matrixStats.benchmarks
logSumExp() benchmarks
This report benchmark the performance of logSumExp() against alternative methods.
Alternative methods
- logSumExp_R()
where
> logSumExp_R <- function(lx, ...) {
+ iMax <- which.max(lx)
+ log1p(sum(exp(lx[-iMax] - lx[iMax]))) + lx[iMax]
+ }
Data
> 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 = "double")
> data <- data[1:4]
Results
n = 1000 vector
> x <- data[["n = 1000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 5331406 284.8 8529671 455.6 8529671 455.6
Vcells 13561677 103.5 34090130 260.1 60562128 462.1
> stats <- microbenchmark(logSumExp = logSumExp(x), logSumExp_R = logSumExp_R(x), unit = "ms")
Table: Benchmarking of logSumExp() and logSumExp_R() on n = 1000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 0.021816 | 0.0227330 | 0.0233099 | 0.0230455 | 0.0237100 | 0.040055 |
| 2 | logSumExp_R | 0.027199 | 0.0282075 | 0.0292453 | 0.0287040 | 0.0292425 | 0.054647 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.00000 | 1.000000 |
| 2 | logSumExp_R | 1.246746 | 1.240817 | 1.254632 | 1.245536 | 1.23334 | 1.364299 |
Figure: Benchmarking of logSumExp() and logSumExp_R() on n = 1000 data. Outliers are displayed as crosses. Times are in milliseconds.
n = 10000 vector
> x <- data[["n = 10000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 5329178 284.7 8529671 455.6 8529671 455.6
Vcells 11376728 86.8 34090130 260.1 60562128 462.1
> stats <- microbenchmark(logSumExp = logSumExp(x), logSumExp_R = logSumExp_R(x), unit = "ms")
Table: Benchmarking of logSumExp() and logSumExp_R() on n = 10000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 0.158267 | 0.169690 | 0.1875225 | 0.180102 | 0.204260 | 0.271811 |
| 2 | logSumExp_R | 0.181882 | 0.194341 | 0.2114098 | 0.206124 | 0.227409 | 0.287387 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 1.00000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 2 | logSumExp_R | 1.14921 | 1.145271 | 1.127384 | 1.144485 | 1.113331 | 1.057305 |
Figure: Benchmarking of logSumExp() and logSumExp_R() on n = 10000 data. Outliers are displayed as crosses. Times are in milliseconds.
n = 100000 vector
> x <- data[["n = 100000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 5329241 284.7 8529671 455.6 8529671 455.6
Vcells 11376770 86.8 34090130 260.1 60562128 462.1
> stats <- microbenchmark(logSumExp = logSumExp(x), logSumExp_R = logSumExp_R(x), unit = "ms")
Table: Benchmarking of logSumExp() and logSumExp_R() on n = 100000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 1.379849 | 1.466273 | 1.53948 | 1.506045 | 1.546134 | 2.092337 |
| 2 | logSumExp_R | 1.578353 | 1.734569 | 2.05354 | 1.868164 | 2.255320 | 8.385314 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 2 | logSumExp_R | 1.143859 | 1.182979 | 1.333918 | 1.240444 | 1.458683 | 4.007631 |
Figure: Benchmarking of logSumExp() and logSumExp_R() on n = 100000 data. Outliers are displayed as crosses. Times are in milliseconds.
n = 1000000 vector
> x <- data[["n = 1000000"]]
> gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 5329304 284.7 8529671 455.6 8529671 455.6
Vcells 11377325 86.9 34090130 260.1 60562128 462.1
> stats <- microbenchmark(logSumExp = logSumExp(x), logSumExp_R = logSumExp_R(x), unit = "ms")
Table: Benchmarking of logSumExp() and logSumExp_R() on n = 1000000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 14.12011 | 15.33734 | 15.43717 | 15.47193 | 15.56384 | 20.06469 |
| 2 | logSumExp_R | 20.44286 | 23.18112 | 24.12157 | 23.37133 | 23.66989 | 31.42130 |
| expr | min | lq | mean | median | uq | max | |
|---|---|---|---|---|---|---|---|
| 1 | logSumExp | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000 |
| 2 | logSumExp_R | 1.447783 | 1.511417 | 1.562564 | 1.510563 | 1.520826 | 1.566 |
Figure: Benchmarking of logSumExp() and logSumExp_R() on n = 1000000 data. Outliers are displayed as crosses. Times are in milliseconds.
