[R] How to remove double for loop?

[Alberto Monteiro]

Jonas Malmros wrote:
> 
> I use double for loops to fill in matrices, but there are surely
> better (and computationally faster) ways to perform that task.
> Could someone show me, given the following example of a double for
> loop, how this could be done? It is much easier to learn by examples.
> 
> Val <- matrix(0, nrow=n+1, ncol=n+1)
> for( i in 0:n){
>     for(j in 0:i){
>         Val[j+1, i+1] <- u^j*d^(i-j)
>     }
> }
> 
You could use outer. Val <- outer(vector1, vector2) does the
tensor product, meaning that each Val[i,j] will be 
vector1[i] * vector2[j].

In this case, instead of the product, you should compute the
expression:

f <- function(j,i) { u^j * d^(i-j) }

but only when j <= i. So, the function is:

f <- function(j,i) { ifelse(j > i, 0, u^j * d^(i-j) }

and the code becomes:

Val <- outer(0:n, 0:n, f)

"Entities should not be needlessly multplied" (Occam's Razor),
so let's do it without the explicit mention of f:

Val <- outer(0:n, 0:n, function(j,i) ifelse(j > i, 0, u^j*d^(i-j)))

(if u and d are positive integers, there might be a much
faster way of filling Val, using matrix multiplication and
rounding down)

Alberto Monteiro