Function that checks multiple combinations of operations between columns of a dataframe - r

Question

Here is a sample of the original dataframe (data provided at the end)
> DATA
N_b N_l A x.sqr_sum e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8
1 7 6 -36 4032 33.8 21.8 9.8 -2.2 -14.2 -26.2 0 0
2 7 4 -27 2268 23.6 11.6 -0.4 -12.4 0.0 0.0 0 0
3 7 4 -27 2268 23.6 11.6 -0.4 -12.4 0.0 0.0 0 0
4 7 6 -36 4032 33.8 21.8 9.8 -2.2 -14.2 -26.2 0 0
5 7 6 -36 4032 33.8 21.8 9.8 -2.2 -14.2 -26.2 0 0
6 7 6 -36 4032 33.8 21.8 9.8 -2.2 -14.2 -26.2 0 0
7 7 8 -45 6300 44.0 32.0 20.0 8.0 -4.0 -16.0 -28 -40
8 7 8 -45 6300 44.0 32.0 20.0 8.0 -4.0 -16.0 -28 -40
9 7 8 -45 6300 44.0 32.0 20.0 8.0 -4.0 -16.0 -28 -40
I want to write a function to calculate R from the equation
I write the code below to calculate R and the N_l responsible for the maximum R.
R <- function(x){
N_b <- x[1]
N_l <- x[2]
N_l_seq <- seq(N_l)
A <- x[3]
x.sqr_sum <- x[4]
e <- x[5:12]
m <- Multi.Presence$m[N_l_seq]
f <- m * (N_l_seq/N_b + A * cumsum(e) / x.sqr_sum)
c(val = max(f), pos = which.max(f))
}
DATA <- cbind(DATA, vars = t(apply(DATA, 1, R)))
In the function above, R is calculated for all possible values of N_l by defining N_l_seq <- seq(N_l). The problem is I don't want to just multiply by cumsum(e) as written in the function. I want to modify it so that it would calculate R for all possible combinations for the same number of e_1, e_2, e_3,... as the current value of N_l.
Example
If N_l = 3, the equation for f is calculated for the cumsum of all possible combinations of 3 of the e_1, e_2, e_3, e_4, e_5, e_6, e_7, e_8, such as cumsum(e_1, e_8, e_6) and cumsum(e_7, e_2, e_4). When N_l = 5, the equation for f is calculated for the cumsum of all possible combinations of 5 of the e_1, e_2, e_3, e_4, e_5, e_6, e_7, e_8, and so on.
PROBLEM
I am not sure how to update the f equation so instead of the cumsum() of all the possible e values, it calculates the cumsum() of all combinations of a number equal to the current N_l of the e values.
DATA
> dput(DATA)
structure(list(N_b = c(7, 7, 7, 7, 7, 7, 7, 7, 7), N_l = c(6,
4, 4, 6, 6, 6, 8, 8, 8), A = c(-36, -27, -27, -36, -36, -36,
-45, -45, -45), x.sqr_sum = c(4032, 2268, 2268, 4032, 4032, 4032,
6300, 6300, 6300), e_1 = c(33.8, 23.6, 23.6, 33.8, 33.8, 33.8,
44, 44, 44), e_2 = c(21.8, 11.6, 11.6, 21.8, 21.8, 21.8, 32,
32, 32), e_3 = c(9.8, -0.399, -0.399, 9.8, 9.8, 9.8, 20, 20, 20),
e_4 = c(-2.2, -12.4, -12.4, -2.2, -2.2, -2.2, 8, 8, 8), e_5 =
c(-14.2, 0, 0, -14.2, -14.2, -14.2, -4, -4, -4), e_6 = c(-26.2,
0, 0, -26.2, -26.2, -26.2, -16, -16, -16), e_7 = c(0, 0, 0, 0,
0, 0, -28, -28, -28), e_8 = c(0, 0, 0, 0, 0, 0, -40, -40, -40),
S = c(12, 9, 9, 12, 12, 12, 15, 15, 15)), row.names = c(1L, 3L,
4L, 115L, 116L, 117L, 199L, 200L, 201L), class = "data.frame")
A dependent variable m is defined in the dataframe below:
> dput(Multi.Presence)
structure(list(N_l = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10), m = c(1.2,
1, 0.85, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65)), row.names = c(NA,
-10L), class = "data.frame")

Answer 1

I am not sure if this is what you want. I guess you should use combn rather than cumsum in your function R.
As the first step, I merged Multi.Presence to DATA so you can read the corresponding value of m with respect to N_l
df <- merge(DATA, Multi.Presence, by = "N_l")
Then, I rewrote function R such that it accepts the rows of df as the argument
R <- function(x){
N_l <- x["N_l"]
N_b <- x["N_b"]
N_l_seq <- seq(N_l)
A <- x["X_ext"]
x.sqr_sum <- x["x.sqr_sum"]
e <- x[grepl("e_\\d",names(x))]
m <- x["m"]
f <- m * (N_l/N_b + A * combn(e,N_l,sum) / x.sqr_sum)
c(val = max(f), pos = which.max(f))
}
Finally, you can execute function R within apply by rows, e.g.,
> apply(df,1,R)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
val 0.4704685 0.4704685 0.7475 0.7475 0.7475 0.7475 0.6685714 0.6685714
pos 56.0000000 56.0000000 28.0000 28.0000 28.0000 28.0000 1.0000000 1.0000000
[,9]
val 0.6685714
pos 1.0000000
Update
I have no clue how you want to deal with the combn, but below is an update
R <- function(x){
# browser()
N_l <- x["N_l"]
N_b <- x["N_b"]
N_l_seq <- seq(N_l)
A <- x["A"]
x.sqr_sum <- x["x.sqr_sum"]
e <- x[grepl("e_\\d",names(x))]
m <- Multi.Presence$m[N_l_seq]
f <- m * sapply(N_l_seq,function(k) N_l/N_b + A * max(combn(e,k,sum)) / x.sqr_sum)
c(val = max(f), pos = which.max(f))
}