如何使用升压平分？ [英] How to use boost bisection?

问题描述

昨天，我与另一升压功能的问题，但幸运的是，你们帮我解决这些问题。今天，我需要知道如何正确使用二分法功能。

Yesterday I had problems with another boost functions but luckily you guys helped me to solve them. Today I would need to know how to use bisection function properly.

因此​​，这里是如何，我认为它应该工作，但从来没有少，似乎我得到这个也是不对的。好了，所以我想用：

So here is how I think it should work but never the less it seems that I'm getting this also wrong. Okay so I would like to use:

template <class F, class T, class Tol>
 std::pair<T, T> 
 bisect(
    F f, 
    T min, 
    T max, 
    Tol tol);

从<一个href=\"http://www.boost.org/doc/libs/1_46_1/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html\"相对=nofollow>这里但我的问题是宽容，因为我不知道如何设置是正确的。我试过

from here but my problem is with tolerance because I don't know how to set it right. I've tried

double value = boost::math::tools::eps_tolerance<double>(0.00001);

和如何我返回时，二分法已经找到了价值？如果结果是对数字作为的std ::对在功能，之后才算分钟+最大/ 2？

and how to I return the value when the bisection has found ? Should the result be pair of numbers as std::pair in the function and after that just calculate min+max/2?

谢谢！

推荐答案

这是一个例子使用的开张。考虑求解方程 X ^ 2 - 3X + 1 = 0 ：

This is an example use of bisect. Consider solving the equation x^2 - 3x + 1 = 0:

struct TerminationCondition  {
  bool operator() (double min, double max)  {
    return abs(min - max) <= 0.000001;
  }
};

struct FunctionToApproximate  {
  double operator() (double x)  {
    return x*x - 3*x + 1;  // Replace with your function
  }
};

// ...
using boost::math::tools::bisect;
double from = 0;  // The solution must lie in the interval [from, to], additionally f(from) <= 0 && f(to) >= 0
double to = 1;
std::pair<double, double> result = bisect(FunctionToApproximate(), from, to, TerminationCondition());
double root = (result.first + result.second) / 2;  // = 0.381966...

编辑：另外，你这是怎么可以自定义函数使用它：

Alternatively, this is how you can use it with custom functions:

double myF(double x)  {
  return x*x*x;
}

double otherF(double x)  {
  return log(abs(x));
}

// ...
std::pair<double, double> result1 = bisect(&myF, from, to, TerminationCondition());
std::pair<double, double> result2 = bisect(&otherF, 0.1, 1.1, TerminationCondition());

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