A iterative and lagging function similar to diff in R, but not just difference?

Question

The diff function in R returns suitably lagged and iterated differences.

x = c(1, 2, 1, 3, 11, 7, 5)
diff(x)
# [1]  1 -1  2  8 -4 -2
diff(x, lag=2)
[1]  0  1 10          


        

Answer 1

In base R, there is the filter function. It is not as friendly and general as zoo::rollapply but it is extremely fast. In your case, you are looking to apply a convolution filter with weights c(1, 1):

itersum <- function(x, n = 2) tail(filter(x, rep(1, n)), sides = 1), -(n-1))

itersum(x)
# 3 3 4 14 18 12

To give you more ideas, here is how the diff and cumsum functions can be re-written in terms of filter:

diff   <- function(x) head(filter(x, c(1, -1)), -1)
cumsum <- function(x) filter(x, 1, method = "recursive")

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In general, if you are looking to roll a binary function, then head and tail is probably the easiest and fastest way to go as it will take advantage of vectorized functions:

itersum     <- function(x) tail(x, -1) + head(x, -1)
diff        <- function(x) tail(x, -1) - head(x, -1)
sign.change <- function(x) tail(sign(x), -1) != head(sign(x), -1)