rolling median

[jangorecki]

New rolling function: median. Towards #2778

Supersede #5692

---

Implementation of rolling median is based on a novel algorithm "sort-median" described by @suomela in 2014 in his paper Median Filtering is Equivalent to Sorting. "sort-median" scales very well, not only for size of input vector but also for size of rolling window. Implementation here is extended to address following limitations present in the paper:

• size of input vector must by divisible by window size
• window size must be an uneven number

Thanks to Jukka for the paper and hints on extending the algo.

rollmedian = function(x, n) {
  ans = rep(NA_real_, nx<-length(x))
  if (n<=nx) for (i in n:nx) ans[i] = median(x[(i-n+1L):(i)])
  ans
}
library(data.table)
setDTthreads(8)
set.seed(108)
x = rnorm(1e5)

n = 100
system.time(rollmedian(x, n))
#   user  system elapsed
#  2.049   0.001   2.051
system.time(frollapply(x, n, median, simplify=unlist))
#   user  system elapsed
#  3.071   0.223   0.436
system.time(frollmedian(x, n))
#   user  system elapsed
#  0.013   0.000   0.004

n = 1000
system.time(rollmedian(x, n))
#   user  system elapsed
#  3.496   0.009   3.507
system.time(frollapply(x, n, median, simplify=unlist))
#   user  system elapsed
#  4.552   0.307   0.632
system.time(frollmedian(x, n))
#   user  system elapsed
#  0.015   0.000   0.004

n = 10000
system.time(rollmedian(x, n))
#   user  system elapsed
# 16.350   0.025  16.382
system.time(frollapply(x, n, median, simplify=unlist))
#   user  system elapsed
# 14.865   0.722   2.267
system.time(frollmedian(x, n))
#   user  system elapsed
#  0.028   0.000   0.005

---

This work was supported by the Medical Research Council, UK [grant number 1573].

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.11%. Comparing base (6f225f3) to head (d379478).
⚠️ Report is 22 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #7315      +/-   ##
==========================================
+ Coverage   99.09%   99.11%   +0.01%     
==========================================
  Files          83       85       +2     
  Lines       16092    16440     +348     
==========================================
+ Hits        15947    16295     +348     
  Misses        145      145              

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[github-actions]

No obvious timing issues in HEAD=frollmedian

Generated via commit d379478

Download link for the artifact containing the test results: ↓ atime-results.zip

Task	Duration
R setup and installing dependencies	2 minutes and 57 seconds
Installing different package versions	42 seconds
Running and plotting the test cases	2 minutes and 52 seconds

[jangorecki]

Updated timings in https://github.com/jangorecki/rollbench

[mcol]

Some grammar fixes/suggestions.