Clip values between a minimum and maximum allowed value in R

Question

In Mathematica there is the command Clip[x, {min, max}] which gives x for min<=x<=max, min for x<min and and max for x>max, see

http://reference.wolfram.com/mathematica/ref/Clip.html (mirror)

What would be the fastest way to achieve this in R? Ideally it should be a function that is listable, and should ideally work on either a single value, vector, matrix or dataframe...

Hollishollister

Answer 1

Rcpp has clamp for this:

cppFunction('NumericVector rcpp_clip( NumericVector x, double a, double b){
    return clamp( a, x, b ) ;
}')

Here is a quick benchmark showing how it performs against other methods discussed :

pmin_pmax_clip <- function(x, a, b) pmax(a, pmin(x, b) )
ifelse_clip <- function(x, a, b) {
  ifelse(x <= a,  a, ifelse(x >= b, b, x))
}
operations_clip <- function(x, a, b) {
  a + (x-a > 0)*(x-a) - (x-b > 0)*(x-b)
}
x <- rnorm( 10000 )
require(microbenchmark)

microbenchmark( 
  pmin_pmax_clip( x, -2, 2 ), 
  rcpp_clip( x, -2, 2 ), 
  ifelse_clip( x, -2, 2 ), 
  operations_clip( x, -2, 2 )
)
# Unit: microseconds
#                        expr      min        lq   median        uq       max
# 1     ifelse_clip(x, -2, 2) 2809.211 3812.7350 3911.461 4481.0790 43244.543
# 2 operations_clip(x, -2, 2)  228.282  248.2500  266.605 1120.8855 40703.937
# 3  pmin_pmax_clip(x, -2, 2)  260.630  284.0985  308.426  336.9280  1353.721
# 4       rcpp_clip(x, -2, 2)   65.413   70.7120   84.568   92.2875  1097.039    

Income

Those times are pretty rockin'. – Mercurochrome

Just pasting the lines for the clamp code in a console session is obviously not what you intended us Rcpp virgins to be doing. – Crux

Almost. See my use of cppFunction in my edit. (but you need the current devel version of Rcpp because clamp has been fixed since the last release). – Income

Very cool. I'm shocked and baffled at how bad the operations_clip() times are .... sometimes. Any ideas why the max values are quite so much larger than the min values for all of these functions? – Generalization

I'm pretty sure this is about memory allocation. operations_clip performs a lot of them, so my guess is that sometimes it takes longer. – Income

@RomainFrancois Just to come back to this - what would be the recommended way to do this for the case where lower and upper limits a and b were not doubles but NumericVectors? Would using RcppArmadillo x.elem(arma::find(x < lower)) = lower.elem(arma::find(x < lower)); x.elem(arma::find(x > upper)) = upper.elem(arma::find(x > upper)); be an OK approach or would there be better ways? Or would using Rcpp sugar functions pmin and pmax pmax(lower, pmin(x, upper)) also work? And in Rcpp code above I think clamp(a, x, b) should be clamp(x, a, b) right? – Hollishollister

Answer 2

Here's a method with nested pmin and pmax setting the bounds:

 fenced.var <- pmax( LB, pmin( var, UB))

It will be difficult to find a method that is faster. Wrapped in a function that defaults to a range of 3 and 7:

fence <- function(vec, UB=7, LB=3) pmax( LB, pmin( vec, UB))

> fence(1:10)
 [1] 3 3 3 4 5 6 7 7 7 7

Crux

Very elegant - that's great! – Hollishollister

I use this one a lot. I have a large dataset that has several variables that are not plausibly real below 0 and that should be sensible constrained at the high end as well. The real trick is remembering to set the max with pmin and set the min with pmax. – Crux

Your 'It will be difficult to find a method that is faster' obviously motivated me to have a look. – Income

Yeah. It still wins the compactness prize ... so far. – Crux

I think the function's arguments UB and LB should be reversed. I suspect fence <- function(vec, LB=3, UB=7) pmax( LB, pmin( vec, UB)) is really what you're after – Prithee

@jf328: You might want to present a counter-example since my experiments showed it to be working in what I thought was a perfectly reasonable manner. pmin( pmax( matrix(1:10,2), 4), 6) Probably best to do this with a new question. – Crux

@42- interesting. You have to put the scalar (4 and 6) as the second argument. If you put them as the first argument as in your answer, then it returns a vector, not a matrix. And the pmax/pmin document does say it only returns a vector. – Weeny

Answer 3

Here's one function that will work for both vectors and matrices.

myClip <- function(x, a, b) {
    ifelse(x <= a,  a, ifelse(x >= b, b, x))
}

myClip(x = 0:10, a = 3,b = 7)
#  [1] 3 3 3 3 4 5 6 7 7 7 7

myClip(x = matrix(1:12/10, ncol=4), a=.2, b=0.7)
# myClip(x = matrix(1:12/10, ncol=4), a=.2, b=0.7)
#      [,1] [,2] [,3] [,4]
# [1,]  0.2  0.4  0.7  0.7
# [2,]  0.2  0.5  0.7  0.7
# [3,]  0.3  0.6  0.7  0.7

And here's another:

myClip2 <- function(x, a, b) {
    a + (x-a > 0)*(x-a) - (x-b > 0)*(x-b)
}

myClip2(-10:10, 0, 4)
# [1] 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 4 4 4 4 4 4

Saltire

Great!! Thanks so much!! My function for this was waaayy slower, but this works quite fast! – Hollishollister

This should be in R's base library! – Fusible

Answer 4

I believe that would be clamp() from the raster package.

library(raster)
clamp(x, lower=-Inf, upper=Inf, ...)

Ari

Wondering why no one has done timings on these alternatives? – Crux