Recursive function: Save output of every call to list - r

Question

I would like to save the output of every function call of the following recursive function to a list. Moreover, I need to know which (j,l)-pair correspond to which entry of the resulting list.
I have created a stripped down version to reproduce the problem. Please let me know if I should provide more information to help solve the problem. Any help is highly appreciated. Thank you.
#the recursive function
phi <- function(phik,j,l,k,d) {
if(j==0) {
diag(d)
}
else{
if(j==1) {
if(l>k) {
0 * diag(d)
}
else{
phik[[l]]
}
}
else {
if(l>k) {
0 + phi(phik,j-1,l,k,d) %*% phik[[1]]
}
else {
phi(phik,j-1,l+1,k,d) + phi(phik,j-1,l,k,d) %*% phik[[1]]
}
}
}
}
#related stuff
set.seed(123456)
phik <- vector(mode="list", length=3)
phik[[1]] <- matrix(rnorm(n=16,mean=0,s=1),nrow=4)
phik[[2]] <- matrix(rnorm(n=16,mean=0,s=1),nrow=4)
phik[[3]] <- matrix(rnorm(n=16,mean=0,s=1),nrow=4)
d <- nrow(phik[[1]])
k <- length(phik)
#function call
phiout <- phi(phik,j=10,l=1,k=k,d=d)

Answer 1

So, it is a little tricky with recursive functions, because if you want the results of the intermediate steps, you have glue them together in a list. Of course, that means when you use the results of the recursion in the function, you have to dig out the value that you want. That sounds a little convoluted, but in your case, I just mean that you have to return a little list of phi, j, and l at every step, but pull out just phi when you do the multiplications. Here is a little example:
#the recursive function
phi <- function(phik,j,l,k,d) {
if(j==0)
list(list(phi=diag(d),j=j,l=l))
else{
if(j==1) {
if(l>k)
list(list(phi=0 * diag(d),j=j,l=l))
else
list(list(phi=phik[[l]],j=j,l=l))
}
else {
if(l>k) {
first<-phi(phik,j-1,l,k,d)
second<-list(list(phi=0 + first[[1]]$phi %*% phik[[1]], j=j,l=l))
c(second,first)
}
else {
first<-phi(phik,j-1,l+1,k,d)
second<-phi(phik,j-1,l,k,d)
third<-list(list(phi=first[[1]]$phi+(second[[1]]$phi %*% phik[[1]]), j=j, l=l))
c(third,first,second)
}
}
}
}
You might be interested in why I nested the results in the first to third cases (when j is 0 or 1). If you look at the other cases, it might become clear. When l>k (and j is not 0 or 1), then there are two calls phi made. In this case, there will be a list returned, with two sets of phi, i, and j, so it is necessarily a list of lists. When I want to pull out phi from a returned value, it is difficult to tell whether it was going to be just a list or a list of lists, so I just standardized them all to the same thing.
I think return statements are ugly, but others disagree. You can add them in if you like, but they are strictly unnecessary (in this case).
Some sample output:
set.seed(123456)
phik <- vector(mode="list", length=3)
phik[[1]] <- matrix(rnorm(n=16,mean=0,s=1),nrow=4)
phik[[2]] <- matrix(rnorm(n=16,mean=0,s=1),nrow=4)
phik[[3]] <- matrix(rnorm(n=16,mean=0,s=1),nrow=4)
d <- nrow(phik[[1]])
k <- length(phik)
phi(phik,j=2,l=3,k,d)
# [[1]]
# [[1]]$phi
# [,1] [,2] [,3] [,4]
# [1,] -0.9087417 -2.064341 -0.9962198 0.7713081
# [2,] -2.9595280 -5.330120 -4.0488408 2.3357631
# [3,] -1.3754167 -3.866457 -0.8592336 1.4135614
# [4,] -0.1021518 -4.332802 0.4883886 -2.2130314
#
# [[1]]$j
# [1] 2
#
# [[1]]$l
# [1] 3
#
#
# [[2]]
# [[2]]$phi
# [,1] [,2] [,3] [,4]
# [1,] 0 0 0 0
# [2,] 0 0 0 0
# [3,] 0 0 0 0
# [4,] 0 0 0 0
#
# [[2]]$j
# [1] 1
#
# [[2]]$l
# [1] 4
#
#
# [[3]]
# [[3]]$phi
# [,1] [,2] [,3] [,4]
# [1,] -1.0461983 1.560074 -1.0713045 0.1582893
# [2,] -2.7488684 1.015088 0.9678209 -0.5019485
# [3,] -1.1298596 1.043994 0.1710325 -0.9659226
# [4,] -0.8616848 -1.115905 -0.8962503 -0.1137341
#
# [[3]]$j
# [1] 1
#
# [[3]]$l
# [1] 3