tan(2 * x) - x - 1;
}
double fun2pic(double x) {
	return 2 / (cos(2 * x) * cos(2 * x));
}
double fun2pic2(double x) {
	return 1 / (2 * (x + 1) * (x + 1) + 2);
}
double fun2prim(double x) {
	return 2 / (cos(2 * x) * cos(2 * x)) - 1;
}


std::tuple<double, double> bisekcja(double(*fun)(double), double a,double b) {
	double rez, e, x, fx;	// reziduum, estymator, x, f(x)
	double fa = fun(a);		// f(a)
	double fb = fun(b);		// f(b)

	std::cout << std::endl << "Bisekcja" << std::endl;

	if (fa * fb > 0) {
		std::cout << "f(a) i f(b) maja ten sam znak";
		return std::make_tuple(12345, 54321);
	}

	if (fa * fb == 0) {
		if (fa == 0) {
			std::cout << "Miejsce zerowe w x = " << a << std::endl;
			return std::make_tuple(a, fa);
		}
		if (fb == 0) {
			std::cout << "Miejsce zerowe w x = " << b << std::endl;
			return std::make_tuple(b, fb);
		}
	}

	std::cout << "IT" << std::setw(9) << "x:" << std::setw(29) << "f(x):" << std::setw(31) << "Estymator:" << std::setw(25) << "Reziduum:" << std::endl;
	std::cout << std::scientific << std::setprecision(16);

	for (int i = 1; i <= MAX_IT; i++) {
		x = (a + b) / 2;
		fx = fun(x);
		e = fabs(b - a) / 2;
		rez = fabs(fx);

		std::cout << std::setw(2) << std::right << i << ".\t" << std::right << std::setw(23) << x << "   " << std::setw(23) << fx << "   " << std::setw(23) << e << "   " << std::setw(23) << rez << std::endl;
		if (e < TOL_X || rez < TOL_F) {
			break;
		}
		if (fa * fx <= 0) {
			b = x;
			fb = fx;
		}
		else {
			a = x;
			fa = fx;
		}
	}
	return std::make_tuple(x, fx);
}
std::tuple<double, double> picard(double(*fun)(double), double(*pic)(double), double x) {
	double fx, e, rez;

	std::cout << std::endl << "Picard" << std::endl;

	if (fabs(pic(x)) > 1) {
		std::cout << "Funkcja rozbiezna!" << std::endl;
		return std::make_tuple(12345, 54321);
	}

	std::cout << "IT" << std::setw(9) << "x:" << std::setw(29) << "f(x):" << std::setw(31) << "Estymator:" << std::setw(25) << "Reziduum:" << std::endl;
	std::cout << std::scientific << std::setprecision(16);

	for (int i = 1; i <= MAX_IT; i++) {
		fx = fun(x);
		e = fabs(x - fx);
		rez = fabs(fx);

		std::cout << std::setw(2) << std::right << i << ".\t" << std::right << std::setw(23) << x << "   " << std::setw(23) << fx << "   " << std::setw(23) << e << "   " << std::setw(23) << rez << std::endl;

		if (e < TOL_X || rez < TOL_F) {
			break;
		}

		x = fx;
	}

	return std::make_tuple(x, fx);
}
std::tuple<double, double> newton(double(*fun)(double), double(*prim)(double), double xn) {
	double xn1, e, rez, fx, fpx;

	std::cout << std::endl << "Newton" << std::endl;
	std::cout << "IT" << std::setw(9) << "x:" << std::setw(29) << "f(x):" << std::setw(31) << "Estymator:" << std::setw(25) << "Reziduum:" << std::endl;
	std::cout << std::scientific << std::setprecision(16);

	for (int i = 1; i <= MAX_IT; i++) {
		fx = fun(xn);
		fpx = prim(xn);
		xn1 = xn - fx / fpx;
		e = fabs(xn - xn1);
		rez = fabs(fx);

		std::cout << std::setw(2) << std::right << i << ".\t" << std::right << std::setw(23) << xn << "   " << std::setw(23) << fx << "   " << std::setw(23) << e << "   " << std::setw(23) << rez << std::endl;

		if (e < TOL_X || rez < TOL_F) {
			break;
		}
		xn = xn1;
	}
	return std::make_tuple(xn, fx);
}
std::tuple<double, double> sieczne(double(*fun)(double), double xn, double xn1) {
	double xn2, fxn2, e, rez;
	double fxn = fun(xn);
	double fxn1 = fun(xn1);

