anyMissing - HenrikBengtsson/matrixStats GitHub Wiki
matrixStats: Benchmark report
This report benchmark the performance of anyMissing() against alternative methods.
- anyNA()
- any() + is.na()
as below
> any_is.na <- function(x) {
+ any(is.na(x))
+ }> rvector <- function(n, mode = c("logical", "double", "integer"), range = c(-100, +100), na_prob = 0) {
+ mode <- match.arg(mode)
+ if (mode == "logical") {
+ x <- sample(c(FALSE, TRUE), size = n, replace = TRUE)
+ } else {
+ x <- runif(n, min = range[1], max = range[2])
+ }
+ storage.mode(x) <- mode
+ if (na_prob > 0)
+ x[sample(n, size = na_prob * n)] <- NA
+ x
+ }
> rvectors <- function(scale = 10, seed = 1, ...) {
+ set.seed(seed)
+ data <- list()
+ data[[1]] <- rvector(n = scale * 100, ...)
+ data[[2]] <- rvector(n = scale * 1000, ...)
+ data[[3]] <- rvector(n = scale * 10000, ...)
+ data[[4]] <- rvector(n = scale * 1e+05, ...)
+ data[[5]] <- rvector(n = scale * 1e+06, ...)
+ names(data) <- sprintf("n = %d", sapply(data, FUN = length))
+ data
+ }
> data <- rvectors(mode = mode)> x <- data[["n = 1000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3053217 163.1 5709258 305.0 5709258 305.0
Vcells 32116601 245.1 54055058 412.5 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 1000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.000359 | 0.000365 | 0.0004554 | 0.0003780 | 0.0003855 | 0.008082 |
| 1 | anyMissing | 0.000934 | 0.000949 | 0.0010638 | 0.0009780 | 0.0010110 | 0.007846 |
| 3 | any_is.na | 0.002283 | 0.002359 | 0.0025444 | 0.0024015 | 0.0024980 | 0.011989 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.0000000 |
| 1 | anyMissing | 2.601671 | 2.600000 | 2.336181 | 2.587302 | 2.622568 | 0.9707993 |
| 3 | any_is.na | 6.359331 | 6.463014 | 5.587509 | 6.353175 | 6.479896 | 1.4834199 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 1000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 10000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050100 162.9 5709258 305 5709258 305.0
Vcells 10479057 80.0 43244047 330 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 10000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.002735 | 0.0027680 | 0.0028186 | 0.0027845 | 0.0028250 | 0.004756 |
| 1 | anyMissing | 0.005714 | 0.0057795 | 0.0059961 | 0.0058725 | 0.0059715 | 0.015570 |
| 3 | any_is.na | 0.017282 | 0.0176325 | 0.0183324 | 0.0177625 | 0.0179375 | 0.039756 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 2.089214 | 2.087970 | 2.127348 | 2.108996 | 2.113805 | 3.273760 |
| 3 | any_is.na | 6.318830 | 6.370123 | 6.504126 | 6.379063 | 6.349558 | 8.359125 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 10000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 100000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050172 162.9 5709258 305 5709258 305.0
Vcells 10479617 80.0 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 100000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.026117 | 0.0261990 | 0.0263233 | 0.026240 | 0.0263320 | 0.028237 |
| 1 | anyMissing | 0.052362 | 0.0524585 | 0.0534622 | 0.052539 | 0.0527015 | 0.088928 |
| 3 | any_is.na | 0.165082 | 0.1665155 | 0.2059161 | 0.167865 | 0.2737035 | 0.319562 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 2.004901 | 2.002309 | 2.030979 | 2.002248 | 2.001424 | 3.149343 |
| 3 | any_is.na | 6.320864 | 6.355796 | 7.822567 | 6.397294 | 10.394330 | 11.317137 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 100000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 1000000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050244 163 5709258 305 5709258 305.0
Vcells 10479666 80 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 1000000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.259394 | 0.271498 | 0.3292668 | 0.3153795 | 0.3550220 | 0.741998 |
| 1 | anyMissing | 0.514958 | 0.521802 | 0.5666086 | 0.5361985 | 0.5619805 | 0.933253 |
| 3 | any_is.na | 1.647475 | 2.685594 | 2.9601964 | 2.7435330 | 2.9737855 | 12.192548 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 1.985235 | 1.921937 | 1.720819 | 1.700169 | 1.582946 | 1.257757 |
| 3 | any_is.na | 6.351246 | 9.891763 | 8.990265 | 8.699148 | 8.376342 | 16.432050 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 1000000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 10000000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050316 163 5709258 305 5709258 305.0
Vcells 10479714 80 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 10000000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 3.192648 | 3.210021 | 3.290707 | 3.221774 | 3.278016 | 3.804310 |
| 1 | anyMissing | 5.256905 | 5.275116 | 5.377196 | 5.310230 | 5.413356 | 6.648744 |
| 3 | any_is.na | 26.604766 | 27.029503 | 29.775117 | 27.262952 | 30.022492 | 40.988404 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 1.646566 | 1.643328 | 1.634055 | 1.648231 | 1.651412 | 1.747687 |
| 3 | any_is.na | 8.333135 | 8.420352 | 9.048243 | 8.462092 | 9.158739 | 10.774202 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on integer+n = 10000000 data. Outliers are displayed as crosses. Times are in milliseconds.
