r - Fastest way to do this double summation?

Question

What is the fastest way to do this summation in R?

This is what I have so far

ans = 0
for (i in 1:dimx[1]){
  for (j in 1:dimx[2]){
    ans = ans + ((x[i,j] - parameters$mu)^2)/(parameters$omega_2[i]*parameters$sigma_2[j])
  }
}

where omega_2, and sigma_2 are omega^2 and sigma^2 respectively.

Answer 1

Nothing fancy:

# sample data
m <- matrix(1:20, 4)
sigma <- 1:ncol(m)
omega <- 1:nrow(m)
mu <- 2

sum(((m - mu) / outer(omega, sigma))^2)