effective way to return only the first argument of "which()"

On 19-09-2012, at 20:02, Bert Gunter wrote:

Well, following up on this observation, which can be put under the
heading of "Sometimes vectorization can be much slower than explicit
loops" , I offer the following:

firsti  <-function(x,k)
{
 i <- 1
 while(x[i]<=k){i <- i+1}
 i
}

system.time(for(i in 1:100)which(x>.99)[1])

  user  system elapsed
  19.1     2.4    22.2

system.time(for(i in 1:100)which.max(x>.99))

  user  system elapsed
 30.45    6.75   37.46

system.time(for(i in 1:100)firsti(x,.99))

  user  system elapsed
  0.03    0.00    0.03

## About a 500 - 1000 fold speedup !

firsti(x,.99)

[1] 122

It doesn't seem to scale too badly, either (whatever THAT means!):
(Of course, the which() versions are essentially identical in timing,
and so are omitted)

system.time(for(i in 1:100)firsti(x,.9999))

  user  system elapsed
  2.70    0.00    2.72

firsti(x,.9999)

[1] 18200

Of course, at some point, the explicit looping is awful -- with k =
.999999, the index was about 360000, and the timing test took 54
seconds.

So I guess the point is -- as always -- that the optimal approach
depends on the nature of the data. Prudence and robustness clearly
demands the vectorized which() approaches if you have no information.
But if you do know something about the data, then you can often write
much faster tailored solutions. Which is hardly revelatory, of course.

And compiling the firsti function can also be quite lucrative!

firsti <- function(x,k)
{
    i <- 1
    while(x[i]<=k){i <- i+1}
    i
}

library(compiler)
firsti.c <- cmpfun(firsti)

firsti(x,.99)

[1] 93

firsti.c(x,.99)

[1] 93

system.time(for(i in 1:100)firsti(x,.99))

   user  system elapsed
  0.014   0.000   0.013

system.time(for(i in 1:100)firsti.c(x,.99))

   user  system elapsed
  0.002   0.000   0.002

system.time(for(i in 1:100)firsti(x,.9999))

   user  system elapsed
  2.148   0.013   2.164

system.time(for(i in 1:100)firsti.c(x,.9999))

   user  system elapsed
  0.393   0.002   0.396

And in a new run (without the above tests)  with k=.999999 the index was 1089653 and the timing for the uncompiled function was 152 seconds and the timing for the compiled function was 28.8 seconds!

Berend