> rvector <- function(n, mode = c("logical", "double", "integer"), range = c(-100, +100), na_prob = 0) {
+ mode <- match.arg(mode)
+ if (mode == "logical") {
+ x <- sample(c(FALSE, TRUE), size = n, replace = TRUE)
+ } else {
+ x <- runif(n, min = range[1], max = range[2])
+ }
+ storage.mode(x) <- mode
+ if (na_prob > 0)
+ x[sample(n, size = na_prob * n)] <- NA
+ x
+ }
> rvectors <- function(scale = 10, seed = 1, ...) {
+ set.seed(seed)
+ data <- list()
+ data[[1]] <- rvector(n = scale * 100, ...)
+ data[[2]] <- rvector(n = scale * 1000, ...)
+ data[[3]] <- rvector(n = scale * 10000, ...)
+ data[[4]] <- rvector(n = scale * 1e+05, ...)
+ data[[5]] <- rvector(n = scale * 1e+06, ...)
+ names(data) <- sprintf("n = %d", sapply(data, FUN = length))
+ data
+ }
> data <- rvectors(mode = mode)> x <- data[["n = 1000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050391 163.0 5709258 305 5709258 305.0
Vcells 16035729 122.4 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 1000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.000505 | 0.0005205 | 0.0006173 | 0.0005375 | 0.0005515 | 0.008371 |
| 1 | anyMissing | 0.000937 | 0.0009790 | 0.0011860 | 0.0010030 | 0.0010505 | 0.016060 |
| 3 | any_is.na | 0.002244 | 0.0023690 | 0.0026005 | 0.0024175 | 0.0025095 | 0.015431 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 1.855446 | 1.880884 | 1.921335 | 1.866046 | 1.904805 | 1.918528 |
| 3 | any_is.na | 4.443564 | 4.551393 | 4.212717 | 4.497674 | 4.550317 | 1.843388 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 1000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 10000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050460 163.0 5709258 305 5709258 305.0
Vcells 16035771 122.4 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 10000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.004266 | 0.0042960 | 0.0043472 | 0.0043225 | 0.0043570 | 0.005866 |
| 1 | anyMissing | 0.005720 | 0.0058035 | 0.0059647 | 0.0058815 | 0.0059995 | 0.011991 |
| 3 | any_is.na | 0.017302 | 0.0175330 | 0.0179555 | 0.0176775 | 0.0178685 | 0.030253 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 1.340834 | 1.350908 | 1.372075 | 1.360671 | 1.376980 | 2.044153 |
| 3 | any_is.na | 4.055790 | 4.081238 | 4.130334 | 4.089647 | 4.101102 | 5.157347 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 10000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 100000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050532 163.0 5709258 305 5709258 305.0
Vcells 16036122 122.4 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 100000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.041876 | 0.0420325 | 0.0422432 | 0.0421405 | 0.0422655 | 0.044177 |
| 1 | anyMissing | 0.052454 | 0.0525240 | 0.0531367 | 0.0526505 | 0.0529340 | 0.077419 |
| 3 | any_is.na | 0.164455 | 0.1668220 | 0.2142914 | 0.1705240 | 0.2727585 | 0.282729 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 1.252603 | 1.249605 | 1.257877 | 1.249404 | 1.252416 | 1.752473 |
| 3 | any_is.na | 3.927190 | 3.968881 | 5.072808 | 4.046558 | 6.453455 | 6.399914 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 100000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 1000000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050604 163.0 5709258 305 5709258 305.0
Vcells 16036530 122.4 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 1000000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 0.456717 | 0.5120315 | 0.5419385 | 0.5531520 | 0.5685105 | 0.685328 |
| 1 | anyMissing | 0.545810 | 0.5804885 | 0.6082866 | 0.6047615 | 0.6236790 | 1.252541 |
| 3 | any_is.na | 1.709426 | 2.7450395 | 2.7931772 | 2.8021115 | 2.8304415 | 9.515550 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 1 | anyMissing | 1.195073 | 1.133697 | 1.122427 | 1.093301 | 1.097040 | 1.827652 |
| 3 | any_is.na | 3.742856 | 5.361075 | 5.154048 | 5.065717 | 4.978697 | 13.884665 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 1000000 data. Outliers are displayed as crosses. Times are in milliseconds.
