Not proper use of Random Generator for Gamma distribution draws in Rcpp

Question

I wrote the following code in Rcpp, for generating Gamma Distribution random variables, however each time that I run it I take the same output. I read that in order to have different realizations I have to use a random generator as explained here Why is this random generator always output the same number

The code that I use is the following, am I doing something wrong?? Basically, I feel that I use the exact same code as in the question posted, but for some reason in my case doesn't work.

  #include <RcppArmadilloExtensions/sample.h>
  #include <random>
  #include <iostream>
  #include <math.h>
  #include<Rmath.h>
  using namespace Rcpp;


// [[Rcpp::depends(RcppArmadillo)]]


// [[Rcpp::export]]

double Gama_Draw_1(double a , double b){
  
  std::default_random_engine generator;
  std::gamma_distribution<double> d(a,b);
  
  return d(generator);
}


// [[Rcpp::export]]


double Gama_Draw_2(double a , double b){
  
  
  std::mt19937 prng{ std::random_device{}() }; 
  std::gamma_distribution<double> d(a,b); 
  return d(prng);
  
  
}

// [[Rcpp::export]]


arma::vec Gama_Draw_3(double a , double b){
  
  arma::vec S(10);
  
  std::random_device rd; 
  std::mt19937 gen(rd()); 
  std::gamma_distribution<> distrib(a, b);
  
  for(int i=0; i<10; ++i){
    S[i] = distrib(gen);
  }
  
  return S;
}

For example,

Gama_Draw_1(1,1)
[1] 0.5719583
Gama_Draw_2(1,1)
[1] 1.065146
Gama_Draw_3(1,1)
           [,1]
 [1,] 1.0651459
 [2,] 0.8683230
 [3,] 2.7298295
 [4,] 0.7930546
 [5,] 0.3722135
 [6,] 0.7317269
 [7,] 0.2569218
 [8,] 2.0916565
 [9,] 0.9033717
[10,] 1.4198487

No matter how many times I run it I always get the same result.

Answer 1

The Rcpp package interfaces the random number generators (and special functions) from R, while properly interfacing the (high-quality) RNG inside R itself.

So I recommend you rely on that as it is in fact easy to use:

> Rcpp::cppFunction("NumericVector mygamma(int n, double a, double b) { return Rcpp::rgamma(n, a, b); }")
> set.seed(123)
> mygamma(3, 0.5, 0.5)
[1] 0.05796143 1.14034608 0.00742452
> mygamma(3, 0.5, 0.5)
[1] 0.0753645 0.2474057 0.0151682
> set.seed(123)
> mygamma(3, 0.5, 0.5)
[1] 0.05796143 1.14034608 0.00742452
>

Resetting the seed gets us the same draw, not resetting gets us different draws. As it should. Also:

> set.seed(123)
> rgamma(3, 0.5, 2.0)
[1] 0.05796143 1.14034608 0.00742452
> 

Note that the second parameter for the Gamma is used as a reciprocal value between the R version and the compiled version.

Edit: For completeness, a working version with C++11 RNG follows. Obviously we cannot double the values from R.

Code

#include <random>
#include <Rcpp.h>

std::mt19937 engine(123);

// [[Rcpp::export]]
Rcpp::NumericVector mygamma(int n, double a, double b) {
  Rcpp::NumericVector v(n);
  std::gamma_distribution<> gamma(a, b);
  for (auto i=0; i<n; i++) {
    v[i] = gamma(engine);
  }
  return v;
}

/*** R
mygamma(3, 0.5, 0.5)
mygamma(3, 0.5, 0.5)
*/

Output

> Rcpp::sourceCpp("~/git/stackoverflow/68235476/answer.cpp")

> mygamma(3, 0.5, 0.5)
[1] 0.168918 1.254678 0.311767

> mygamma(3, 0.5, 0.5)
[1] 0.0451722 0.5485451 0.0443048
>