# Re: [R] How to remove double loop?

From: Alberto Monteiro <albmont_at_centroin.com.br>
Date: Wed, 19 Mar 2008 19:37:40 -0200

Jonas Malmros wrote:
>
> But what if I had a matrix, where the last column was filled with
> values first (again, a for loop), and the rest was filled by using a
> double loop?
>
Killing one of those loops is quite simple. The other may be harder.

> OVal <- matrix(0, n+1, n+1)
>
> for(i in 0:n){
> OVal[i+1, n+1] <- max(Val[i+1, n+1]-K, 0)
> }
>
This is straightforward: notice that most R arithmetic functions that operate in scalars also operate in vectors, matrices and arrays. For example, sin(pi) is zero, but sin(c(0,pi/2,pi,3*pi/2)) is c(0, 1, 0, -1) (with some rounding errors).

The loop in _i_ is just to take the max of a column? So:

OVal[1:(n+1), n+1] <- # this is a vector   max(Val[1:(n+1), n+1] - # this is another vector

• K, 0) # vector - scalar = vector, max(vector) = vector

or, in one line:

OVal[1:(n+1), n+1] <- max(Val[1:(n+1), n+1] - K, 0)

You can drop the indices, as you are taking all of them:

OVal[,n+1] <- max(Val[,n+1] - K, 0)

> for(i in seq(n,1, by=-1)){
> for(j in 0:(i-1)){
> OVal[j+1, i] <- a*((1-p)*OVal[j+1, i+1]+p*OVal[j+2, i+1])
> }
> }
>
The inner loop is simple, but somehow tricky.

You are computing each j-th term as the same j-th term combined with the (j+1)-th term. So, you take a combination of js in the 1:i range and combine with js in the 2:(i+1) range... So:

OVal[1:i, i] <- a*((1-p)*OVal[1:i, i+1] + p*OVal[2:(i+1), i+1])

The outer loop (in i) probably can't be optimized.

Alberto Monteiro

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