This is related to the question R - transform upward diagonals to rows:
I am given a matrix, data frame or data table. I would like to create a new matrix by shifting row i by (i-1) cells, but without truncating the rows, i.e. additional columns are added (additionall cells are set to NA).
As an example, suppose I am given the following matrix
mat<-matrix(seq(1:100),nrow=20, byrow = TRUE)
> structure(mat)
V1 V2 V3 V4 V5
1: 1 2 3 4 5
2: 6 7 8 9 10
3: 11 12 13 14 15
4: 16 17 18 19 20
5: 21 22 23 24 25
6: 26 27 28 29 30
7: 31 32 33 34 35
8: 36 37 38 39 40
9: 41 42 43 44 45
10: 46 47 48 49 50
11: 51 52 53 54 55
12: 56 57 58 59 60
13: 61 62 63 64 65
14: 66 67 68 69 70
15: 71 72 73 74 75
16: 76 77 78 79 80
17: 81 82 83 84 85
18: 86 87 88 89 90
19: 91 92 93 94 95
20: 96 97 98 99 100
> dput(mat)
structure(list(V1 = c(1L, 6L, 11L, 16L, 21L, 26L, 31L, 36L, 41L,
46L, 51L, 56L, 61L, 66L, 71L, 76L, 81L, 86L, 91L, 96L), V2 = c(2L,
7L, 12L, 17L, 22L, 27L, 32L, 37L, 42L, 47L, 52L, 57L, 62L, 67L,
72L, 77L, 82L, 87L, 92L, 97L), V3 = c(3L, 8L, 13L, 18L, 23L,
28L, 33L, 38L, 43L, 48L, 53L, 58L, 63L, 68L, 73L, 78L, 83L, 88L,
93L, 98L), V4 = c(4L, 9L, 14L, 19L, 24L, 29L, 34L, 39L, 44L,
49L, 54L, 59L, 64L, 69L, 74L, 79L, 84L, 89L, 94L, 99L), V5 = c(5L,
10L, 15L, 20L, 25L, 30L, 35L, 40L, 45L, 50L, 55L, 60L, 65L, 70L,
75L, 80L, 85L, 90L, 95L, 100L)), row.names = c(NA, -20L), class = c("data.table","data.frame"))
The desired result looks as follows:
> dput(res)
structure(c(1L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, 2L, 6L, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 3L, 7L, 11L, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
4L, 8L, 12L, 16L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 5L, 9L, 13L, 17L, 21L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 10L, 14L, 18L, 22L,
26L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, 15L, 19L, 23L, 27L, 31L, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 20L, 24L, 28L, 32L, 36L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
25L, 29L, 33L, 37L, 41L, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, 30L, 34L, 38L, 42L, 46L, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 35L,
39L, 43L, 47L, 51L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 40L, 44L, 48L, 52L, 56L, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 45L, 49L, 53L,
57L, 61L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 50L, 54L, 58L, 62L, 66L, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 55L, 59L, 63L, 67L, 71L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
60L, 64L, 68L, 72L, 76L, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, 65L, 69L, 73L, 77L, 81L, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 70L,
74L, 78L, 82L, 86L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 75L, 79L, 83L, 87L, 91L, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 80L, 84L, 88L,
92L, 96L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 85L, 89L, 93L, 97L, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 90L, 94L, 98L, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 95L,
99L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 100L), .Dim = c(20L, 24L))
Is there an easy and short way to do this?
An option would be
out <- matrix(NA, nrow(mat)+4, nrow(mat)+4)
for(i in seq_len(nrow(out))) out[i, (i:(i+4))] <- unlist(mat[i])
out[1:nrow(mat), ]