Identify sequences between identical values - r

Question

I have a large matrix:
id v1 v2 v3 v4 v5 v6 v7 v8
1001 37 15 30 37 4 11 35 37
2111 44 31 44 30 24 39 44 18
3121 43 49 39 34 44 43 26 24
4532 45 31 26 33 12 47 37 15
5234 23 27 34 23 30 34 23 4
6345 9 46 39 34 8 43 26 24
For each row (id), I would like to identify intervals of numbers in column v1 to v8. An interval is here defined as a sequence of numbers which starts and ends with the same number.
For example, in the first row, there are two sequences which both start and ends with 37: From column 1 to 4 (37, 15, 30, 37) and from column 4 to column 8 (37, 4, 11, 35, 37).
The focal value should only occur in start and end positions. For example, in the first row, the sequence from 37 at V1, to 37 at V8 is not included, because 37 also occurs in V4.
For each interval, I want the index of the start and end columns, the focal start and end value, and the sequence of numbers in between.
Desired output:
1001 [v1] to [v4] 37 to 37: 15,30
1001 [v4] to [v8] 37 to 37: 4, 11, 35
2111 [v1] to [v3] 44 to 44: 31
2111 [v3] to [v7] 44 to 44: 30, 24, 39
Any suggestions? Algorithm?
I managed to code for the indices for a vector not a matrix,
a <- which(x == 37)
from <- a[!(a-1) %in% a]
to <- a[!(a+1) %in% a]
rbind(from, to)

Answer 1

Very brute-force method. Get unique elements for the given row, check if they are present more than once but not side-by-side, then lapply through each, getting the elements of the row x between them.
apply(m, 1, function(x) {
u <- unique(x)
u <- u[sapply(u, function(u) any(diff(which(x == u)) > 1))]
lapply(setNames(u, u), function(u){
ind <- which(x == u)
lapply(seq(length(ind) - 1),
function(i) x[seq(ind[i] + 1, ind[i + 1] - 1)])
})
})
Output:
# [[1]]
# [[1]]$`37`
# [[1]]$`37`[[1]]
# [1] 15 30
#
# [[1]]$`37`[[2]]
# [1] 4 11 35
#
#
#
# [[2]]
# [[2]]$`44`
# [[2]]$`44`[[1]]
# [1] 31
#
# [[2]]$`44`[[2]]
# [1] 30 24 39
#
#
#
# [[3]]
# [[3]]$`43`
# [[3]]$`43`[[1]]
# [1] 49 39 34 44
#
#
#
# [[4]]
# named list()
#
# [[5]]
# [[5]]$`23`
# [[5]]$`23`[[1]]
# [1] 27 34
#
# [[5]]$`23`[[2]]
# [1] 30 34
#
#
# [[5]]$`34`
# [[5]]$`34`[[1]]
# [1] 23 30
#
#
#
# [[6]]
# named list()
Edit: Henrik's answer inspired me to do a join-based version
library(data.table)
library(magrittr)
d <- melt(as.data.table(m), "id", variable.name = 'ci')[, ci := rowid(id)]
setorder(d, id)
options(datatable.nomatch = 0)
d[d, on = .(id, value, ci > ci)
, .(id, value, i.ci, x.ci)
, mult = 'first'] %>%
.[d, on = .(id, i.ci < ci, x.ci > ci)
, .(id, value, from_ci = x.i.ci, to_ci = x.x.ci, i.value)] %>%
.[, .(val = .(i.value))
, by = setdiff(names(.), 'i.value')]
# id value from_ci to_ci val
# 1: 1001 37 1 4 15,30
# 2: 1001 37 4 8 4,11,35
# 3: 2111 44 1 3 31
# 4: 2111 44 3 7 30,24,39
# 5: 3121 43 1 6 49,39,34,44
# 6: 5234 23 1 4 27,34
# 7: 5234 34 3 6 23,30
# 8: 5234 23 4 7 30,34

Answer 2

Here's a data.table alternative.
Convert matrix to data.table and melt to long format. Create a column index 'ci' to keep track of the original columns (rowid(id)). Order by 'id'.
For each 'id' and 'value' (by = .(id, value)), check if number of rows is larger than one (if(.N > 1)), i.e. if there is at least one sequence. If so, grab the row index (.I) of the sequences and their column indexes (in the original data). For each sequence, grab the corresponding values between start and end index. Wrap in list twice (.(.() to create a list column.
library(data.table)
d <- melt(as.data.table(m), id.vars = "id")
d[ , `:=`(
ci = rowid(id),
variable = NULL)]
setorder(d, id)
d2 <- d[ , if(.N > 1){
.(from = .I[-.N], to = .I[-1],
from_ci = ci[-.N], to_ci = ci[ -1])
}, by = .(id, value)]
d2[ , val := .(.(d$value[seq(from + 1, to - 1)])), by = 1:nrow(d2)]
d2[ , `:=`(from = NULL, to = NULL)]
# id value from_ci to_ci val
# 1: 1001 37 1 4 15,30
# 2: 1001 37 4 8 4,11,35
# 3: 2111 44 1 3 31
# 4: 2111 44 3 7 30,24,39
# 5: 3121 43 1 6 49,39,34,44
# 6: 5234 23 1 4 27,34
# 7: 5234 23 4 7 30,34
# 8: 5234 34 3 6 23,30