Rcpp - How to compute a matrix where rowSums is exactly 1

Question

I am trying to create a matrix with random numbers where the rowSums should exactly be 1.

I already have a condition which checks if the rowSums is not 1 and tries to correct it.

When I print out the result it looks correct but if I test if all values are 1 it gives me some FALSE values.

How can I correct that?

library(Rcpp)

cppFunction('
NumericMatrix imembrandc(int n, int k) {
  NumericMatrix u( n , k );
  IntegerVector sequ = seq(1,100);
  NumericVector sampled;
  for (int i=0; i < k; ++i) {
    sampled = sample(sequ, n);
    u(_,i) = sampled / sum(sampled);
  }

  if (is_true(any(rowSums(u) != 1))) {
    u(_,1) = u(_,1) + (1 - rowSums(u));
  }

  return(u);
}')

When I print out the rowSums of the result it looks correct:

res = imembrandc(n = 10, k = 5)
rowSums(res)

[1] 1 1 1 1 1 1 1 1 1 1

But checking it gives some FALSEs:

rowSums(res) == 1

[1] TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE

Answer 1

The canonical way to generate n random numbers that sum to 1 is to generate n - 1 values from [0,1), add 0 and 1 to the list and take the difference of the sorted list. Of course, this depends on the distribution you want for the random numbers. This can be expressed in R as

set.seed(42)
v <- diff(sort(c(0, runif(5), 1)))
v
#> [1] 0.28613953 0.35560598 0.18870211 0.08435842 0.02226937 0.06292459
sum(v)
#> [1] 1

^{Created on 2019-05-24 by the reprex package (v0.2.1)}

In your case in C++:

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
NumericMatrix imembrandc(int n, int k) {
  NumericMatrix u(n, k);
  for (int i = 0; i < n; ++i) {
    NumericVector row = runif(k - 1);
    row.push_back(0.0);
    row.push_back(1.0);
    u(i, _) = diff(row.sort());
  }
  return u;
}

/*** R
set.seed(42)
res = imembrandc(n = 10, k = 5)
rowSums(res)
rowSums(res) == 1
all.equal(rowSums(res),rep(1, nrow(res)))
*/

Note that I am generating rows to begin with, while you were generating columns and then tried to correct the rowSum. Output:

> set.seed(42)

> res = imembrandc(n = 10, k = 5)

> rowSums(res)
 [1] 1 1 1 1 1 1 1 1 1 1

> rowSums(res) == 1
 [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

> all.equal(rowSums(res),rep(1, nrow(res)))
[1] TRUE

BTW, all.equal gives TRUE also for your matrix, since the difference is really small. But I find it better to avoid the problem from the beginning.