| findInterval | R Documentation |
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.
findInterval(x, vec, rightmost.closed = FALSE, all.inside = FALSE,
left.open = FALSE)
x |
numeric. |
vec |
numeric, sorted (weakly) increasingly, of length |
rightmost.closed |
logical; if true, the rightmost interval,
|
all.inside |
logical; if true, the returned indices are coerced
into |
left.open |
logical; if true all the intervals are open at left
and closed at right; in the formulas below, ≤ should be
swapped with < (and > with ≥), and
|
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.
left.open = TRUE is occasionally useful, e.g., for survival data.
For (anti-)symmetry reasons, it is equivalent to using
“mirrored” data, i.e., the following is always true:
identical(
findInterval( x, v, left.open= TRUE, ...) ,
N - findInterval(-x, -v[N:1], left.open=FALSE, ...) )
where N <- length(vec) as above.
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, length.out = 201), +100)
it <- findInterval(tt, X)
tt[it < 1 | it >= N] # only first and last are outside range(X)
## 'left.open = TRUE' means "mirroring" :
N <- length(v)
stopifnot(identical(
findInterval( x, v, left.open=TRUE) ,
N - findInterval(-x, -v[N:1])))
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