R fill several empty matrices with loop - r

Question

I would like to fill my created empty matrices with a loop:
First I have created my empty matrizes, which works fine:
for(q in (15:30)){
assign(paste0("P",q), matrix(, nrow = q, ncol = q+1))}
But now when I want to fill these matrices with my formula, I get an dimension mistake:
for(c in (1:q+1)){
for(i in (1:q)){assign(paste0("P",q)[i,c],
((((((q-c) + 1 -(q-c+1- i))/q)^.69)/(((((q-c) + 1 - (q-c+1-i))/q)^.69+(((1 - ((q-c) + 1 -(q-c+1-i))/q))^.69))^(1/.69))) - (((((q-c)-(q-c+1-i))/q)^.69)/(((((q-c) - (q-c+1-i))/q)^.69+(((1 - ((q-c)-(q-c+1-i))/q))^.69))^(1/.69)))))}}}
Nevertheless when I use this loop for a single matrix it works e.g.:
t <- 20
c <- 1
i <- 1
for(c in (1:t+1)){
for(i in (1:t)){P20[i,c]<-( (((((t-c) + 1 -(t-c+1-i))/t)^.69)/
(((((t-c) + 1 - (t-c+1-i))/t)^.69+(((1 - ((t-c) + 1 -(t-c+1-i))/t))^.69))^(1/.69))) -
(((((t-c)-(t-c+1-i))/t)^.69)/(((((t-c) - (t-c+1-i))/t)^.69+(((1 - ((t-c)-(t-c+1-i))/t))^.69))^(1/.69))))}}
The formula is giving out probability weights according to Cummulative Prospect Theory, if anyone is interested.
Do you guys have an idea how I can make this more elegant? Should I better write a user-defined function?

Answer 1

If you are happy with your resultant matrices being in a list with the same names you were assigning to you could do something like:
l = lapply(15:30, function(q){
t = q
matrix(apply(expand.grid(1:q,1:(q+1)),1,
function(x){
i = x[1]
c = x[2]
( (((((t-c) + 1 -(t-c+1-i))/t)^.69)/
(((((t-c) + 1 - (t-c+1-i))/t)^.69+(((1 - ((t-c) + 1 -(t-c+1-i))/t))^.69))^(1/.69))) -
(((((t-c)-(t-c+1-i))/t)^.69)/(((((t-c) - (t-c+1-i))/t)^.69+(((1 - ((t-c)-(t-c+1-i))/t))^.69))^(1/.69))))
}),nrow = q, ncol = q+1, byrow = TRUE)
})
names(l) = paste0("P",15:30)
I have used bits like t=q and i=x[1]; c=x[2] such that I could just copy paste your formula for probability.
What we are doing here is using lapply to loop over the given row numbers in your question, we then use expand.grid to give the pairs of indicies for all cells in the resultant vector. To the indicies we apply a function which given row i, column c calculates the probability according to your formula. The values are then cast as a matrix such that the result has the appropriate structure.
You end up with a list l of matrices with components called "P15", "P16", ...