Divide by sum by factor and carry back - r

Question

I have a data.table that looks like:
A <- c(1,3,5,20,21,21)
B <- c(1, 2, 3, 4, 5, 6)
C <- c("I","I","II","II","III","III")
D <- c(0.7, 0.3, 0.5, 0.9, 4, 7)
M <- data.table(A,B,C,D)
My question is similar to R help: divide values by sum produced through factor with a few extra considerations. A specifies a date (I'm simply using integers here). B are individuals. C is a classification in the individual belongs to. D is a value variable.
For each classification c of C, for each day a of A, divide the value D by the sum of the values for all individuals in c, carrying backward when needed such that 0<x-a<=N where x is the date of another individual (meaning that we pick the smallest x-a and use that as an approximation for the value of the other individual in group c on day a).
Let's say N=5. Here's my expected output.
A <- c(1,3,5,20,21,21)
B <- c(1, 2, 3, 4, 5, 6)
C <- c("I","I","II","II","III","III")
D <- c(0.7/(0.7+0.3), 0.3/(0.3), 0.5/(0.5), 0.9/(0.9), 4/(4+7), 7/(4+7))
M <- data.table(A,B,C,D)
Note that the values for group B are not carried backward for individual 3, as the length is greater than 5 (20-5). Is there a nice way of doing this in data.table?
For each value in D, I wish to divide by the sum of all the values of the same group (either I, II,II) on that day. However, you'll notice for some groups, observations do not exist on that day. I'll try and walk through the logic on a few observations.
Edit: Let me try and walk through a few cases.
For individual 1 (column B) on day 1 (column A), the individual is of group I (column C). Other individuals of group I are: 2. For each of those others, we see that for individual 2, their nearest observation is on day 3 and 3-1<=5, so we'll use 0.3 in the denominator.
For individual 3 (column B) on day 5 (column A), the individual is of group II (column C). Other individuals of group II are: 3. For each of those others, we see that for individual 3, their nearest observation is on day 20 and 20-5>5, so we cannot use their observation in the denominator.

Answer 1

This, I think, will give you your answer:
A <- c(1,3,5,20,21,21, 7)
B <- c(1, 2, 3, 4, 5, 6, 7)
C <- c("I","I","II","II","III","III", "I")
V <- c(0.7, 0.3, 0.5, 0.9, 4, 7, 0.1)
N=5
#Put data into a frame
test = data.frame(A,B,C,V)
#order the data
test = test[order(as.numeric(test$C), test$A),]
#Get the 'rollback' possibilities for each value
Roll = sapply(test$A, FUN = function(x){paste(which(test$A < (x+N) & test$A >= x), collapse=",")})
#Get the groupings
Group = sapply(test$C, FUN = function(x){paste(which(test$C == x), collapse=",")})
#Intersect the values
ToGet = apply(cbind(Roll, Group), MARGIN=1, FUN=function(x){intersect(unlist(strsplit(x[1],",")), unlist(strsplit(x[2],",")))})
#Calculate the denominators
test$D = sapply(ToGet, FUN=function(x){sum(test$V[as.numeric(x)])})
test$Calc = test$V/test$D
Output:
> test
A B C V D Calc
1 1 1 I 0.7 1.0 0.7000000
2 3 2 I 0.3 0.4 0.7500000
7 7 7 I 0.1 0.1 1.0000000
3 5 3 II 0.5 0.5 1.0000000
4 20 4 II 0.9 0.9 1.0000000
5 21 5 III 4.0 11.0 0.3636364
6 21 6 III 7.0 11.0 0.6363636

Answer 2

The questions is tagged with data.table, so here is a data.table solution which uses non-equi joins to identify individuals within each group to treat them as cohort if the observations fall within a date window of 5 days.
library(data.table) # CRAN version 1.10.4 used
# set length of date window in days
N <- 5L
# give columns more semantic names according to OP's description
setnames(M, c("day", "id", "grp", "val"))
# prepare data for non-equi join: allowable date range
ranged <- M[, .(start = day, end = day + N, co.id = id, grp)]
# non-equi join to determine cohort
joined <- M[ranged, on = c("grp", "day>=start", "day<=end")]
# compute denominator for each cohort
grouped <- joined[, .(den = sum(val)), by = co.id]
# final update on join and order
result <- M[grouped, on = c("id==co.id"), calc := val / den][order(grp, id)]
result
# day id grp val calc
#1: 1 1 I 0.7 0.7000000
#2: 3 2 I 0.3 0.7500000
#3: 7 7 I 0.1 1.0000000
#4: 5 3 II 0.5 1.0000000
#5: 20 4 II 0.9 1.0000000
#6: 21 5 III 4.0 0.3636364
#7: 21 6 III 7.0 0.6363636
Data
A <- c(1,3,5,20,21,21, 7)
B <- c(1, 2, 3, 4, 5, 6, 7)
C <- c("I","I","II","II","III","III", "I")
D <- c(0.7, 0.3, 0.5, 0.9, 4, 7, 0.1)
M <- data.table(A,B,C,D)
Compact versions
For those who prefer compact code, here is a more convoluted version:
joined <- M[M[, .(start = day, end = day + N, co.id = id, grp)],
on = c("grp", "day>=start", "day<=end")]
M[joined[, .(den = sum(val)), by = co.id], on = c("id==co.id"),
calc := val / den][order(grp, id)]
Or, as a "one-liner":
M[M[M[, .(start = day, end = day + N, co.id = id, grp)],
on = c("grp", "day>=start", "day<=end")
][, .(den = sum(val)), co.id],
on = c("id==co.id"), calc := val / den][order(grp, id)]