Question

我想使用两个boost库来执行任务，我不确定如何继续。

我有一行函数代码，给出了N，x和B值的答案：

double ans = cdf(boost::math::binomial mybinom(N, x), B);

让我们将其表示为ans = f（B，N，x）。

我想找到它的根，即x的值，在该值处，函数例如是y = f（x），导致y = 0.

我的代码，形式为y = f（B，N，x）涉及一个小的重新排列以否定ans：

double myfun = function(B, N, x, ans){
    double output = (cdf(boost::math::binomial mybinom(N, x), B) - ans);
    return output;
}

到目前为止一切顺利。现在我知道在Boost中，根头中的算法将帮助我们找到根，所以在阅读时我看到TOMS算法748将接受因为它的主要参数'f'是一元函子。一个例子如下：

#include <iostream>
#include <sstream>
#include <string>


#include <boost/math/tools/roots.hpp>

class Test {
public:
    double operator()(const double x) {
        return x * cos(x);
    }
};

// see: 
// http://www.boost.org/doc/libs/1_47_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html

int main(int argc, char** argv) {
    Test t;
    typedef std::pair<double, double> Result;
    boost::uintmax_t max_iter=500;
    boost::math::tools::eps_tolerance<double> tol(30);

    Result r1 = boost::math::tools::toms748_solve(t, 1.0, 2.0, tol, max_iter);
    std::cout << "root bracketed: [ " << r1.first << " , " << r1.second <<  " ]" << std::endl;
    std::cout << "f("<< r1.first << ")=" << t(r1.first) << std::endl;
    std::cout << "f("<< r1.second << ")=" << t(r1.second) << std::endl;
    std::cout << "max_iter=" << max_iter << std::endl;
    return 0;
}

好的，现在我遇到了问题。我看到的每个例子（对于这个和类似的算法）都需要一个一元仿函数。并显示一个只有x作为参数的函数，例如x * cos(x)。但是你看到我的函数有参数B，N，x和ans。那么如何从f（B，N，x，ans）得到一元函子，即f（x），使得boost算法可以接受它作为输入来找到根？

我想到的一件事可能是（我在这里不知道因为我从未听说过一个一元仿函数），从我收集到的，一元函子是类，类可以有函数和变量，那么可以设计一元仿函数类，所以在创建时，你提供B和N以及ans，其值是成员变量，然后一元仿函数的double operator()(const double x){}内的函数可以使用B和N和ans因为它们是成员变量而不需要在运算符中提供，因此是一元的。因此，就我而言，我在创建对象时指定B和N变量，但就boost算法和一元运算符而言，它们是成员变量，并且只是函数体内已有的值？

我想象的是：

class Test {
public:
    double operator()(const double x) {
        return (cdf(boost::math::binomial mybinom(N, x), B) - ans);
    }
private:
    int B;
    int N;
    double ans;
};

我在这里是正确的路线还是我在错误的树上咆哮？

- 编辑 -

以下是我目前为解决此问题而制作的代码：

#include <iostream>
#include <boost/math/distributions/binomial.hpp>
#include <boost/math/tools/roots.hpp>



class MyBinom
{
    public:
        MyBinom(int n, int b, double p);
        double operator()(const double x);

    private:
        int N;
        int B;
        double P;
};


MyBinom::MyBinom(int n, int b, double p)
            : N(n), B(b), P(p)
        {/* Body intentionally empty */}


double MyBinom::operator()(const double x)
{
    boost::math::binomial myBinomial(N, x);
    return (cdf(myBinomial, B) - P);
}



int main()
{
    MyBinom myBinom95(4715, 75, 0.95); // Create the Class with the unary operator.

    boost::uintmax_t max_iter=500; // Set max iterations.

    boost::math::tools::eps_tolerance<double> tol(30); //Set the eps tolerance.

    std::pair<double, double> r1 = boost::math::tools::toms748_solve(myBinom95, 0, 1, tol, max_iter); // use the toms solve algorithm.

    std::cout << "Let's take a look at the root" << std::endl;
    std::cout << "root bracketed: [ " << r1.first << " , " << r1.second <<  " ]" << std::endl;
    std::cout << "f("<< r1.first << ")=" << myBinom95(r1.first) << std::endl;
    std::cout << "f("<< r1.second << ")=" << myBinom95(r1.second) << std::endl;
    std::cout << "max_iter=" << max_iter << std::endl;

    return 0;
}

然而它无法编译 - 与增强标题有关：

$ g++ main.cpp -o test
In file included from /usr/include/boost/math/tools/roots.hpp:32:0,
                 from /usr/include/boost/math/special_functions/detail/igamma_inverse.hpp:16,
                 from /usr/include/boost/math/special_functions/gamma.hpp:1528,
                 from /usr/include/boost/math/special_functions/beta.hpp:15,
                 from /usr/include/boost/math/distributions/binomial.hpp:83,
                 from main.cpp:2:
/usr/include/boost/math/tools/toms748_solve.hpp: In function 'std::pair<T, T> boost::math::tools::toms748_solve(F, const T&, const T&, Tol, uintmax_t&, const Policy&) [with F = MyBinom, T = int, Tol = boost::math::tools::eps_tolerance<double>, Policy = boost::math::policies::policy<boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy>, uintmax_t = long unsigned int]':
/usr/include/boost/math/tools/toms748_solve.hpp:475:71:   instantiated from 'std::pair<T, T> boost::math::tools::toms748_solve(F, const T&, const T&, Tol, uintmax_t&) [with F = MyBinom, T = int, Tol = boost::math::tools::eps_tolerance<double>, uintmax_t = long unsigned int]'
main.cpp:41:100:   instantiated from here
/usr/include/boost/math/tools/toms748_solve.hpp:467:81: error: no matching function for call to 'toms748_solve(MyBinom&, const int&, const int&, double, double, boost::math::tools::eps_tolerance<double>&, uintmax_t&, const boost::math::policies::policy<boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy>&)'
/usr/include/boost/math/tools/toms748_solve.hpp:467:81: note: candidates are:
/usr/include/boost/math/tools/toms748_solve.hpp:283:17: note: template<class F, class T, class Tol, class Policy> std::pair<T, T> boost::math::tools::toms748_solve(F, const T&, const T&, const T&, const T&, Tol, uintmax_t&, const Policy&)
/usr/include/boost/math/tools/toms748_solve.hpp:458:24: note: template<class F, class T, class Tol> std::pair<T, T> boost::math::tools::toms748_solve(F, const T&, const T&, const T&, const T&, Tol, uintmax_t&)
/usr/include/boost/math/tools/toms748_solve.hpp:464:24: note: template<class F, class T, class Tol, class Policy> std::pair<T, T> boost::math::tools::toms748_solve(F, const T&, const T&, Tol, uintmax_t&, const Policy&)
/usr/include/boost/math/tools/toms748_solve.hpp:473:24: note: template<class F, class T, class Tol> std::pair<T, T> boost::math::tools::toms748_solve(F, const T&, const T&, Tol, uintmax_t&)

谢谢，本。

Answer 1

以下是正确的：

class Test {
public:
    Test(int B, int N, int ans) : B(B), N(N), ans(ans) {}

    double operator()(const double x) const {
        return (cdf(boost::math::binomial mybinom(N, x), B) - ans);
    }
private:
    int B;
    int N;
    double ans;
};

请注意，大多数情况下，Functor都会被复制，所以如果你想要检索一些'可变'信息（就像调用你的仿函数多少次），你必须传递一个额外的指针（一个更简单的计数器是不够的）

一元仿函数可以有成员变量吗？

1 个答案: