findInterval: Find Interval Numbers or Indices
In robertzk/monadicbase: The R Base Package

Description Usage Arguments Details Value Author(s) See Also Examples

Given a vector of non-decreasing breakpoints in vec, find the interval containing each element of x; i.e., if i <- findInterval(x,v), for each index j in x v[i[j]] ≤ x[j] < v[i[j] + 1] where v[0] := - Inf, v[N+1] := + Inf, and N <- length(v). At the two boundaries, the returned index may differ by 1, depending on the optional arguments rightmost.closed and all.inside.

1	findInterval(x, vec, rightmost.closed = FALSE, all.inside = FALSE)

`x`	numeric.
`vec`	numeric, sorted (weakly) increasingly, of length `N`, say.
`rightmost.closed`	logical; if true, the rightmost interval, `vec[N-1] .. vec[N]` is treated as closed, see below.
`all.inside`	logical; if true, the returned indices are coerced into `1,...,N-1`, i.e., `0` is mapped to `1` and `N` to `N-1`.

The function findInterval finds the index of one vector x in another, vec, where the latter must be non-decreasing. Where this is trivial, equivalent to apply( outer(x, vec, ">="), 1, sum), as a matter of fact, the internal algorithm uses interval search ensuring O(n * log(N)) complexity where n <- length(x) (and N <- length(vec)). For (almost) sorted x, it will be even faster, basically O(n).

This is the same computation as for the empirical distribution function, and indeed, findInterval(t, sort(X)) is identical to n * Fn(t; X[1],..,X[n]) where Fn is the empirical distribution function of X[1],..,X[n].

When rightmost.closed = TRUE, the result for x[j] = vec[N] ( = max(vec)), is N - 1 as for all other values in the last interval.

vector of length length(x) with values in 0:N (and NA) where N <- length(vec), or values coerced to 1:(N-1) if and only if all.inside = TRUE (equivalently coercing all x values inside the intervals). Note that NAs are propagated from x, and Inf values are allowed in both x and vec.

Martin Maechler

approx(*, method = "constant") which is a generalization of findInterval(), ecdf for computing the empirical distribution function which is (up to a factor of n) also basically the same as findInterval(.).

x <- 2:18
v <- c(5, 10, 15) # create two bins [5,10) and [10,15)
cbind(x, findInterval(x, v))

N <- 100
X <- sort(round(stats::rt(N, df = 2), 2))
tt <- c(-100, seq(-2, 2, len = 201), +100)
it <- findInterval(tt, X)
tt[it < 1 | it >= N] # only first and last are outside range(X)