Sampling by group without repetition using data.table - r

Question

I'll use a hypothetical scenario to illustrate the question. Here's a table with musicians and the instrument they play and a table with the composition for a band:
musicians <- data.table(
instrument = rep(c('bass','drums','guitar'), each = 4),
musician = c('Chas','John','Paul','Stuart','Andy','Paul','Peter','Ringo','George','John','Paul','Ringo')
)
band.comp <- data.table(
instrument = c('bass','drums','guitar'),
n = c(2,1,2)
)
To avoid arguments about who is best with which instrument, the band will be assembled by sortition. Here's how I'm doing:
musicians[band.comp, on = 'instrument'][, sample(musician, n), by = instrument]
instrument V1
1: bass Paul
2: bass Chas
3: drums Andy
4: guitar Paul
5: guitar George
The problem is: since there are musicians who play more than one instrument, it can happen that one person is drawn more than once.
One can build a for loop that, for each subsequent subset of instruments, draws musicians and then eliminates those from the rest of the table. But I would like suggestions on how to do this using data.table. Mainly because the kind of problem I need to solve in real life with this logic involves data bases with hundreds of thousands of rows. And also because I'm trying to better understand the data.table syntax.
As a reference, I tried some tips from Andrew Brooks blog, but couldn't come up with a solution.

Answer 1

This can be a solution, first you select an instrument by musician and then you select the musicians of your sample. But it may be that when selecting an instrument per musician your sample size is larger than the population then you will get an error (but in your real data this may not be a problem).
musicians[, .(instrument = sample(instrument, 1)), by = musician][band.comp, on = 'instrument'][, sample(musician, n), by = instrument]

Answer 2

You could expand the band comp into sum(band.comp$n) distinct positions and keep sampling until you find a feasible composition:
roles = musicians[,
CJ(posn = 1:band.comp[.BY, on=.(instrument), x.n], musician = musician)
, by=instrument]
set.seed(1)
while (TRUE){
roles[sample(1:.N), keep := !duplicated(.SD, by="musician") & !duplicated(.SD, by=c("instrument", "posn"))][]
if (sum(roles$keep) == sum(band.comp$n)) break
}
setorder(roles[keep == TRUE, !"keep"])[]
instrument posn musician
1: bass 1 Stuart
2: bass 2 John
3: drums 1 Andy
4: guitar 1 George
5: guitar 2 Paul
There's probably something you could do with linear programming or a bipartite graph to answer the question of whether a feasible comp exists, but it's unclear what "sampling" even means in terms of the distribution over feasible comps.

Answer 3

Came across a relevant post: Randomly draw rows from dataframe based on unique values and column values and eddi's answer is perfect for this OP:
#keep number of musicians per instrument in 1 data.table
musicians[band.comp, n:=n, on=.(instrument)]
#for storing the musician that has been sampled so far
m <- c()
musicians[, {
#exclude sampled musician before sampling
res <- .SD[!musician %chin% m][sample(.N, n[1L])]
m <- c(m, res$musician)
res
}, by=.(instrument)]
sample output:
instrument musician n
1: bass Stuart 2
2: bass Chas 2
3: drums Paul 1
4: guitar John 2
5: guitar Ringo 2
Or more succinctly with error handling as well:
m <- c()
musicians[
band.comp,
on=.(instrument),
j={
s <- setdiff(musician, m)
if (length(s) < n) stop(paste("Not enough musicians playing", .BY))
res <- sample(s, n)
m <- c(m, res)
res
},
by=.EACHI]