Appendix
Session information
R version 4.1.1 Patched (2021-08-10 r80727)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.5 LTS
Matrix products: default
BLAS: /home/hb/software/R-devel/R-4-1-branch/lib/R/lib/libRblas.so
LAPACK: /home/hb/software/R-devel/R-4-1-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_1.4-7 matrixStats_0.60.1 ggplot2_3.3.5
[4] knitr_1.33 R.devices_2.17.0 R.utils_2.10.1
[7] R.oo_1.24.0 R.methodsS3_1.8.1-9001 history_0.0.1-9000
loaded via a namespace (and not attached):
[1] Biobase_2.52.0 httr_1.4.2 splines_4.1.1
[4] bit64_4.0.5 network_1.17.1 assertthat_0.2.1
[7] highr_0.9 stats4_4.1.1 blob_1.2.2
[10] GenomeInfoDbData_1.2.6 robustbase_0.93-8 pillar_1.6.2
[13] RSQLite_2.2.8 lattice_0.20-44 glue_1.4.2
[16] digest_0.6.27 XVector_0.32.0 colorspace_2.0-2
[19] Matrix_1.3-4 XML_3.99-0.7 pkgconfig_2.0.3
[22] zlibbioc_1.38.0 genefilter_1.74.0 purrr_0.3.4
[25] ergm_4.1.2 xtable_1.8-4 scales_1.1.1
[28] tibble_3.1.4 annotate_1.70.0 KEGGREST_1.32.0
[31] farver_2.1.0 generics_0.1.0 IRanges_2.26.0
[34] ellipsis_0.3.2 cachem_1.0.6 withr_2.4.2
[37] BiocGenerics_0.38.0 mime_0.11 survival_3.2-13
[40] magrittr_2.0.1 crayon_1.4.1 statnet.common_4.5.0
[43] memoise_2.0.0 laeken_0.5.1 fansi_0.5.0
[46] R.cache_0.15.0 MASS_7.3-54 R.rsp_0.44.0
[49] progressr_0.8.0 tools_4.1.1 lifecycle_1.0.0
[52] S4Vectors_0.30.0 trust_0.1-8 munsell_0.5.0
[55] tabby_0.0.1-9001 AnnotationDbi_1.54.1 Biostrings_2.60.2
[58] compiler_4.1.1 GenomeInfoDb_1.28.1 rlang_0.4.11
[61] grid_4.1.1 RCurl_1.98-1.4 cwhmisc_6.6
[64] rappdirs_0.3.3 startup_0.15.0 labeling_0.4.2
[67] bitops_1.0-7 base64enc_0.1-3 boot_1.3-28
[70] gtable_0.3.0 DBI_1.1.1 markdown_1.1
[73] R6_2.5.1 lpSolveAPI_5.5.2.0-17.7 rle_0.9.2
[76] dplyr_1.0.7 fastmap_1.1.0 bit_4.0.4
[79] utf8_1.2.2 parallel_4.1.1 Rcpp_1.0.7
[82] vctrs_0.3.8 png_0.1-7 DEoptimR_1.0-9
[85] tidyselect_1.1.1 xfun_0.25 coda_0.19-4
Total processing time was 9.71 secs.
Reproducibility
To reproduce this report, do:
html <- matrixStats:::benchmark('logSumExp')
Copyright Henrik Bengtsson. Last updated on 2021-08-25 19:14:55 (+0200 UTC). Powered by RSP.