Split apply combine in data.table

In this code, I want to create and store an interpolation function for
each date.  It seems that data.table saves the same interpolation
function (for the last date) for all three dates.  How can this problem
be fixed?

Thanks,
Naresh

mydt <- list(data.table(date = as.IDate("2025-01-01"), x = c(1, 2, 3), y = c(3, 4, 5)), data.table(date = as.IDate("2025-01-15"), x = c(1, 2, 3), y = c(9, 8, 7)), data.table(date = as.IDate("2025-01-31"), x = c(1, 2, 3), y = c(10, 12, 9)))
mydt <- rbindlist(mydt)
myapprox <- mydt[, list(yfunc = list(approxfun(x, y, rule = 2))), by =
list(date)]
testdt <- data.table(date = as.IDate(c("2025-01-01", "2025-01-15",
"2025-01-31")), x = 2)
testdt <- merge(testdt, myapprox, by = "date")
testdt[, let(yapprox = yfunc[[1]](x)), by = .I]
testdt <- merge(testdt, mydt, by = c("date", "x"))
testdt
Key: <date, x>
       date     x         yfunc yapprox     y
     <IDat> <num>        <list>   <num> <num>
1: 2025-01-01     2 <function[1]>      12     4
2: 2025-01-15     2 <function[1]>      12     8
3: 2025-01-31     2 <function[1]>      12    12

Using split function, it is possible to get the desired result.
mydtsplit <- split(mydt, f = mydt$date)
splitapprox <- lapply(mydtsplit, function(dt) dt[, approxfun(x, y,
rule = 2)])
newdt <- data.table(date = as.IDate(c("2025-01-01", "2025-01-15",
"2025-01-31")), x = 2)
newdt[, let(yfunc = splitapprox[as.character(date)]), by = .I]
newdt[, let(yapprox = yfunc[[1]](x)), by = .I]
newdt <- merge(newdt, mydt, by = c("date", "x"))
newdt
Key: <date, x>
       date     x         yfunc yapprox     y
     <IDat> <num>        <list>   <num> <num>
1: 2025-01-01     2 <function[1]>       4     4
2: 2025-01-15     2 <function[1]>       8     8
3: 2025-01-31     2 <function[1]>      12    12


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