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Apply function to multiple vectors and output pairwise comparisons to matrix

I have 3 vectors containing more than 1500 character string elements which I want to pairwise compare for outputting the number of matching elements between them.

A reduced tibble of my data:

va <- c("6a460daf68eb0410b51d79e495fbccc7", "e1b32017108e17e41bdabc44bac4df3c", "6ac1327da92d8584008db04b4eaf62d0", "b01a2322e2ca99315646d79cf157cb20", "12dadc27059ea5d3c8cc54e9a28cc4f6", "be73c9685b743a646f2eb0480eee2f8d")
vb <- c("6a460daf68eb0410b51d79e495fbccc7", "e1b32017108e17e41bdabc44bac4df3c","JQ183785.1.1345", "DQ794886.1.1390", "HQ791014.1.1450", "EU764755.1.1328")
vc <- c("6a460daf68eb0410b51d79e495fbccc7", "JQ183785.1.1345", "DQ794886.1.1390", "HQ791014.1.1450", "b01a2322e2ca99315646d79cf157cb20", "EF532786.1.1364")

I have made a function for outputting the number of coincident elements between two vectors:

sharing <- function(v1, v2, share=TRUE){
  if(isTRUE(share)){sh <- length(v1[ v1 %in% v2])}
  else if (isFALSE(share)){sh <- length(v1[ ! v1 %in% v2])}
  return(sh)
}

So, applying this function 9 times (one for each pairwise comparison including self-comparison), I would be able to get 9 numbers with shared elements:

> sharing(va,va); sharing(va,vb); sharing(va,vc)
[1] 6
[1] 2
[1] 2
> sharing(vb,va); sharing(vb,vb); sharing(vb,vc)
[1] 2
[1] 6
[1] 4
> sharing(vc,va); sharing(vc,vb); sharing(vc,vc)
[1] 2
[1] 4
[1] 6

But I would like to get this as a matrix:

    va   vb   vc
va   6    2    2
vb   2    6    4
vc   2    4    6

Is there any premade function or code which can make this?

Thanks for the help!

One option is outer to apply the sharing function on pairwise combination of vector s in a list ('lst1')

lst1 <- mget(paste0("v", letters[1:3])) # placed the vectors in a list
out <- outer(lst1, lst1, FUN = Vectorize(sharing)) #apply the sharing
dimnames(out) <- list(names(lst1), names(lst1)) # set the dim names

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