Calculating a rolling division in r data table - r

Question

I have a data table like this:
a group
1: 1 a
2: 2 a
3: 3 a
4: 4 a
5: 5 a
6: 6 a
The sample can be created from the code below:
structure(list(a = 1:100, group = c("a", "a", "a", "a", "a",
"a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a",
"a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a",
"a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a", "a",
"a", "a", "a", "a", "a", "a", "b", "b", "b", "b", "b", "b", "b",
"b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b",
"b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b",
"b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b", "b",
"b", "b", "b", "b")), .Names = c("a", "group"), row.names = c(NA,
-100L), class = c("data.table", "data.frame"), .internal.selfref = <pointer: 0x0000000004790788>)
For each row in each group I would like to:
take value in column a
divide it by value in column a lagged by 2 and subtract 1
divide it by value in column a lagged by 4 and subtract 1
divide it by value in column a lagged by 6 and subtract 1
sum result of steps 2-4 and return it in a new column
So for rows 1-6, I would have NA, and then 7/5 + 7/3 + 7/1 - 3, 8/6 + 8/4 + 8/2 - 3, 9/7 + 9/5 + 9/3 - 3, 10/8 + 10/6 + 10/4 - 3
So based on the table reported in the first chunk, I would like to get a new column, say metric_1, which would, on the 10th row have the value 2.416667
Please note that the values in column a will not in practice correspond to row numbers, but would be some measurements.
The final output would then look like this:
a group metric_1
1: 1 a NA
2: 2 a NA
3: 3 a NA
4: 4 a NA
5: 5 a NA
6: 6 a NA
7: 7 a 7.733333
8: 8 a 4.333333
9: 9 a 3.085714
10: 10 a 2.416667
I already tried some versions with Reduce which works like a champ if I need to sum some values in a vector, but I haven't been able to tweak it into enabling me to do the division like this.

Answer 1

I'm not sure if this is exactly what you're looking for but perhaps it will help:
library(dplyr)
the_data %>% group_by(group) %>%
mutate(metric_1 = (a/lag(a, 2)-1)+( a/lag(a,4)-1) + (a/lag(a, 6) - 1 )) %>%
ungroup()

Answer 2

found one possible solution as:
dt[,
list(a, Reduce(`+`, lapply(shift(a, seq(2, 6, by = 2)),
function(x) a/x - 1))),
by = "group"]
But it is rather slow.