我可以使用 RcppNumerical 在重复的一维积分中躲避 'abstract class'

Question

我正在寻找用于二维数值积分的确定性线程安全 Rcpp 算法。 RcppNumerical 为 Cuba 提供了一个用于多维集成的部分接口，但从我的试验来看，在 RcppParallel 中似乎不是线程安全的，它可能使用了 Monte Carlo 方法。这让我回到了重复的一维积分。我已经成功地将它与（非线程安全的）R 函数 Rdqags 一起使用，但是我的（可能是幼稚的）RcppNumerical 编码无法编译，因为嵌套的 class 是抽象的。可能是由于 operator() 虚函数。

任何人都可以在 RcppNumerical 或其他替代方案中提出解决此问题的方法吗？

下面是我模拟 https://github.com/yixuan/RcppNumerical 中的二维示例的测试代码。它会给出类似

的错误

cannot declare variable 'f2' to be of abstract type 'Normal2'

cannot declare variable 'f1' to be of abstract type 'Normal1'

默里

// [[Rcpp::depends(RcppEigen)]]
// [[Rcpp::depends(RcppNumerical)]]
#include <RcppNumerical.h>
using namespace Numer;

// P(a1 < X1 < b1, a2 < X2 < b2), (X1, X2) ~ N([0], [1   rho])
//                                            ([0], [rho   1])

class Normal2: public Func
{
private:
    const double rho;
    const double x;
    double const1;  // 2 * (1 - rho^2)
    double const2;  // 1 / (2 * PI) / sqrt(1 - rho^2)
public:
    Normal2(const double& rho_, const double& x_) : rho(rho_), x(x_)
    {
        const1 = 2.0 * (1.0 - rho * rho);
        const2 = 1.0 / (2 * M_PI) / std::sqrt(1.0 - rho * rho);
    }
   
    // PDF of bivariate normal
    double operator()(const double& y)
    {
        double z = x * x - 2 * rho * x * y + y * y;
        return const2 * std::exp(-z / const1);
    }
};


class Normal1: public Func
{
private:
    const double rho;
    double a2, b2;
public:
    Normal1(const double& rho_, const double& a2_, const double& b2_) : rho(rho_), a2(a2_), b2(b2_) {}

    // integral in y dimension for given x
    double operator()(const double& x)
    {
        Normal2 f2(rho, x);
        double err_est;
        int err_code;
        const double res = integrate(f2, a2, b2, err_est, err_code);
        return res;
    }
};

// [[Rcpp::export]]
Rcpp::List integrate_test3()
{
    double a1 = -1.0;
    double b1 =  1.0;
    double a2 = -1.0;
    double b2 =  1.0;
    Normal1 f1(0.5, a2, b2);  // rho = 0.5
   
    double err_est;
    int err_code;
    const double res = integrate(f1, a1, b1, err_est, err_code);
    return Rcpp::List::create(
        Rcpp::Named("approximate") = res,
        Rcpp::Named("error_estimate") = err_est,
        Rcpp::Named("error_code") = err_code
    );
}

Answer 1

Numer::Func class 是一个抽象 class 因为一个未定义的方法：

    virtual double operator()(const double& x) const = 0;

现在您正在为

提供实施

    double operator()(const double& x)

这使得上述方法未定义，因此 class 抽象。您应该将其更改为

    double operator()(const double& x) const

Normal1 和 Normal2 都可以编译您的代码。

顺便说一句，我的编译器 (gcc 9.2) 对这个问题甚至很明确：

59094915.cpp: In member function ‘double Normal1::operator()(const double&)’:
59094915.cpp:43:17: error: cannot declare variable ‘f2’ to be of abstract type ‘Normal2’
   43 |         Normal2 f2(rho, x);
      |                 ^~
59094915.cpp:9:7: note:   because the following virtual functions are pure within ‘Normal2’:
    9 | class Normal2: public Func
      |       ^~~~~~~
In file included from /usr/local/lib/R/site-library/RcppNumerical/include/integration/wrapper.h:13,
                 from /usr/local/lib/R/site-library/RcppNumerical/include/RcppNumerical.h:16,
                 from 59094915.cpp:3:
/usr/local/lib/R/site-library/RcppNumerical/include/integration/../Func.h:26:20: note:  ‘virtual double Numer::Func::operator()(const double&) const’
   26 |     virtual double operator()(const double& x) const = 0;
      |                    ^~~~~~~~
59094915.cpp: In function ‘Rcpp::List integrate_test3()’:
59094915.cpp:58:13: error: cannot declare variable ‘f1’ to be of abstract type ‘Normal1’
   58 |     Normal1 f1(0.5, a2, b2);  // rho = 0.5
      |             ^~
59094915.cpp:32:7: note:   because the following virtual functions are pure within ‘Normal1’:
   32 | class Normal1: public Func
      |       ^~~~~~~
In file included from /usr/local/lib/R/site-library/RcppNumerical/include/integration/wrapper.h:13,
                 from /usr/local/lib/R/site-library/RcppNumerical/include/RcppNumerical.h:16,
                 from 59094915.cpp:3:
/usr/local/lib/R/site-library/RcppNumerical/include/integration/../Func.h:26:20: note:  ‘virtual double Numer::Func::operator()(const double&) const’
   26 |     virtual double operator()(const double& x) const = 0;
      |                    ^~~~~~~~

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