Check if each number in a vector is between some numbers in another vector in R - r

Question

Say I have two vectors, A and B. A has 15 variables and B has 28 variables.
A = c(13,14,29,31,32,39,42,51,59,61,68,91,102,109,120)
B = c(26,26,28,29,30,30,33,38,41,42,45,46,47,47,49,49,80,81,86,86,90,90,92,100,101,105,105,107)
I want a 14 by 27 matrix, Z, where a i by j entry is 1 if (B_j,B_{j+1}] overlaps with (A_i, A_{i+1}].
For instance, the (3,4) entry of Z would be 1 since (29,31] and (29,30] overlap, with 30 as a common number. Is there a fast way to compute this?
I have the following code:
Z = matrix(0, length(A)-1, length(B)-1)
for (i in 1:(length(A)-1)){
nn = which(B > A[i] & B <= A[(i+1)])
if (length(nn)>0){
Z[i,(nn-1)] = 1}}
It works well but my A and B vector often contain 30,000+ elements and it is incredibly slow. Making of the matrix Z even takes unnecessarily long time. Can anyone help with this?
Ideally, there is a vectorized solution to this or a well written function from a package that can do this like cutting a cake.

Answer 1

Here's an option using matrix multiplication. As commented the matrix can get big, and you'll have to see if the speed improvement is worth it:
res1 <- outer(A, B, FUN = function(A, B){B > A})
res2 <- outer(A, B, FUN = function(A, B){B <= A})
dim(res1); dim(res2)
res3 <- (res1[-nrow(res1),] + res2[-1,]) == 2
image(res3)
dim(res3)
op <- par(mfcol=c(1,2))
image(Z, main="Z")
image(res3, main="res3")
par(op)

Answer 2

If closed Intervals [B_j,B_{j+1}] and [A_i, A_{i+1}] are ok for you as well you could use
A <- as.integer(c(13,14,29,31,32,39,42,51,59,61,68,91,102,109,120))
B <- as.integer(c(26,26,28,29,30,30,33,38,41,42,45,46,47,47,49,49,80,81,86,86,90,90,92,100,101,105,105,107))
DT_A <- data.table(A0 = A, A1 = shift(A, type = "lead"), key=c("A0", "A1"))[-length(A)]
DT_B <- data.table(B0 = B, B1 = shift(B, type = "lead"), key=c("B0", "B1"))[-length(B)]
ind_true <- foverlaps(DT_A, DT_B, type="any", mult="all", which=TRUE)[!is.na(yid)]
mat <- matrix(0, length(A)-1, length(B)-1)
mat[ind_true$xid, ind_true$yid] = 1

Answer 3

This answer uses matrix indexing and relies on expand.grid though there are much faster implementations of it. You lag your vectors to create matrices of A and B, then with a function that does simple boolean check, we can index into the matrices with an expanded grid. Then it returns a matrix.
overlap = function(id,x1,x2){
idA = id[,1]
idB = id[,2]
o = (x1[idA,1] >= x2[idB,1] & x1[idA,1] <= x2[idB,2]) | (x1[idA,2] >= x2[idB,1] & x1[idA,2] <= x2[idB,2]) |
(x1[idA,1] <= x2[idB,1] & x1[idA,2] >= x2[idB,1]) | (x1[idA,1] <= x2[idB,2] & x1[idA,2] >= x2[idB,2])
matrix(o,nrow=nrow(x1))
}
A = c(13,14,29,31,32,39,42,51,59,61,68,91,102,109,120)
nA = cbind(lag(A),A)[-1,]
B = c(26,26,28,29,30,30,33,38,41,42,45,46,47,47,49,49,80,81,86,86,90,90,92,100,101,105,105,107)
nB = cbind(lag(B),B)[-1,]
expand.grid.jc <- function(seq1,seq2) {
cbind(Var1 = rep.int(seq1, length(seq2)),
Var2 = rep.int(seq2, rep.int(length(seq1),length(seq2))))
}
ids = expand.grid.jc(1:nrow(nA),1:nrow(nB))
overlap(ids,nA,nB)