Perform row-wise operation in datatable with multiple elements - r

Question

I have the following data table:
library(data.table)
set.seed(1)
DT <- data.table(ind=1:100,x=sample(100),y=sample(100),group=c(rep("A",50),rep("B",50)))
Now the problem I have is that I need to take every value in column "x" (that is, each given ID), and add all the existing values in column "y" to it. I also need to do it separately per column "group". Let's assume we start with ID = 1. This element has the value: x_1 = 68, and y_1 = 76. We also see y_2 = 39, y_3 = 24, etc. So what I want to compute is the sums x_1 + y_1, x_1 + y2, x_1 + y_3, etc. But not only for x_1, but also for x_2, x_3, etc. So for x_2 it would look like: x_2 + y_1, x_2 + y_2, x_2 + y_3, etc. This should also be done separately per column "group" (in this regard the dataset should simple be split by group).
Edit: Exemplary code to do this only for X_1 and group A:
current_X <- DT[1,x] # not needed, just to illustrate
vector_current_X <- rep(DT[1,x],nrow(DT[group == "A"]))
DT[group == "A",copy_current_X := vector_current_X]
DT[,sum_current_X_Y := copy_current_X + y]
DT
One apparent issue with this approach is that if it were applied to all x, then a lot of columns would be added to the final DT. So I am not sure if it is the best approach. In the end, I am just looking for the lowest sum (per element x) with each element y, and per group.
I know how to do operations per group, and I also know the lapply functions. The issue is that from my understanding, I need to include a row-wise loop. And next, the structure of the result will be different from the original data table, because we have many additional observations. I have seen before that you can save lists inside a data.table, but I am unsure if that is the best approach. My dataset is much larger, so efficiency is important.
Thanks for any hints how to approach this.

Answer 1

You can do this:
DT[, .(.BY$x+DT[group==.BY$group,y]), by=.(x,group)]
This returns N rows per x, where N is the size of x's group. We leverage the special (.BY), which is available in j when utilizing by. Basically, .BY is a named list, containing the values of the grouping variables. Here, I'm adding the value of x (.BY$x) to the vector of y values from the subset of DT where the group is equal to the current group value (.BY$group)
Output:
x group V1
<int> <char> <int>
1: 68 A 144
2: 68 A 107
3: 68 A 92
4: 68 A 121
5: 68 A 160
---
4996: 4 B 25
4997: 4 B 66
4998: 4 B 83
4999: 4 B 27
5000: 4 B 68
You can also accomplish this via a join:
DT[,!c("y")][DT[, .(y,group)], on=.(group), allow.cartesian=T][, total:=x+y][order(ind)]
Output:
ind x group y total
<int> <int> <char> <int> <int>
1: 1 68 A 76 144
2: 1 68 A 39 107
3: 1 68 A 24 92
4: 1 68 A 53 121
5: 1 68 A 92 160
---
4996: 100 4 B 21 25
4997: 100 4 B 62 66
4998: 100 4 B 79 83
4999: 100 4 B 23 27
5000: 100 4 B 64 68

Answer 2

If I understand correctly, the requested result requires a cross join where each element of x is combined with each element of y (within each group).
This can be accomplished easily using the CJ() function:
DT[, CJ(x, y, sorted = FALSE), by = group][, sum_x_y := x + y][]
group x y sum_x_y
1: A 68 76 144
2: A 68 39 107
3: A 68 24 92
4: A 68 53 121
5: A 68 92 160
---
4996: B 4 21 25
4997: B 4 62 66
4998: B 4 79 83
4999: B 4 23 27
5000: B 4 64 68