Nested user defined functions using apply in R - r

Question

How would the following be written using apply?
# Variables
age <- 1:100
Y <- age+5
d <- 0.25
dx <- 5
a_x <- 1:dx
Yd <- matrix( 0, nrow=max(age), ncol=dx )
# Nested loop is computationally inefficient?
for (a in age){
for (ax in a_x){
Yd[a,ax] <- (Y[[a]] * (1 - d) ** (ax-1))
}
}
My model has a lot of these nested for loop structures, because I am incompetent. I am hoping to improve the computational time using apply. I find the apply functions rather confusing to get into. I am looking for a solution that illustrates how one can obtain such nested structures using apply. Hopefully, from there on I can apply (pun intended) the solution to even more complicated nested for loops (4-5 loops within each other).
For example
Ydi <- rep( list(), 6)
for (i in 1:6){
Ydi[[i]] <- matrix( 0, nrow=max(age), ncol=dx )
}
# Nested loop is computationally inefficient?
for (i in 1:6){
for (a in age){
for (ax in a_x){
Ydi[[i]][a,ax] <- (Y[[a]] * (1 - d) ** (ax-1)) + i
}
}
}

Answer 1

I would use expand.grid instead:
df <- data.frame(expand.grid(a = age, ax = a_x))
df[['Yd']] <- (df[['a']] + 5) * (1 - d) ** (df[['ax']] - 1)
This is infinitely extendable (subject to memory constraints) - each additional nested loop will just be an additional variable in your expand.grid call. For example:
new_col <- 1:2
df_2 <- data.frame(expand.grid(a = age, ax = a_x, nc = new_col))
df_2[['Yd']] <- (df_2[['a']] + 5) * (1 - d) ** (df_2[['ax']] - 1) + df_2[['nc']]
This essentially switches to a tidy data format, which is an easier way of storing multi-dimensional data.
For easier syntax, and faster speed, you can use the data.table package:
library(data.table)
dt_3 <- data.table(expand.grid(a = age, ax = a_x, nc = new_col))
dt_3[ , Yd := (a + 5) * (1 - d) ** (ax - 1) + nc]