Why does it take so much time for R to compute m for loop with basic calculations?-CodePudding

Why does the computation of the following code in R take so much time? It takes many minutes, so I have interruped the calculations.

My aim is to adapt my simulated random numbers (sumzv, dim(sumzv) = 1000000 x 10) to my market model S_t (geometric brownian motion). The vectors m and s describe the drift and the deviation of the GBM and are vectors containing 10 numbers. DEL is the variable for the time steps. S_0 is a vector containing 10 stock prices at time 0.

n <- 1000000
k <- 10

S_t <- data.frame(matrix(0, nrow = n, ncol = k))

i <- 1
j <- 1
t <- 10

for (j in 1:k) {
  
  for (i in 1:n) {
    S_t[i, j] <- S_0[j] * exp(m[j] * t * DEL   s[j] * sqrt(DEL) * sumzv[i, j])
  
  }
  
}

Thank you for your help. Please keep in mind that I'm a beginner :)

Unfortunately, I couldn't find any helpful information so far on the internet. Some pages said, vectorization is helpful to speed up an R Code, but this doesn't seem helpful to me. I tried to break down the data frames into vectors but this got very complex.

CodePudding user response：

The following code with vectorized inner loop is equivalent to the posted code.
It also pre-computes some inner loop vectors, fac1 and fac2.

S_t <- data.frame(matrix(0, nrow = n, ncol = m))
fac1 <- m * t * DEL
fac2 <- s * sqrt(DEL)
for (j in 1:k) {
  S_t[, j] <- S_0[j] * exp(fac1[j]   fac2[j] * sumzv[, j])
}

The fully vectorized version of the loop on j above is the one-liner below. The transposes are needed because R is column major and we are multiplying by row vectors indexed on j = 1:k.

S_t2 <- t(S_0 * exp(fac1   fac2 * t(sumzv)))

CodePudding user response：

I'm not going to try to solve your entire issue but you mention vectorisation, so here is an example of that and the benefits; I calculate the same info twice; once in a double loop form like your general approach; and one where the outer loop is switched our for vectorisation. On my system the first version takes 1second to calculate; and the second version .2 seconds (or 5x faster).

If you are comfortable with the double for loop approach in terms of your comprehension; you may find it easier to implement the double loop in RCPP or similar.