Question

I’m finding inconsistent results when executing the function below for a vector of inputs. It appears that the output columns are re-ordered when the vectorized input is used. Is there a better way to vectorize this function?

func <- function(t, alpha) { exp(matrix(-rep(t,7), ncol=7)*1:7*alpha) }

# correct    
rbind(func(3, 0.02), func(4, 0.02))

#incorrect
func(c(3, 4), 0.02)

> rbind(func(3, 0.02), func(4, 0.02))
          [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
[1,] 0.9417645 0.8869204 0.8352702 0.7866279 0.7408182 0.6976763 0.6570468
[2,] 0.9231163 0.8521438 0.7866279 0.7261490 0.6703200 0.6187834 0.5712091

> func(c(3, 4), 0.02)
          [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
[1,] 0.9417645 0.8352702 0.7408182 0.6570468 0.8869204 0.7866279 0.6976763
[2,] 0.8521438 0.7261490 0.6187834 0.9231163 0.7866279 0.6703200 0.5712091

Answer 1

There’s nothing incorrect or inconsistent about the results, only your understanding of R’s recycling rules and how element-by-element operations are applied. 😉

R stores and operates on objects in column-major order (including recycling rules). Your example would only work if R were row-major order. Column-major ordering means matrix(-rep(t,7), ncol=7)*1:7 produces results like:

3*1 3*3 3*5 3*7 3*2 3*4 3*6
4*2 4*4 4*6 4*1 4*3 4*5 4*7

This is because, internally, a matrix is just a vector with dim attribute. You can see this by running:

> as.vector(matrix(-rep(3:4,7), ncol=7))
 [1] -3 -4 -3 -4 -3 -4 -3 -4 -3 -4 -3 -4 -3 -4

See how the first two elements of the vector are the first column of the matrix? That’s why you get “inconsistent” results when you multiply by 1:7. You’re really asking R to do:

> (foo <- as.vector(matrix(-rep(3:4,7), ncol=7)) * 1:7)
 [1]  -3  -8  -9 -16 -15 -24 -21  -4  -6 -12 -12 -20 -18 -28

Turn it back into a “matrix” via:

> dim(foo) <- c(2,7)
> foo
     [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]   -3   -9  -15  -21   -6  -12  -18
[2,]   -8  -16  -24   -4  -12  -20  -28

If you want to take advantage of the recycling rules, you need to start with the transpose of your current matrix. Then multiply by 1:7 and transpose that result. Speaking of transpose, you may want to avoid naming variables t, since that’s the name of the transpose function.

func <- function(v, alpha) {
  t(exp(matrix(-rep(v,7), nrow=7, byrow=TRUE)*1:7*alpha))
}