Manipulating data.table column recursively on other column condition - r

Question

I need to calculate a formula in a data frame. Each set of values across few columns have to be, lets say simplicity sake, aggregated. However, I do not want calculation across rows. I want to calculate each set with another set based on condition else where.
This is what I mean:
I have a data.table.
data = data.table(A = c("a","c","b","b","a"),
B = c(1:5),
C = c(1:5)
)
setorder(data, by=A)
> data
A B C
1: a 1 1
2: a 5 5
3: b 3 3
4: b 4 4
5: c 2 2
In column D I need to have and aggregate of values in B and C and values B and C when A is "a". As I have more than one "a", multiple aggregations are needed. From every aggregate minimum should be written in.
Here is an example.
For row 1: (1+1)+(1+1)=4, (5+5)+(1+1)=12, so 4 is minimum - D1 =4.
For row 3: (3+3)+(1+1)=8, (3+3)+(5+5)=16, D3 = 8. And so on.
This is what I expect
> data_new
A B C D
1: a 1 1 4
2: a 5 5 12
3: b 3 3 8
4: b 4 4 10
5: c 2 2 6
I tried this and run into issues.
for (i in data)data[i, D:=(min((data[i,B+C]) + (data[a=="a",(B+C)])))]
The expression below for minimum selection works fine on its own when I substitute i for a row number returning list of two numbers for min() returns proper value. Below answer is 8.
min((data[3,B+C]) + (data[A=="a",(B+C)]))
My previous attempts involved grid.expansion() and intersection(). However, with the size of my data set I ran into memory issue and Rstudio quit on me. As a side note, I need to run the calculations as I could not project the smallest outcome by "a" beforehand - it is a set of coordinates and they do not correlate with the magnitude of an answer.
Any suggestion where is my glaring issue

Answer 1

You can store the value of B + C where A = 'a' in a variable (val). For each row you can take minimum of B + C + val value.
library(data.table)
val <- data[A =='a', B + C]
data[, D := min(B + C + val), seq_len(nrow(data))]
data
# A B C D
#1: a 1 1 4
#2: a 5 5 12
#3: b 3 3 8
#4: b 4 4 10
#5: c 2 2 6
You can also use lapply :
data[, D := lapply(B + C, function(x) min(x + val))]

Answer 2

An option is also to replicate the 'a' rows after taking the min of 'B', 'C' and then do a direct + with the 'B', 'C' columns. The advantage is that, we don't have to group or loop
library(data.table)
Reduce(`+`, (data[A == 'a', .(B = min(B), C = min(C))][rep(seq_len(.N), nrow(data))] + data[, .(B, C)]))
#[1] 4 12 8 10 6
Or in a single line
data[, D := B + C + min(B[A== 'a']) + min(C[A== 'a'])]
data$D
#[1] 4 12 8 10 6