matrixStats.benchmarks

varDiff() benchmarks

This report benchmark the performance of varDiff() against alternative methods.

Alternative methods

Data type “integer”

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 = mode)
> data <- data[1:4]

Results

n = 1000 vector

All elements

> x <- data[["n = 1000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	0.017263	0.0178385	0.0188864	0.0182005	0.0189145	0.059060
3	diff	0.018631	0.0198580	0.0213724	0.0207305	0.0216830	0.048038
1	varDiff	0.025264	0.0258230	0.0272910	0.0269710	0.0279700	0.050698

	expr	min	lq	mean	median	uq	max
2	var	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
3	diff	1.079245	1.113210	1.131626	1.139007	1.146369	0.8133762
1	varDiff	1.463477	1.447599	1.445007	1.481882	1.478760	0.8584152

Figure: Benchmarking of varDiff(), var() and diff() on integer+n = 1000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 10000 vector

All elements

> x <- data[["n = 10000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	0.061549	0.0658010	0.0772253	0.0771285	0.0829330	0.117829
1	varDiff	0.086036	0.0914765	0.1084281	0.1030400	0.1145355	0.270556
3	diff	0.136121	0.1465270	0.1715013	0.1679355	0.1787390	0.288329

	expr	min	lq	mean	median	uq	max
2	var	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	varDiff	1.397846	1.390199	1.404049	1.335952	1.381061	2.296175
3	diff	2.211587	2.226820	2.220791	2.177347	2.155222	2.447012

Figure: Benchmarking of varDiff(), var() and diff() on integer+n = 10000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 100000 vector

All elements

> x <- data[["n = 100000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	0.431308	0.462691	0.5831113	0.5545305	0.713080	1.008892
1	varDiff	0.586627	0.604608	0.8273098	0.7255340	0.858775	7.446869
3	diff	1.033404	1.195533	1.5823960	1.3441620	2.049228	7.357465

	expr	min	lq	mean	median	uq	max
2	var	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	varDiff	1.360112	1.306721	1.418785	1.308375	1.204318	7.381235
3	diff	2.395977	2.583868	2.713712	2.423964	2.873769	7.292619

Figure: Benchmarking of varDiff(), var() and diff() on integer+n = 100000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 1000000 vector

All elements

> x <- data[["n = 1000000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	4.750307	5.166704	5.893678	5.490694	5.815732	13.54519
1	varDiff	6.524512	6.974064	8.068979	7.444474	7.972615	30.54505
3	diff	11.344527	12.450922	15.369838	13.484686	19.657373	25.57203

	expr	min	lq	mean	median	uq	max
2	var	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	varDiff	1.373493	1.349809	1.369091	1.355835	1.370871	2.255048
3	diff	2.388167	2.409839	2.607852	2.455916	3.380034	1.887905

Figure: Benchmarking of varDiff(), var() and diff() on integer+n = 1000000 data. Outliers are displayed as crosses. Times are in milliseconds.

Data type “double”

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 = mode)
> data <- data[1:4]

Results

n = 1000 vector

All elements

> x <- data[["n = 1000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	0.015324	0.015781	0.0169349	0.0159940	0.017029	0.054035
3	diff	0.014798	0.016656	0.0176397	0.0174040	0.018085	0.046717
1	varDiff	0.021714	0.022524	0.0241851	0.0231655	0.024547	0.045064

	expr	min	lq	mean	median	uq	max
2	var	1.0000000	1.000000	1.000000	1.000000	1.000000	1.0000000
3	diff	0.9656748	1.055446	1.041621	1.088158	1.062012	0.8645693
1	varDiff	1.4169930	1.427286	1.428122	1.448387	1.441482	0.8339780

Figure: Benchmarking of varDiff(), var() and diff() on double+n = 1000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 10000 vector

All elements

> x <- data[["n = 10000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	0.049441	0.0533505	0.0588828	0.0590235	0.0622830	0.094233
1	varDiff	0.062076	0.0679135	0.0754562	0.0729925	0.0807265	0.167566
3	diff	0.066900	0.0747475	0.0830154	0.0850790	0.0883370	0.108227

	expr	min	lq	mean	median	uq	max
2	var	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	varDiff	1.255557	1.272968	1.281465	1.236668	1.296124	1.778209
3	diff	1.353128	1.401065	1.409842	1.441443	1.418316	1.148504

Figure: Benchmarking of varDiff(), var() and diff() on double+n = 10000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 100000 vector

All elements

> x <- data[["n = 100000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	0.326733	0.353135	0.4040287	0.4083090	0.4307145	0.598747
1	varDiff	0.411866	0.474849	0.5457040	0.5212120	0.5764060	0.812143
3	diff	0.515145	0.615211	1.0233537	0.6881855	0.8975840	7.984266

	expr	min	lq	mean	median	uq	max
2	var	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	varDiff	1.260558	1.344667	1.350656	1.276514	1.338255	1.356404
3	diff	1.576654	1.742141	2.532874	1.685453	2.083942	13.334958

Figure: Benchmarking of varDiff(), var() and diff() on double+n = 100000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 1000000 vector

All elements

> x <- data[["n = 1000000"]]
> stats <- microbenchmark(varDiff = varDiff(x), var = var(x), diff = diff(x), unit = "ms")

Table: Benchmarking of varDiff(), var() and diff() 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	var	3.667983	4.397274	4.62480	4.560160	4.844445	5.584471
1	varDiff	5.217178	5.504392	6.41692	5.689897	6.244734	21.075055
3	diff	7.226720	7.597451	10.51134	8.235660	14.475874	21.908809

	expr	min	lq	mean	median	uq	max
2	var	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	varDiff	1.422356	1.251774	1.387502	1.247741	1.289050	3.773868
3	diff	1.970216	1.727764	2.272821	1.806002	2.988138	3.923166

Figure: Benchmarking of varDiff(), var() and diff() on double+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_0.60.0     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] rstudioapi_0.13         rappdirs_0.3.3          startup_0.15.0-9000    
[67] labeling_0.4.2          bitops_1.0-7            base64enc_0.1-3        
[70] boot_1.3-28             gtable_0.3.0            DBI_1.1.1              
[73] markdown_1.1            R6_2.5.1                lpSolveAPI_5.5.2.0-17.7
[76] rle_0.9.2               dplyr_1.0.7             fastmap_1.1.0          
[79] bit_4.0.4               utf8_1.2.2              parallel_4.1.1         
[82] Rcpp_1.0.7              vctrs_0.3.8             png_0.1-7              
[85] DEoptimR_1.0-9          tidyselect_1.1.1        xfun_0.25              
[88] coda_0.19-4            

Total processing time was 14.04 secs.

Reproducibility

To reproduce this report, do:

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