[R] How to remove double loop?
Alberto Monteiro
albmont at centroin.com.br
Wed Mar 19 22:37:40 CET 2008
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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