data.table's frank() function has some useful features which aren't available in base R's rank() function (see ?frank). E.g., we can reverse the order of the ranking by prepending the variable with a minus sign:
library(data.table)
# create reproducible data
set.seed(1L)
dt <- data.table(x = c(rep("a", 5), rep("b", 5)),
y = abs(rnorm(10)) * 10, z = abs(rnorm(10)) * 10)
# rank y descending, z ascending
dt[, rank_y := frank(-y), x][, rank_z := frank(z), x][]
x y z rank_y rank_z
1: a 6.264538 15.1178117 3 4
2: a 1.836433 3.8984324 5 1
3: a 8.356286 6.2124058 2 2
4: a 15.952808 22.1469989 1 5
5: a 3.295078 11.2493092 4 3
6: b 8.204684 0.4493361 1 2
7: b 4.874291 0.1619026 4 1
8: b 7.383247 9.4383621 2 5
9: b 5.757814 8.2122120 3 4
10: b 3.053884 5.9390132 5 3
If there are many columns which are to be ranked individually, some descending, some ascending, we can do this in two steps
# first rank all columns in descending order
cols_desc <- c("y")
dt[, paste0("rank_", cols_desc) := lapply(.SD, frankv, ties.method = "min", order = -1L),
.SDcols = cols_desc, by = x][]
# then rank all columns in ascending order
cols_asc <- c("z")
dt[, paste0("rank_", cols_asc) := lapply(.SD, frankv, ties.method = "min", order = +1L),
.SDcols = cols_asc, by = x][]
x y z rank_y rank_z
1: a 6.264538 15.1178117 3 4
2: a 1.836433 3.8984324 5 1
3: a 8.356286 6.2124058 2 2
4: a 15.952808 22.1469989 1 5
5: a 3.295078 11.2493092 4 3
6: b 8.204684 0.4493361 1 2
7: b 4.874291 0.1619026 4 1
8: b 7.383247 9.4383621 2 5
9: b 5.757814 8.2122120 3 4
10: b 3.053884 5.9390132 5 3