Created
May 5, 2013 18:15
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| #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); | |
| } |
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