Can I dodge 'abstract class' in repeated 1-D integration using RcppNumerical

Question

I am looking for a deterministic threadsafe Rcpp algorithm for 2-D numerical integration. RcppNumerical provides a partial interface to Cuba for multidimensional integration, but from my trials that appears not to be threadsafe in RcppParallel, and it probably uses a Monte Carlo method. That throws me back on repeated 1-dimensional integration. I have used this successfully with the (not threadsafe) R function Rdqags, but my (possibly naive) coding for RcppNumerical fails to compile because the nested class is abstract. Perhaps due to the operator() virtual function.

Can anyone suggest a way around this in RcppNumerical, or some alternative?

My test code emulating the 2-D example from https://github.com/yixuan/RcppNumerical is below. It gives errors like

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

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

Murray

// [[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

The Numer::Func class is an abstract class because of one undefined method:

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

Now you are providing an implementation for

    double operator()(const double& x)

which leaves the above method undefined and hence the class abstract. You should change this to

    double operator()(const double& x) const

for both Normal1 and Normal2 to have your code compile.

BTW, my compiler (gcc 9.2) is even quite explicit about this problem:

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;
      |                    ^~~~~~~~