使用 constexpr if 定义并声明 const std::array

问题描述 投票：0回答：4

我正在尝试实现高斯-勒让德求积，并且我想要一个模板化函数 将点数作为模板参数。 现在我有这个：

template<int number_of_quadrature_points>
double gaussian_quadrature_integral_core(double (*f)(double), double from, double to){
    double scaling_factor = (to-from)/2;   
    double average_factor = (from+to)/2;
    std::array<double, number_of_quadrature_points> factors;
    std::array<double, number_of_quadrature_points> points;
    if constexpr(number_of_quadrature_points == 2){
        factors = {1, 1};
        points = {-1.0/sqrt(3), 1.0/sqrt(3)};
    }
    if constexpr(number_of_quadrature_points == 3){
        factors = {5.0/9.0, 8.0/9.0, 5.0/9.0};
        points = {-sqrt(3.0/5.0), 0, sqrt(3.0/5.0)};
    }
    
    double sum = 0;

    for(int i = 0; i < number_of_quadrature_points; i++){
        sum += factors.at(i)*((*f)(scaling_factor*points.at(i)+average_factor));
    }

    sum *= scaling_factor;
    return sum;
}

如您所见，当模板参数发生变化时，不仅数组大小发生变化，而且内容也发生变化，但对于给定的大小，内容是众所周知的。出于这个原因，我认为如果 std::arrays 是 const static 会更好，因为该函数被调用很多次。

现在我只能使用 if constexpr 来声明数组，但是如何使用它来定义和声明数组，以便它在 if constexpr 范围之外可见并且数组只定义一次？

c++ arrays stl containers constexpr
4个回答
1
投票

添加两个辅助函数就足够了（如果您使用的是 C++20）：

template<unsigned N>
constexpr auto init_factors() {
    std::array<double, N> rv;
    if constexpr(N == 2){
        rv = {1., 1.};
    } else {
        rv = {5.0/9.0, 8.0/9.0, 5.0/9.0};
    }
    return rv;
}

template<unsigned N>
constexpr auto init_points() {
    std::array<double, N> rv;
    if constexpr(N == 2){
        rv = {-1.0/std::sqrt(3.), 1.0/std::sqrt(3.)};
    } else {
        rv = {-std::sqrt(3.0/5.0), 0, std::sqrt(3.0/5.0)};
    }
    return rv;
}

template<unsigned number_of_quadrature_points>
double gaussian_quadrature_integral_core(double (*f)(double), double from,
                                                              double to)
{
    static constexpr auto factors = init_factors<number_of_quadrature_points>();
    static constexpr auto points = init_points<number_of_quadrature_points>();
[...]

为了防止使用错误的点数，您可以添加 

static_assert

template<unsigned number_of_quadrature_points>
double
gaussian_quadrature_integral_core(double (*f)(double), double from,
                                                       double to)
{
    static_assert(number_of_quadrature_points==2||number_of_quadrature_points==3);

...或者如果您想稍后进行专业化，请阻止使用 SFINAE 进行匹配：

#include <type_traits>

template<unsigned number_of_quadrature_points>
std::enable_if_t<number_of_quadrature_points==2||number_of_quadrature_points==3,
                 double>
gaussian_quadrature_integral_core(double (*f)(double), double from,
                                                       double to)
{
1
投票

您可能有模板变量：

template <std::size_t N>
static constexpr std::array<double, N> factors;

template <std::size_t N>
static constexpr std::array<double, N> points;

template <>
constexpr std::array<double, 2> factors<2>{{1, 1}};
template <>
constexpr std::array<double, 2> points<2>{{-1.0 / sqrt(3), 1.0 / sqrt(3)}};

template <>
constexpr std::array<double, 3> factors<3>{{5.0 / 9.0, 8.0 / 9.0, 5.0 / 9.0}};
template <>
constexpr std::array<double, 3> points<3>{{-sqrt(3.0 / 5.0), 0, sqrt(3.0 / 5.0)}};

