solve.h
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上传日期:2022-07-26
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- // solve.h
- //
- // Copyright (C) 2001, Chris Laurel <claurel@shatters.net>
- //
- // This program is free software; you can redistribute it and/or
- // modify it under the terms of the GNU General Public License
- // as published by the Free Software Foundation; either version 2
- // of the License, or (at your option) any later version.
- #include <utility>
- // Solve a function using the bisection method. Returns a pair
- // with the solution as the first element and the error as the second.
- template<class T, class F> std::pair<T, T> solve_bisection(F f,
- T lower, T upper,
- T err,
- int maxIter = 100)
- {
- T x = 0.0;
- for (int i = 0; i < maxIter; i++)
- {
- x = (lower + upper) * (T) 0.5;
- if (upper - lower < 2 * err)
- break;
- T y = f(x);
- if (y < 0)
- lower = x;
- else
- upper = x;
- }
- return std::make_pair(x, (upper - lower) / 2);
- }
- // Solve using iteration; terminate when error is below err or the maximum
- // number of iterations is reached.
- template<class T, class F> std::pair<T, T> solve_iteration(F f,
- T x0,
- T err,
- int maxIter = 100)
- {
- T x = 0;
- T x2 = x0;
- for (int i = 0; i < maxIter; i++)
- {
- x = x2;
- x2 = f(x);
- if (abs(x2 - x) < err)
- return std::make_pair(x2, x2 - x);
- }
- return std::make_pair(x2, x2 - x);
- }
- // Solve using iteration method and a fixed number of steps.
- template<class T, class F> std::pair<T, T> solve_iteration_fixed(F f,
- T x0,
- int maxIter)
- {
- T x = 0;
- T x2 = x0;
- for (int i = 0; i < maxIter; i++)
- {
- x = x2;
- x2 = f(x);
- }
- return std::make_pair(x2, x2 - x);
- }