89 lines
2.0 KiB
C++
89 lines
2.0 KiB
C++
// 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 <cmath>
|
|
#include <utility>
|
|
|
|
#pragma once
|
|
|
|
namespace celmath
|
|
{
|
|
|
|
// 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 = static_cast<T>(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 < static_cast<T>(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)
|
|
{
|
|
using std::abs;
|
|
|
|
T x = static_cast<T>(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 = static_cast<T>(0);
|
|
T x2 = x0;
|
|
|
|
for (int i = 0; i < maxIter; i++)
|
|
{
|
|
x = x2;
|
|
x2 = f(x);
|
|
}
|
|
|
|
return std::make_pair(x2, x2 - x);
|
|
}
|
|
|
|
} // namespace celmath
|