> x <- data[["n = 10000000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 3050676 163.0 5709258 305 5709258 305.0
Vcells 16036578 122.4 34595238 264 56666022 432.4
> stats <- microbenchmark(anyMissing = anyMissing(x), anyNA = anyNA(x), any_is.na = any_is.na(x), unit = "ms")Table: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 10000000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 5.540831 | 5.668875 | 5.864548 | 5.749500 | 6.116903 | 7.339590 |
| 1 | anyMissing | 5.925187 | 6.040297 | 6.211277 | 6.157669 | 6.256903 | 7.233605 |
| 3 | any_is.na | 27.431948 | 28.496416 | 33.181975 | 28.905825 | 35.312683 | 250.630057 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 2 | anyNA | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.0000000 |
| 1 | anyMissing | 1.069368 | 1.065520 | 1.059123 | 1.070992 | 1.022887 | 0.9855598 |
| 3 | any_is.na | 4.950873 | 5.026821 | 5.658062 | 5.027537 | 5.772968 | 34.1476918 |
Figure: Benchmarking of anyMissing(), anyNA() and any_is.na() on double+n = 10000000 data. Outliers are displayed as crosses. Times are in milliseconds.
R version 3.6.1 Patched (2019-08-27 r77078)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.3 LTS
Matrix products: default
BLAS: /home/hb/software/R-devel/R-3-6-branch/lib/R/lib/libRblas.so
LAPACK: /home/hb/software/R-devel/R-3-6-branch/lib/R/lib/libRlapack.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] microbenchmark_1.4-6 matrixStats_0.55.0-9000 ggplot2_3.2.1
[4] knitr_1.24 R.devices_2.16.0 R.utils_2.9.0
[7] R.oo_1.22.0 R.methodsS3_1.7.1 history_0.0.0-9002
loaded via a namespace (and not attached):
[1] Biobase_2.45.0 bit64_0.9-7 splines_3.6.1
[4] network_1.15 assertthat_0.2.1 highr_0.8
[7] stats4_3.6.1 blob_1.2.0 robustbase_0.93-5
[10] pillar_1.4.2 RSQLite_2.1.2 backports_1.1.4
[13] lattice_0.20-38 glue_1.3.1 digest_0.6.20
[16] colorspace_1.4-1 sandwich_2.5-1 Matrix_1.2-17
[19] XML_3.98-1.20 lpSolve_5.6.13.3 pkgconfig_2.0.2
[22] genefilter_1.66.0 purrr_0.3.2 ergm_3.10.4
[25] xtable_1.8-4 mvtnorm_1.0-11 scales_1.0.0
[28] tibble_2.1.3 annotate_1.62.0 IRanges_2.18.2
[31] TH.data_1.0-10 withr_2.1.2 BiocGenerics_0.30.0
[34] lazyeval_0.2.2 mime_0.7 survival_2.44-1.1
[37] magrittr_1.5 crayon_1.3.4 statnet.common_4.3.0
[40] memoise_1.1.0 laeken_0.5.0 R.cache_0.13.0
[43] MASS_7.3-51.4 R.rsp_0.43.1 tools_3.6.1
[46] multcomp_1.4-10 S4Vectors_0.22.1 trust_0.1-7
[49] munsell_0.5.0 AnnotationDbi_1.46.1 compiler_3.6.1
[52] rlang_0.4.0 grid_3.6.1 RCurl_1.95-4.12
[55] cwhmisc_6.6 rappdirs_0.3.1 labeling_0.3
[58] bitops_1.0-6 base64enc_0.1-3 boot_1.3-23
[61] gtable_0.3.0 codetools_0.2-16 DBI_1.0.0
[64] markdown_1.1 R6_2.4.0 zoo_1.8-6
[67] dplyr_0.8.3 bit_1.1-14 zeallot_0.1.0
[70] parallel_3.6.1 Rcpp_1.0.2 vctrs_0.2.0
[73] DEoptimR_1.0-8 tidyselect_0.2.5 xfun_0.9
[76] coda_0.19-3 Total processing time was 17.93 secs.
To reproduce this report, do:
html <- matrixStats:::benchmark('anyMissing')Copyright Henrik Bengtsson. Last updated on 2019-09-10 20:33:53 (-0700 UTC). Powered by RSP.
<script> var link = document.createElement('link'); link.rel = 'icon'; link.href = "data:image/png;base64,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" document.getElementsByTagName('head')[0].appendChild(link); </script>