mn4.cpp

#include <iostream>
#include <vector>

using std::cout;
using std::cin;

template <class T>
struct Fun {
  const T operator()(T x) {
		return std::log(x+2) - 2*x*x + 1;
	}

	T d1(T x) {
		return 1.0 / (x+2) - 4*x;
	}

	T d2(T x) {
		return - 1.0 / ((x+2.0)*(x+2.0)) - 4.0;
	}
};

template <class T>
std::pair<T, unsigned> bisection (T a, T b, T eps = 1e-6, unsigned it_bnd = 10000) {
	if (a > b) {
		std::swap(a, b);
	}

	Fun<T> f;
	if (f(a) * f(b) > 0) {
		throw std::runtime_error("No solution in this interval");
	}

	unsigned it_cnt = 0;
	for (; std::abs(b - a) >= eps && it_bnd > it_cnt; ++it_cnt) {
		T c = (a + b) / 2.0;

		if (f(a) * f(c) <= 0.0) {
			b = c;
		} else {
			a = c;
		}
	}

	T fa = f(a), fx = f((a + b) / 2.0), fb = f(b);
	if ( (fa > fx && fx > fb) || (fa < fx && fx < fb) ) {
		return std::make_pair((a + b) / 2.0, it_cnt);
	} else {
		std::runtime_error("Znaleziono asymptote pionowa!");
	}
}

template <class T>
std::pair<T, unsigned> tangents (T a, T b, T eps = 1e-6, unsigned it_bnd = 10000) {
	if (a > b) {
		std::swap(a, b);
	}

	Fun<T> f;
	if (f(a) * f(b) > 0) {
		throw std::runtime_error("No solution in this interval");
	}

	T xk;
	if (f(a) * f.d2(a) > 0) {
		xk = a;
	} else if (f(b) * f.d2(b) > 0) {
		xk = b;
	} else {
		throw std::runtime_error("Przedzial nie spelnia zalozen!");
	}

	T m = std::min(std::abs(f.d1(a)), std::abs(f.d1(b)));

	unsigned it_cnt = 0;
	for (; std::abs(f(xk)) / m >= eps && it_bnd > it_cnt; ++it_cnt) {
		xk = xk - (f(xk) / f.d1(xk));
	}

	if (xk >= a && xk <= b) {
		return std::make_pair(xk, it_cnt);
	} else {
		std::runtime_error("Znaleziono asymptote pionowa!");
	}
}

template<class T>
void start (T eps) {
	std::pair<T, unsigned> sol;

	try {
		sol = bisection<T>(-0.8, -0.7, eps);
		cout << "Bisekcje:\t" << sol.first << "\n";
		cout << "Ilosc iteracji:\t" << sol.second << "\n\n";
	} catch (std::runtime_error e) {
		cout << e.what() << "\n\n";
	}

	try {
		sol = tangents<T>(-0.8, -0.7, eps);
		cout << "Styczne:\t" << sol.first << "\n";
		cout << "Ilosc iteracji:\t" << sol.second << "\n\n";
	} catch (std::runtime_error e) {
		cout << e.what() << "\n\n";
	}
}


int main () {
	cout.setf(std::ios::adjustfield);
	//cout.setf(ios::fixed);
	cout.precision(10);

	start<double>(1e-11);
}