Faster way to find the first TRUE value in a vector - r

Question

In one function I very often need to use code like:
which(x==1)[1]
which(x>1)[1]
x[x>10][1]
where x is a numeric vector. summaryRprof() shows that I spend >80% of the time on relational operators. I wonder if there is a function that does comparison only till the first TRUE value is reached to speed up my code. For-loop is slower than the options provided above.

Answer 1

I don't know of a pure R way to do this, so I wrote a C function to do it for the quantstrat package. This function was written with a specific purpose in mind, so it's not as general as I would like. For example, you may notice that it only works on real/double/numeric data, so be sure to coerce Data to that before calling the .firstCross function.
#include <R.h>
#include <Rinternals.h>
SEXP firstCross(SEXP x, SEXP th, SEXP rel, SEXP start)
{
int i, int_rel, int_start;
double *real_x=NULL, real_th;
if(ncols(x) > 1)
error("only univariate data allowed");
/* this currently only works for real x and th arguments
* support for other types may be added later */
real_th = asReal(th);
int_rel = asInteger(rel);
int_start = asInteger(start)-1;
switch(int_rel) {
case 1: /* > */
real_x = REAL(x);
for(i=int_start; i<nrows(x); i++)
if(real_x[i] > real_th)
return(ScalarInteger(i+1));
break;
case 2: /* < */
real_x = REAL(x);
for(i=int_start; i<nrows(x); i++)
if(real_x[i] < real_th)
return(ScalarInteger(i+1));
break;
case 3: /* == */
real_x = REAL(x);
for(i=int_start; i<nrows(x); i++)
if(real_x[i] == real_th)
return(ScalarInteger(i+1));
break;
case 4: /* >= */
real_x = REAL(x);
for(i=int_start; i<nrows(x); i++)
if(real_x[i] >= real_th)
return(ScalarInteger(i+1));
break;
case 5: /* <= */
real_x = REAL(x);
for(i=int_start; i<nrows(x); i++)
if(real_x[i] <= real_th)
return(ScalarInteger(i+1));
break;
default:
error("unsupported relationship operator");
}
/* return number of observations if relationship is never TRUE */
return(ScalarInteger(nrows(x)));
}
And here's the R function that calls it:
.firstCross <- function(Data, threshold=0, relationship, start=1) {
rel <- switch(relationship[1],
'>' = ,
'gt' = 1,
'<' = ,
'lt' = 2,
'==' = ,
'eq' = 3,
'>=' = ,
'gte' = ,
'gteq' = ,
'ge' = 4,
'<=' = ,
'lte' = ,
'lteq' = ,
'le' = 5)
.Call('firstCross', Data, threshold, rel, start)
}
Some benchmarks, just for fun.
> library(quantstrat)
> library(microbenchmark)
> firstCross <- quantstrat:::.firstCross
> set.seed(21)
> x <- rnorm(1e6)
> microbenchmark(which(x > 3)[1], firstCross(x,3,">"), times=10)
Unit: microseconds
expr min lq median uq max neval
which(x > 3)[1] 9482.081 9578.072 9597.3870 9690.448 9820.176 10
firstCross(x, 3, ">") 11.370 11.675 31.9135 34.443 38.614 10
> which(x>3)[1]
[1] 919
> firstCross(x,3,">")
[1] 919
Note that firstCross will yield a larger relative speedup the larger Data is (because R's relational operators have to finish comparing the entire vector).
> x <- rnorm(1e7)
> microbenchmark(which(x > 3)[1], firstCross(x,3,">"), times=10)
Unit: microseconds
expr min lq median uq max neval
which(x > 3)[1] 94536.21 94851.944 95799.857 96154.756 113962.794 10
firstCross(x, 3, ">") 5.08 5.507 25.845 32.164 34.183 10
> which(x>3)[1]
[1] 97
> firstCross(x,3,">")
[1] 97
...and it won't be appreciably faster if the first TRUE value is near the end of the vector.
> microbenchmark(which(x==last(x))[1], firstCross(x,last(x),"eq"),times=10)
Unit: milliseconds
expr min lq median uq max neval
which(x == last(x))[1] 92.56311 93.85415 94.38338 98.18422 106.35253 10
firstCross(x, last(x), "eq") 86.55415 86.70980 86.98269 88.32168 92.97403 10
> which(x==last(x))[1]
[1] 10000000
> firstCross(x,last(x),"eq")
[1] 10000000

Answer 2

Base R provides Position and Find for locating the first index and value, respectively, for which a predicate returns a true value. These higher-order functions return immediately upon the first hit.
f<-function(x) {
r<-vector("list",3)
r[[1]]<-which(x==1)[1]
r[[2]]<-which(x>1)[1]
r[[3]]<-x[x>10][1]
return(r)
}
p<-function(f,b) function(a) f(a,b)
g<-function(x) {
r<-vector("list",3)
r[[1]]<-Position(p(`==`,1),x)
r[[2]]<-Position(p(`>`,1),x)
r[[3]]<-Find(p(`>`,10),x)
return(r)
}
The relative performance depends greatly on the probability of finding a hit early relative to the cost of the predicate vs the overhead of Position/Find.
library(microbenchmark)
set.seed(1)
x<-sample(1:100,1e5,replace=TRUE)
microbenchmark(f(x),g(x))
Unit: microseconds
expr min lq mean median uq max neval cld
f(x) 5034.283 5410.1205 6313.861 5798.4780 6948.5675 26735.52 100 b
g(x) 587.463 650.4795 1013.183 734.6375 950.9845 20285.33 100 a
y<-rep(0,1e5)
microbenchmark(f(y),g(y))
Unit: milliseconds
expr min lq mean median uq max neval cld
f(y) 3.470179 3.604831 3.791592 3.718752 3.866952 4.831073 100 a
g(y) 131.250981 133.687454 137.199230 134.846369 136.193307 177.082128 100 b

Answer 3

That's a nice question and answer... just to add any() is no faster than which() or match()but both are quicker than [] which I guess may create a big vector useless T,F's. So I'm guessing No ..short of the answer above.
v=rep('A', 10e6)
v[5e6]='B'
v[10e6]='B'
microbenchmark(which(v=='B')[1])
Unit: milliseconds
expr min lq median uq max neval
which(v == "B")[1] 332.3788 337.6718 344.4076 347.1194 503.4022 100
microbenchmark(any(v=='B'))
Unit: milliseconds
expr min lq median uq max neval
any(v == "B") 334.4466 335.114 335.6714 347.5474 356.0261 100
microbenchmark(v[v=='B'][1])
Unit: milliseconds
expr min lq median uq max neval
v[v == "B"][1] 601.5923 605.3331 609.191 612.0689 707.1409 100
microbenchmark(match("B", v))
Unit: milliseconds
expr min lq median uq max neval
match("B", v) 339.2872 344.7648 350.5444 359.6746 915.6446 100
Any other ideas out there?