	if ((xn - xn1 == 0) || (fxn - fxn1 == 0)) {
		std::cout << "Bledne xn i xn1" << std::endl;
		return std::make_tuple(12345, 54321);
	}
	std::cout << std::endl << "Sieczne" << std::endl;
	std::cout << "IT" << std::setw(9) << "x:" << std::setw(29) << "f(x):" << std::setw(31) << "Estymator:" << std::setw(25) << "Reziduum:" << std::endl;

	for (int i = 1; i <= MAX_IT; i++) {
		fxn = fun(xn);
		fxn1 = fun(xn1);

		if ((xn - xn1 == 0) || (fxn - fxn1 == 0)) {
			std::cout << "Bledne xn i xn1" << std::endl;
			return std::make_tuple(12345, 54321);
		}

		xn2 = xn1 - fxn1 / ((fxn1 - fxn) / (xn1 - xn));
		fxn2 = fun(xn2);
		e = fabs(xn - xn1);
		rez = fabs(fxn2);

		std::cout << std::setw(2) << std::right << i << ".\t" << std::right << std::setw(23) << xn2 << "   " << std::setw(23) << fxn2 << "   " << std::setw(23) << e << "   " << std::setw(23) << rez << std::endl;

		if (e < TOL_X || rez < TOL_F) {
			break;
		}
		xn = xn1;
		xn1 = xn2;
	}
	return std::make_tuple(xn2, fxn2);
}


int main()
{
	std::cout << "Funkcja sin^2(x/4) - x = 0";
	std::tuple<double, double> f1_picard = picard(fun1, fun1pic, 1);
	std::tuple<double, double> f1_bisekcja = bisekcja(fun1, -1, 2);
	std::tuple<double, double> f1_newton = newton(fun1, fun1prim, 1);
	std::tuple<double, double> f1_sieczne = sieczne(fun1, 1, 3);
	std::cout << std::endl << "Obliczone x0:" << std::endl;
	std::cout << "Metoda Picarda:\t\t" << "x = " << std::get<0>(f1_picard) << "\tf(x) = " << std::setw(23) << std::get<1>(f1_picard) << std::endl;
	std::cout << "Metoda bisekcji:\t" << "x = " <<  std::get<0>(f1_bisekcja) << "\tf(x) = " << std::setw(23) << std::get<1>(f1_bisekcja) << std::endl;
	std::cout << "Metoda Newtona:\t\t" << "x = " << std::get<0>(f1_newton) << "\tf(x) = " << std::setw(23) << std::get<1>(f1_newton) << std::endl;
	std::cout << "Metoda siecznych:\t" << "x = " << std::get<0>(f1_sieczne) << "\tf(x) = " << std::setw(23) << std::get<1>(f1_sieczne) << std::endl;

	std::cout << "Funkcja tg(2x) - x - 1 = 0";
	std::tuple<double, double> f2_picard = picard(fun2, fun2pic2, 1);
	std::tuple<double, double> f2_bisekcja = bisekcja(fun2, -1, 2);
	std::tuple<double, double> f2_newton = newton(fun2, fun2prim, 1);
	std::tuple<double, double> f2_sieczne = sieczne(fun2, 1, 3);
	std::cout << std::endl << "Obliczone x0:" << std::endl;
	std::cout << "Metoda Picarda:\t\t" << "x = " << std::get<0>(f2_picard) << "\tf(x) = " << std::setw(23) << std::get<1>(f2_picard) << std::endl;
	std::cout << "Metoda bisekcji:\t" << "x = " << std::get<0>(f2_bisekcja) << "\tf(x) = " << std::setw(23) << std::get<1>(f2_bisekcja) << std::endl;
	std::cout << "Metoda Newtona:\t\t" << "x = " << std::get<0>(f2_newton) << "\tf(x) = " << std::setw(23) << std::get<1>(f2_newton) << std::endl;
	std::cout << "Metoda siecznych:\t" << "x = " << std::get<0>(f2_sieczne) << "\tf(x) = " << std::setw(23) << std::get<1>(f2_sieczne) << std::endl;
}

// Run program: Ctrl + F5 or Debug > Start Without Debugging menu
// Debug program: F5 or Debug > Start Debugging menu

// Tips for Getting Started:
//   1. Use the Solution Explorer window to add/manage files
//   2. Use the Team Explorer window to connect to source control
//   3. Use the Output window to see build output and other messages
//   4. Use the Error List window to view errors
//   5. Go to Project > Add New Item to create new code files, or Project > Add Existing Item to add existing code files to the project
//   6. In the future, to open this project again, go to File > Open > Project and select the .sln file