Computing the Levenshtein ratio of each element of

I have a data.table dt with 3 columns:

id
name as string
threshold as num

A sample is:

dt <- <- data.table(nid = c("n1","n2", "n3", "n4"), rname = c("apple", "pear", "banana", "kiwi"), maxr = c(0.5, 0.8, 0.7, 0.6))

nid | rname  | maxr
n1  | apple  |  0.5
n2  | pear   |  0.8
n3  | banana |  0.7
n4  | kiwi   |  0.6

I have a second table dt.ref with 2 columns:

id
name as string

A sample is:

dt.ref <- <- data.table(cid = c("c1", "c2", "c3", "c4", "c5", "c6"), cname = c("apple", "maple", "peer", "dear", "bonobo", "kiwis"))

cid | cname
c1  | apple
c2  | maple
c3  | peer
c4  | dear
c5  | bonobo
c6  | kiwis

For each rname of dt, I would like to compute the Levenshtein ratio with each cname of dt.ref as such:

Lr = 1 - (stringdist(cname, rname, method = "lv") / pmax(nchar(cname),nchar(rname)))

Then, I would like to find max(Lr) over the cname for each rname of dt and get as an output the following data.table:

nid | rname  | maxr | maxLr | cid
n1  | apple  |  0.5 | 1     | c1
n2  | pear   |  0.8 | 0.75  | c3
n2  | pear   |  0.8 | 0.75  | c4
n3  | banana |  0.7 | 0.33  | c5
n4  | kiwi   |  0.6 | 0.8   | c6

Basically, we take dt and add 2 columns, the maximum Levenshtein ratio and the corresponding cid, knowing that ties are all added, 1 per row as for n2.

I use data.table but the solution can use dplyr or any other package.

You can try something like this:

f1 <- function(x, y) {
  require(stringdist)
  require(matrixStats)
  dis  <- stringdistmatrix(x, y, method = "lv")
  mat <- sapply(nchar(y), function(i) pmax(i, nchar(x)))
  r <- 1 - dis / mat
  w <- apply(r, 1, function(x) which(x==max(x)))
  m <- rowMaxs(r)
  list(m = m, w = w)
}

r <- f1(dt[[2]], dt.ref[[2]])
r
$m
[1] 1.0000000 0.7500000 0.3333333 0.8000000

$w
$w[[1]]
[1] 1

$w[[2]]
[1] 3 4

$w[[3]]
[1] 5

$w[[4]]
[1] 6


dt[, maxLr := r$m ]
#dtnew <- dt[rep(1:.N, sapply(r$w, length)),]
dtnew <- dt[rep(1:.N, lengths(r$w),] # thanks to Frank
dtnew[, cid := dt.ref[unlist(r$w), 1]]

Results:

dtnew
   nid  rname maxr     maxLr cid
1:  n1  apple  0.5 1.0000000  c1
2:  n2   pear  0.8 0.7500000  c3
3:  n2   pear  0.8 0.7500000  c4
4:  n3 banana  0.7 0.3333333  c5
5:  n4   kiwi  0.6 0.8000000  c6