然后

template<int number_of_quadrature_points>
double gaussian_quadrature_integral_core(double (*f)(double), double from, double to)
{
    const double scaling_factor = (to - from) / 2;   
    const double average_factor = (from + to) / 2;
    double sum = 0;

    for(int i = 0; i < number_of_quadrature_points; i++){
        sum += factors<number_of_quadrature_points>[i]
           * ((*f)(scaling_factor * points<number_of_quadrature_points>[i] + average_factor));
    }

    sum *= scaling_factor;
    return sum;
}

演示

请注意，如果您没有 constexpr 

constexpr
（而 
const
没有），则必须将 
sqrt
替换为 
std::
。

0
投票

您可以使用本主题中类似的内容： 有没有办法在 C++ 模板特化中对常量值参数设置条件？

因此，我们使用 std::enable_if 和 SFINAE 创建两个模板专业化。我们通过模板参数number_of_quadrature_points来区分它们。这样我们就有了全局参数，不必多次定义和实例化。此代码使用 c++17 编译。

我还建议使用现代方法 std::function<> 而不是函数指针。

#include <array>
#include <cmath>
#include <iostream>
#include <functional>

template<int number_of_quadrature_points, typename E=void>
struct gaussian_quadrature_params
{

};

template<int number_of_quadrature_points>
struct gaussian_quadrature_params<number_of_quadrature_points, std::enable_if_t<(number_of_quadrature_points==2)> >
{
    constexpr static const std::array<double, number_of_quadrature_points> factors = {1, 1};
    constexpr static const std::array<double, number_of_quadrature_points> points = {-1.0/sqrt(3), 1.0/sqrt(3)};
};

template<int number_of_quadrature_points>
struct gaussian_quadrature_params<number_of_quadrature_points, std::enable_if_t<(number_of_quadrature_points==3)> >
{
    constexpr static const std::array<double, number_of_quadrature_points> factors = {5.0/9.0, 8.0/9.0, 5.0/9.0};
    constexpr static const std::array<double, number_of_quadrature_points> points = {-sqrt(3.0/5.0), 0, sqrt(3.0/5.0)};
};


double f(double x)
{
    return x;
}


template<int number_of_quadrature_points>
double gaussian_quadrature_integral_core(std::function<double(double)> f, double from, double to){
    double scaling_factor = (to-from)/2;   
    double average_factor = (from+to)/2;
    
    double sum = 0;

    for(int i = 0; i < number_of_quadrature_points; i++){
        sum += gaussian_quadrature_params<number_of_quadrature_points>::factors.at(i)*(f(scaling_factor*gaussian_quadrature_params<number_of_quadrature_points>::points.at(i)+average_factor));
    }

    sum *= scaling_factor;
    return sum;
}

int main()
{
   std::cout << gaussian_quadrature_integral_core<2>(f, -1.0, 1.0) << std::endl;
   std::cout << gaussian_quadrature_integral_core<3>(f, -1.0, 1.0) << std::endl;
}
0
投票

怎么样

// N: number_of_quadrature_points
template<int N>
double gaussian_quadrature_integral_core(double (*f)(double), double from, double to)
{
    constexpr std::array<double, N> factors = []()
        ->std::array<double, N>{
        if constexpr(N == 2)
            return {1.0, 1.0};
        else if constexpr(N == 3)
            return {5.0 / 9.0, 8.0 / 9.0, 5.0 / 9.0};
        // ... other N cases
    }();

    constexpr std::array<double, N> points= []()->auto{
        if constexpr(N == 2)
            return std::array<double, N>{-1.0 / std::sqrt(3), 1.0 / std::sqrt(3)};
        else if constexpr(N == 3)
            return std::array<double, N>{-std::sqrt(3.0 / 5.0), 0, std::sqrt(3.0 / 5.0)};
        // ... other N cases
    }();

    double scaling_factor = (to - from) / 2;
    double average_factor = (from + to) / 2;
    double sum = 0;
    for (int i = 0; i < N; i++)
        sum += factors.at(i)*((*f)(scaling_factor * points.at(i) + average_factor));

    sum *= scaling_factor;
    return sum;
}

使用 

if constexpr
声明和定义数组。

最新问题
© www.soinside.com 2019 - 2024. All rights reserved.