Calculating distance between two variables and generating new variable - r

Question

I would like to create a variable called spill which is given as the sum of the distances between vectors of each row multiplied by the stock value. For example, consider
firm us euro asia africa stock year
A 1 4 3 5 46 2001
A 2 0 1 3 889 2002
B 2 3 1 1 343 2001
B 0 2 1 3 43 2002
C 1 3 4 2 345 2001
I would like to create a vector which basically takes the distance between two firms at time t and generates the spill variable. For example, take for Firm A in the year 2001 it would be 0.204588 (which is the cosine distance between firm A and B at time t i.e, in 2001 (1,4,3,5) and (2,3,1,1) (i.e. similarity between the investments in us, euro, asia, africa) and then multiplied by 343, and then to calculate the distance between A and C in 2001 as .10528 * 345 , hence the spill variable is = 0.2045883 * 343+ 0.1052075 * 345 = 106.4704 for the year 2001 for firm A.
I want to get a table including spill like this
firm us euro asia africa stock year spill
A 1 4 3 5 46 2001 106.4704
A 2 0 1 3 889 2002
B 2 3 1 1 343 2001
B 0 2 1 3 43 2002
C 1 3 4 2 345 2001
Can anyone please advise?
Here are the codes for stata[https://www.statalist.org/forums/forum/general-stata-discussion/general/1409182-calculating-distance-between-two-variables-and-generating-new-variable]. I have about 3,000 firms and 30 years. It runs well but very slowly.
dt <- data.frame(id=c("A","A","B","B","C"),us=c(1,2,2,0,1),euro=c(4,0,3,2,3),asia=c(3,1,1,1,4),africa=c(5,3,1,3,2),stock=c(46,889,343,43,345),year=c(2001,2002,2001,2002,2001))

Answer 1

Given the minimal info on how to calculate the similarity distance I've used a formula from Find cosine similarity between two arrays which will return different numbers than yours but should give the same resulting info.
I split the data by year so we can compare the unique ids. I take those individual lists and use lapply to run a for loop comparing all possibilities.
dt <- data.frame(id=c("A","A","B","B","C"), us=c(1,2,2,0,1),euro=c(4,0,3,2,3),asia=c(3,1,1,1,4),africa=c(5,3,1,3,2),stock=c(46,889,343,43,345),year=c(2001,2002,2001,2002,2001))
geo <- c("us","euro","asia","africa")
s <- lapply(split(dt, dt$year), function(a) {
n <- nrow(a)
for(i in 1:n){
csim <- rep(0, n) # reset results of cosine similarity *stock vector
for(j in 1:n){
x <- unlist(a[i,geo])
y <- unlist(a[j,geo])
csim[j] <- (1-(x %*% y / sqrt(x%*%x * y%*%y)))*a[j,"stock"]
}
a$spill[i] <- sum(csim)
}
a
})
do.call(rbind, s)
# id us euro asia africa stock year spill
#2001.1 A 1 4 3 5 46 2001 106.47039
#2001.3 B 2 3 1 1 343 2001 77.93231
#2001.5 C 1 3 4 2 345 2001 72.96357
#2002.2 A 2 0 1 3 889 2002 12.28571
#2002.4 B 0 2 1 3 43 2002 254.00000