Why is the diag function so slow? [in R 3.2.0 or earlier]

Question

I was looking at the benchmarks in this answer, and wanted to compare them with diag (used in a different answer). Unfortunately, it seems that diag takes ages:

nc  <- 1e4
set.seed(1)
m <- matrix(sample(letters,nc^2,replace=TRUE), ncol = nc)

microbenchmark(
  diag = diag(m),
  cond = m[row(m)==col(m)],
  vec  = m[(1:nc-1L)*nc+1:nc],
  mat  = m[cbind(1:nc,1:nc)],
times=10)

Comments: I tested these with identical. I took "cond" from one of the answers to this homework question. Results are similar with a matrix of integers, 1:26 instead of letters.

Results:

Unit: microseconds
 expr         min          lq         mean       median          uq         max neval
 diag  604343.469  629819.260  710371.3320  706842.3890  793144.019  837115.504    10
 cond 3862039.512 3985784.025 4175724.0390 4186317.5260 4312493.742 4617117.706    10
  vec     317.088     329.017     432.9099     350.1005     629.460     651.376    10
  mat     272.147     292.953     441.7045     345.9400     637.506     706.860    10

It is just a matrix-subsetting operation, so I don't know why there's so much overhead. Looking inside the function, I see a few checks and then c(m)[v], where v is the same vector used in the "vec" benchmark. Timing these two...

v <- (1:nc-1L)*nc+1:nc
microbenchmark(diaglike=c(m)[v],vec=m[v])
# Unit: microseconds
#      expr        min          lq        mean     median          uq        max neval
#  diaglike 579224.436 664853.7450 720372.8105 712649.706 767281.5070 931976.707   100
#       vec    334.843    339.8365    568.7808    646.799    663.5825   1445.067   100

...it seems I have found my culprit. So, the new variation on my question is: Why is there a seemingly unnecessary and very time-consuming c in diag?

Answer 1

Summary

As of R version 3.2.1 (World-Famous Astronaut) diag() has received an update. The discussion moved to r-devel where it was noted that c() strips non-name attributes and may have been why it was placed there. While some people worried that removing c() would cause unknown issues on matrix-like objects, Peter Dalgaard found that, "The only case where the c() inside diag() has an effect is where M[i,j] != M[(i-1)*m+j] AND c(M) will stringize M in column-major order, so that M[i,j] == c(M)[(i-1)*m+j]."

Luke Tierney tested @Frank 's removal of c(), finding it did not effect anything on CRAN or BIOC and so was implemented to replace c(x)[...] with x[...] on line 27. This leads to relatively large speedups in diag(). Below is a speed test showing the improvement with R 3.2.1's version of diag().

library(microbenchmark)
nc  <- 1e4
set.seed(1)
m <- matrix(sample(letters,nc^2,replace=TRUE), ncol = nc)

    microbenchmark(diagOld(m),diag(m))
    Unit: microseconds
           expr        min          lq        mean      median         uq        max neval
     diagOld(m) 451189.242 526622.2775 545116.5668 531905.5635 540008.704 682223.733   100
        diag(m)    222.563    646.8675    644.7444    714.4575    740.701   1015.459   100