logSumExp

matrixStats: Benchmark report

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 3233776 172.8    5709258 305.0  5709258 305.0
Vcells 9537828  72.8   24515964 187.1 57084605 435.6
> 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	0.013519	0.0136465	0.0140762	0.0137110	0.0138315	0.042578
2	logSumExp_R	0.018184	0.0186770	0.0195850	0.0189745	0.0196315	0.050636

	expr	min	lq	mean	median	uq	max
1	logSumExp	1.00000	1.000000	1.000000	1.000000	1.000000	1.000000
2	logSumExp_R	1.34507	1.368629	1.391356	1.383889	1.419333	1.189253

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 3231548 172.6    5709258 305.0  5709258 305.0
Vcells 7352879  56.1   24515964 187.1 57084605 435.6
> 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	0.129478	0.1301875	0.1335535	0.1331955	0.1369590	0.149231
2	logSumExp_R	0.160116	0.1629015	0.1673604	0.1682595	0.1702905	0.182990

	expr	min	lq	mean	median	uq	max
1	logSumExp	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	logSumExp_R	1.236627	1.251284	1.253133	1.263252	1.243369	1.22622

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 3231611 172.6    5709258 305.0  5709258 305.0
Vcells 7352921  56.1   24515964 187.1 57084605 435.6
> 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	1.297379	1.406465	1.426832	1.436896	1.449534	1.599034
2	logSumExp_R	1.566383	1.770138	2.034313	1.826766	2.242275	7.980019

	expr	min	lq	mean	median	uq	max
1	logSumExp	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	logSumExp_R	1.207344	1.258573	1.425756	1.271328	1.546894	4.990525

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 3231674 172.6    5709258 305.0  5709258 305.0
Vcells 7353476  56.2   24515964 187.1 57084605 435.6
> 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	13.14968	14.46200	14.53545	14.60917	14.76055	15.22525
2	logSumExp_R	16.84121	18.01362	19.41297	18.21380	18.44415	31.28326

	expr	min	lq	mean	median	uq	max
1	logSumExp	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	logSumExp_R	1.280731	1.245582	1.335561	1.246738	1.249558	2.054696

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 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 8.57 secs.

Reproducibility

To reproduce this report, do:

html <- matrixStats:::benchmark('logSumExp')

Copyright Henrik Bengtsson. Last updated on 2019-09-10 20:58:37 (-0700 UTC). Powered by RSP.

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