How to use Rcpp to do numerical integration in C++ within R

Question

I was wondering how Rcpp could be used to perform numerical integration by calling C++ in R. My current setup takes a really long time and is highly error prone.

I think I need something better than default R numerical integration package. Would doing numerical integration in C++ within R solve these problems?

funk <- function(x,b) { 10^b * exp(-x/10) }

lambda <- function(y,k) { exp(-k*y) }

funk1 <- function(y,x,xb,b,k) { 
funk(x-xb-y,b) *exp(- integrate(lambda, lower=0, upper = y, k=k)$value) }

funk2 <-function(x,xb,b,k) { 
integrate(funk1, lower= 0, upper=x-xb, x=x,xb=xb, b=b,k=k)$value }

funk2_vc <- Vectorize(funk2)

Thanks in advance for help!

Answer 1

You'd have a lot easier time using RcppNumerical with Rcpp (and yes, it would make it faster).

The code is a port of NumericalIntegration, which combines relevant parts of Quantlib and a few other C++ libraries like LibLBFGS.

Here's a nice tutorial to get you started.

To compute integration of a function, first define a function inherited from the Func class:

class Func
{
public:
    virtual double operator()(const double& x) const = 0;
    virtual void   operator()(double* x, const int n) const
    {
        for(int i = 0; i < n; i++)
            x[i] = this->operator()(x[i]);
    }
};

The tutorial and package documentation should be enough to suit your needs, but if you need more help check out the documentation for the C++ library NumericalIntegration.