findInterval {base} R Documentation

## Find Interval Numbers or Indices

### Description

Find the indices of `x` in `vec`, where `vec` must be sorted (non-decreasingly); i.e., if `i <- findInterval(x,v)`, we have v[i[j]] <= x[j] < v[i[j] + 1] where v[0] := - Inf, v[N+1] := + Inf, and `N <- length(vec)`. 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.

### 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.

### Value

vector of length `length(x)` with values in `0:N` (and `NA`) where `N <- length(vec)`, or values coerced to `1:(N-1)` iff `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`.

### Author(s)

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(.).
```N <- 100