Rcpp - how to use a distribution function in the C++ code

Question

I'm writing a Metropolis-Hastings algorithm for a N(0,1) distribution:

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
NumericVector metropolis(int R, double b, double x0){
    NumericVector y(R);
    y(1) = x0;
    for(int i=1; i<R; ++i){
       y(i) = y(i-1);
       double xs = y(i)+runif(1, -b,b)[0];
       double a = dnorm(xs, 0, 1)[0]/dnorm(y(i), 0, 1)[0];
       NumericVector A(2);
       A(0) = 1;
       A(1) = a;
       double random = runif(1)[0];
       if(random <= min(A)){
            y[i] = xs;
       }
   }
   return y;
}

but every time I try to compile the function, this error occurs:

Line 12: no matching function for call to 'dnorm4'

I tried to write a trivial function using dnorm, like

NumericVector den(NumericVector y, double a, double b){
    NumericVector x = dnorm(y,a,b);
    return x;
}

and it works. Does someone know why I have this type of error in the Metropolis code? Are there some other ways to use density functions in the C++ code like in R?

Answer 1

Within Rcpp there are two sets of samplers - scalar and vector - split by namespaces R:: and Rcpp::. They are divided such that:

• Scalar returns a single value (e.g. double or int)
• Vector returns multiple values (e.g. NumericVector or IntegerVector)

In this case, you want to be using the scalar sampling space and not the vector sampling space.

This is evident since:

double a = dnorm(xs, 0, 1)[0]/dnorm(y(i), 0, 1)[0];

Invokes the subset operator [0] to obtain the only element in the vector.

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The second part of this problem is the missing part of the fourth parameter as hinted by

Line 12: no matching function for call to 'dnorm4'

If you look at the R definition of the dnorm function, you see:

dnorm(x, mean = 0, sd = 1, log = FALSE)

In this case, you've supplied all but the fourth parameter.

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As a result, you'll probably want the following:

// [[Rcpp::export]]
NumericVector metropolis(int R, double b, double x0){
    NumericVector y(R);
    y(1) = x0; // C++ indices start at 0, you should change this!
    for(int i=1; i<R; ++i){ // C++ indices start at 0!!!
        y(i) = y(i-1);
        double xs = y(i) + R::runif(-b, b);
        double a = R::dnorm(xs, 0.0, 1.0, false)/R::dnorm(y(i), 0.0, 1.0, false);
        NumericVector A(2);
        A(0) = 1;
        A(1) = a;
        double random = R::runif(0.0, 1.0);
        if(random <= min(A)){
            y[i] = xs;
        }
    }
    return y;
}

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Side note:

C++ indices start at 0 not 1. As a result, your vector above is slightly problematic as you being by filling the y vector at y(1) and not y(0). I'll leave this as an exercise for you to correct though.