XY problems

One can easily fall for an XY problem even when one tries to avoid it.

Numerical integration over an infinite interval in Rcpp

On Stack Overflow the question was asked how to numerically integrate a function over a infinite range in Rcpp, e.g. by using RcppNumerical. As an example, the integral \[ \int_{-\infty}^{\infty} \mathrm{d}x \exp\left(-\frac{(x-\mu)^4}{2}\right) \] was given. Using RcppNumerical is straight forward. One defines a class that extends Numer::Func for the function and an interface function that calls Numer::integrate on it: // [[Rcpp::depends(RcppEigen)]] // [[Rcpp::depends(RcppNumerical)]] #include <RcppNumerical.h> class exp4: public Numer::Func { private: double mean; public: exp4(double mean_) : mean(mean_) {} double operator()(const double& x) const { return exp(-pow(x-mean, 4) / 2); } }; // [[Rcpp::export]] Rcpp::NumericVector integrate_exp4(const double &mean, const double &lower, const double &upper) { exp4 function(mean); double err_est; int err_code; const double result = Numer::integrate(function, lower, upper, err_est, err_code); return Rcpp::NumericVector::create(Rcpp::Named("result") = result, Rcpp::Named("error") = err_est); } This works fine for finite ranges: