Faster alternative to `range(which(..))`

Question

Let be a sequence of TRUE and FALSE in R

v = c(F,F,F,F,F,F,T,F,T,T,F,T,T,T,T,T,F,T,F,T,T,F,F,F,T,F,F,F,F,F)

I would like to get the the positions of the first and the last TRUE. One way to achieve this is

range(which(v)) # 7 25

but this solution is relatively slow as it must check every element of the vector to get the position of each TRUE and then loop over all positions, evaluating two if statements at each position (I think) in order to get the maximum and the minimum values. It would be much more strategic to search for the first TRUE starting one from the beginning and one from the end and just return those positions.

Is there a faster alternative to range(which(..))?

Answer 1

The simplest approach I can think of that doesn't involve searching the entire vector would be an Rcpp solution:

library(Rcpp)
cppFunction(
"NumericVector rangeWhich(LogicalVector x) {
  NumericVector ret(2, NumericVector::get_na());
  int n = x.size();
  for (int idx=0; idx < n; ++idx) {
    if (x[idx]) {
      ret[0] = idx+1;  // 1-indexed for R
      break;
    }
  }
  if (R_IsNA(ret[0]))  return ret;  // No true values
  for (int idx=n-1; idx >= 0; --idx) {
    if (x[idx]) {
      ret[1] = idx + 1;  // 1-indexed for R
      break;
    }
  }
  return ret;
}")
rangeWhich(v)
# [1]  7 25

We can benchmark on a fairly long vector (length 1 million) with random entries. We would expect to get pretty large efficiency gains from not searching through the whole thing with which:

set.seed(144)
bigv <- sample(c(F, T), 1000000, replace=T)
library(microbenchmark)
# range_find from @PierreLafortune
range_find <- function(v) {
i <- 1
while(!v[i]) {
  i <- i +1
}
j <- length(v)
while(!v[j]) {
  j <- j-1
}
c(i,j)
}
# shortCircuit from @JoshuaUlrich
shortCircuit <- compiler::cmpfun({
  function(x) {
    first <- 1
    while(TRUE) if(x[first]) break else first <- first+1
    last <- length(x)
    while(TRUE) if(x[last]) break else last <- last-1
    c(first, last)
  }
})
microbenchmark(rangeWhich(bigv), range_find(bigv), shortCircuit(bigv), range(which(bigv)))
# Unit: microseconds
#                expr      min        lq        mean     median         uq       max neval
#    rangeWhich(bigv)    1.476    2.4655     9.45051     9.0640    13.7585    46.286   100
#    range_find(bigv)    1.445    2.2930     8.06993     7.2055    11.8980    26.893   100
#  shortCircuit(bigv)    1.114    1.6920     7.30925     7.0440    10.2210    30.758   100
#  range(which(bigv)) 6821.180 9389.1465 13991.84613 10007.9045 16698.2230 58112.490   100

The Rcpp solution is a good deal faster (more than 500x faster) than max(which(v)) because it doesn't need to iterate through the whole vector with which. For this example it has a near-identical runtime (in fact, slightly slower) than range_find from @PierreLafortune and shortCircuit from @JoshuaUlrich.

Using Joshua's excellent example of some worst-case behavior where the true value is in the very middle of the vector (I'm repeating his experiment with all proposed functions so we can see the whole picture), we see a very different situation:

bigv2 <- rep(FALSE, 1e6)
bigv2[5e5-1] <- TRUE
bigv2[5e5+1] <- TRUE
microbenchmark(rangeWhich(bigv2), range_find(bigv2), shortCircuit(bigv2), range(which(bigv2)))
# Unit: microseconds
#                 expr        min          lq        mean      median         uq        max neval
#    rangeWhich(bigv2)    546.206    555.3820    593.1385    575.3790    599.055    979.924   100
#    range_find(bigv2) 400057.083 406449.0075 434515.1142 411881.4145 427487.041 697529.163   100
#  shortCircuit(bigv2)  74942.612  75663.7835  79095.3795  76761.5325  79703.265 125054.360   100
#  range(which(bigv2))    632.086    679.0955    761.9610    700.1365    746.509   3924.941   100

For this vector the looping base R solutions are much slower than the original solution (100-600x slower) and the Rcpp solution is barely faster than range(which(bigv2)) (which makes sense, because they're both looping through the whole vector once).

As usual, this needs to come with a disclaimer -- you need to compile your Rcpp function, which also takes time, so this will only be a benefit if you have very large vectors or are repeating this operation many times. From the comments on your question it sounds like you indeed have a large number of large vectors, so this could be a good option for you.

Answer 2

match is quick as it stops when it finds the value searched for:

c(match(T,v),length(v)-match(T,rev(v))+1)
[1]  7 25

But you would have to test the speeds.

Update:

range_find <- function(v) {
i <- 1
j <- length(v)
while(!v[i]) {
  i <- i+1
}
while(!v[j]) {
  j <- j-1
}
c(i,j)
}

Benchmark

v <- rep(v, 5e4)
microbenchmark(
  rangeWhich = rangeWhich(v),
  range_find = range_find(v),
  richwhich = {w <- which(v)
               w[c(1L, length(w))]},
  match = c(match(T,v),length(v)-match(T,rev(v))+1)
)
Unit: microseconds
       expr       min         lq        mean    median         uq        max neval
 rangeWhich     1.284     3.2090    16.50914    20.211    26.7875     29.836   100
 range_find     9.945    21.4945    32.02652    26.948    34.1660    144.042   100
  richwhich  2941.756  3022.5975  3243.02081  3130.227  3247.6405   5403.911   100
      match 45696.329 46771.8175 50662.45708 47359.526 48718.6055 131439.661   100

This approach matches your proposed strategy:

"It would be much more strategic to search for the first TRUE starting one from the beginning and one from the end and just return those positions."