base (version 3.2.1)

# findInterval: Find Interval Numbers or Indices

## Description

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]] \le 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`.

## Usage

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

## Arguments

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`.

## Value

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 `NA`s are propagated from `x`, and `Inf` values are allowed in both `x` and `vec`.

## Details

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.

`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(.)`.

## Examples

Run this code
``````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)
``````

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