Efficient creation of a matrix of offsets

Question

Goal

I want to use a long vector of numbers, to create a matrix where each column is a successive offset (lag or lead) of the original vector. If n is the maximum offset, the matrix will have dimensions [length(vector), n * 2 + 1] (because we want offsets in both directions, and include the 0 offset, i.e. the original vector).

Example

To illustrate, consider the following vector:

test <- c(2, 8, 1, 10, 7, 5, 9, 3, 4, 6)

[1]  2  8  1 10  7  5  9  3  4  6

Expected output

Now we create offsets of values, let's say for n == 3:

      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
 [1,]   NA   NA   NA    2    8    1   10
 [2,]   NA   NA    2    8    1   10    7
 [3,]   NA    2    8    1   10    7    5
 [4,]    2    8    1   10    7    5    9
 [5,]    8    1   10    7    5    9    3
 [6,]    1   10    7    5    9    3    4
 [7,]   10    7    5    9    3    4    6
 [8,]    7    5    9    3    4    6   NA
 [9,]    5    9    3    4    6   NA   NA
[10,]    9    3    4    6   NA   NA   NA

I am looking for an efficient solution. data.table or tidyverse solutions more than welcome.

Returning only the rows that have no NA's (i.e. rows 4 to 7) is also ok.

Current solution

lags  <- lapply(3:1, function(x) dplyr::lag(test, x))
leads <- lapply(1:3, function(x) dplyr::lead(test, x))
l <- c(lags, test, leads)
matrix(unlist(l), nrow = length(test))

Answer 1

In base R, you can use embed to get rows 4 through 7. You have to reverse the column order, however.

embed(test, 7)[, 7:1]
     [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    2    8    1   10    7    5    9
[2,]    8    1   10    7    5    9    3
[3,]    1   10    7    5    9    3    4
[4,]   10    7    5    9    3    4    6

data

test <- c(2, 8, 1, 10, 7, 5, 9, 3, 4, 6)

Answer 2

This will produce what you need...

n <- 3
t(embed(c(rep(NA,n), test, rep(NA,n)), length(test)))[length(test):1,]

      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
 [1,]   NA   NA   NA    2    8    1   10
 [2,]   NA   NA    2    8    1   10    7
 [3,]   NA    2    8    1   10    7    5
 [4,]    2    8    1   10    7    5    9
 [5,]    8    1   10    7    5    9    3
 [6,]    1   10    7    5    9    3    4
 [7,]   10    7    5    9    3    4    6
 [8,]    7    5    9    3    4    6   NA
 [9,]    5    9    3    4    6   NA   NA
[10,]    9    3    4    6   NA   NA   NA