rolling function using previous row values [R]

I have some sites (a,b,c) where the soil has a certain maximum capacity (100,200). For each period of time (every row in my dataset), I have calculated the change in water content (change).

set.seed(2023)
db <- data.table(ID=c(rep("a",3),rep("b",3),rep("c",3)),
                 capacity=c(rep(100,3),rep(200,6)),
                 prc=round(runif(9,1,100),0),
                 evpt=round(runif(9,1,100),0))

db[prc>=evpt,change:=prc-evpt]
db[prc<evpt,change:=exp(-((evpt-prc)/capacity))]


   ID capacity prc evpt     change
1:  a      100  39   20 19.0000000
2:  a      100  74   35 39.0000000
3:  a      100  67   19 48.0000000
4:  b      200  49   78  0.8650223
5:  b      200  41   70  0.8650223
6:  b      200  94   75 19.0000000
7:  c      200  74   51 23.0000000
8:  c      200  67   71  0.9801987
9:  c      200  77   73  4.0000000

At time 0 the site hold the maximum capacity of water. Then, if prc >evpt, change is the water added to the previous content, without exceeding the maximum capacity. If prc < evpt, change is a multiplier of the previous water content, thus reducing the content.

# draft function
new_content <- function(change,capacity,prc,evpt){
  if (prc>evpt) {
    min(change+previous_content,capacity)
    } else {
      previous_content*change
    }
}

Then I should apply the function for each site to get a new column (content) showing the temporal variation of water content. As in the following output calculated in Excel:

> db
   ID capacity prc evpt     change  content
1:  a      100  39   20 19.0000000 100.0000
2:  a      100  74   35 39.0000000 100.0000
3:  a      100  67   19 48.0000000 100.0000
4:  b      200  49   78  0.8650223 173.0045
5:  b      200  41   70  0.8650223 149.6527
6:  b      200  94   75 19.0000000 168.6527
7:  c      200  74   51 23.0000000 200.0000
8:  c      200  67   71  0.9801987 196.0397
9:  c      200  77   73  4.0000000 200.0000

The problem I cannot solve is how to define the variable previous_content, i.e. at the beginning equal to the maximum capacity and then to the content of the previous row.

I checked the documentation of both data.table::frollapply and zoo:rollapply but I was not able even to write a starting draft for that. Any help? Thanks!

Assuming the input shown in the Note at the end content2 generated using Reduce is the same as content:

db[, content2 := Reduce(function(x, i) with(.SD[i, ], {
    if (prc > evpt) min(change+x, capacity)
    else x * change
  }), 1:.N, init = capacity[1], acc = TRUE)[-1], by = ID]

db
##    ID capacity prc evpt     change  content content2
## 1:  a      100  39   20 19.0000000 100.0000 100.0000
## 2:  a      100  74   35 39.0000000 100.0000 100.0000
## 3:  a      100  67   19 48.0000000 100.0000 100.0000
## 4:  b      200  49   78  0.8650223 173.0045 173.0045
## 5:  b      200  41   70  0.8650223 149.6527 149.6527
## 6:  b      200  94   75 19.0000000 168.6527 168.6527
## 7:  c      200  74   51 23.0000000 200.0000 200.0000
## 8:  c      200  67   71  0.9801987 196.0397 196.0397
## 9:  c      200  77   73  4.0000000 200.0000 200.0000

In the example in the question capacity is always constant within ID and change is multiplied if it is <= 1 and added otherwise. If those are true generally we can simplify the above:

db[, content3 := Reduce(function(x, change) 
      if (change > 1) min(change + x, capacity[1]) else x * change, 
      change, init = capacity[1], acc = TRUE)[-1], 
    by = ID]

Note

library(data.table)

Lines <-  "ID capacity prc evpt     change  content
a      100  39   20 19.0000000 100.0000
a      100  74   35 39.0000000 100.0000
a      100  67   19 48.0000000 100.0000
b      200  49   78  0.8650223 173.0045
b      200  41   70  0.8650223 149.6527
b      200  94   75 19.0000000 168.6527
c      200  74   51 23.0000000 200.0000
c      200  67   71  0.9801987 196.0397
c      200  77   73  4.0000000 200.0000"
db <- fread(Lines)