matrixStats.benchmarks

---

madDiff() benchmarks on subsetted computation

This report benchmark the performance of madDiff() on subsetted computation.

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)

Results

n = 1000 vector

> x <- data[["n = 1000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5344253 285.5    7916910 422.9  7916910 422.9
Vcells 17011428 129.8   36893127 281.5 57430649 438.2
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	0.076442	0.0799290	0.0881440	0.084452	0.0942640	0.146663
2	madDiff(x, idxs)	0.079360	0.0860325	0.0954273	0.092769	0.1014305	0.166170
3	madDiff(x[idxs])	0.079384	0.0846570	0.1001273	0.092774	0.1021840	0.528362

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	madDiff(x, idxs)	1.038173	1.076361	1.082629	1.098482	1.076026	1.133006
3	madDiff(x[idxs])	1.038487	1.059152	1.135951	1.098541	1.084019	3.602558

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on integer+n = 1000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 10000 vector

> x <- data[["n = 10000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5341851 285.3    7916910 422.9  7916910 422.9
Vcells 15882129 121.2   36893127 281.5 57430649 438.2
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	0.241986	0.2458525	0.2896286	0.2729940	0.3160605	0.421982
3	madDiff(x[idxs])	0.255741	0.2593270	0.2991417	0.2801310	0.3266175	0.555078
2	madDiff(x, idxs)	0.256148	0.2596000	0.3065501	0.2874185	0.3367050	0.453426

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
3	madDiff(x[idxs])	1.056842	1.054807	1.032846	1.026143	1.033402	1.315407
2	madDiff(x, idxs)	1.058524	1.055918	1.058425	1.052838	1.065318	1.074515

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on integer+n = 10000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 100000 vector

> x <- data[["n = 100000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5341923 285.3    7916910 422.9  7916910 422.9
Vcells 15945689 121.7   36893127 281.5 57430649 438.2
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	2.129314	2.160170	2.517114	2.199688	2.609695	9.828779
2	madDiff(x, idxs)	2.286819	2.313893	2.534705	2.338712	2.615870	8.736546
3	madDiff(x[idxs])	2.284914	2.316596	2.636846	2.380107	2.775296	8.292508

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	madDiff(x, idxs)	1.073970	1.071162	1.006988	1.063202	1.002366	0.8888740
3	madDiff(x[idxs])	1.073075	1.072413	1.047567	1.082021	1.063456	0.8436967

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on integer+n = 100000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 1000000 vector

> x <- data[["n = 1000000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5341995 285.3    7916910 422.9  7916910 422.9
Vcells 16575738 126.5   36893127 281.5 57430649 438.2
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	19.21814	20.16101	23.29995	21.41715	26.30154	40.84189
3	madDiff(x[idxs])	22.07896	23.91887	31.53210	26.59459	30.84588	417.09725
2	madDiff(x, idxs)	22.23748	23.95018	27.84580	26.91693	31.03340	44.13918

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
3	madDiff(x[idxs])	1.148860	1.186392	1.353312	1.241743	1.172778	10.212487
2	madDiff(x, idxs)	1.157109	1.187945	1.195101	1.256793	1.179908	1.080733

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on integer+n = 1000000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 10000000 vector

> x <- data[["n = 10000000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5342067 285.3    7916910 422.9  7916910 422.9
Vcells 22875786 174.6   36893127 281.5 57430649 438.2
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	223.9843	235.0427	281.9048	241.0282	255.6912	658.2526
2	madDiff(x, idxs)	346.1576	371.1629	416.0227	383.7330	400.6054	805.2715
3	madDiff(x[idxs])	356.6291	382.9311	461.8421	394.5892	420.1714	818.3962

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	madDiff(x, idxs)	1.545455	1.579130	1.475756	1.592067	1.566755	1.223347
3	madDiff(x[idxs])	1.592206	1.629198	1.638291	1.637108	1.643277	1.243286

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on integer+n = 10000000 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)

Results

n = 1000 vector

> x <- data[["n = 1000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5342148 285.4    7916910 422.9  7916910 422.9
Vcells 21432997 163.6   66913630 510.6 65932233 503.1
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	0.084334	0.089016	0.0934545	0.0923530	0.0964715	0.131338
3	madDiff(x[idxs])	0.087137	0.091671	0.0992167	0.0970800	0.1033340	0.227260
2	madDiff(x, idxs)	0.088080	0.093526	0.0981428	0.0974065	0.1023410	0.121016

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
3	madDiff(x[idxs])	1.033237	1.029826	1.061659	1.051184	1.071135	1.7303446
2	madDiff(x, idxs)	1.044419	1.050665	1.050167	1.054719	1.060842	0.9214089

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on double+n = 1000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 10000 vector

> x <- data[["n = 10000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5342211 285.4    7916910 422.9  7916910 422.9
Vcells 21442479 163.6   66913630 510.6 65932233 503.1
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	0.276932	0.2947845	0.3392882	0.3269570	0.3602870	0.532405
3	madDiff(x[idxs])	0.289242	0.3073325	0.3624250	0.3411220	0.3887430	0.615523
2	madDiff(x, idxs)	0.289653	0.3109800	0.3649975	0.3464645	0.4050515	0.652488

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
3	madDiff(x[idxs])	1.044451	1.042567	1.068192	1.043324	1.078982	1.156118
2	madDiff(x, idxs)	1.045935	1.054940	1.075774	1.059664	1.124247	1.225548

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on double+n = 10000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 100000 vector

> x <- data[["n = 100000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5342283 285.4    7916910 422.9  7916910 422.9
Vcells 21537360 164.4   66913630 510.6 65932233 503.1
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	2.769695	2.946010	3.229999	3.038127	3.485053	5.296025
2	madDiff(x, idxs)	2.929154	3.088465	3.437747	3.206155	3.358687	9.822420
3	madDiff(x[idxs])	2.930527	3.164171	3.544953	3.267368	3.988570	10.072499

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.0000000	1.000000
2	madDiff(x, idxs)	1.057573	1.048355	1.064318	1.055307	0.9637404	1.854678
3	madDiff(x[idxs])	1.058069	1.074053	1.097509	1.075455	1.1444787	1.901898

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on double+n = 100000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 1000000 vector

> x <- data[["n = 1000000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5342355 285.4    7916910 422.9  7916910 422.9
Vcells 22482804 171.6   66913630 510.6 66909510 510.5
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	27.67178	29.77384	31.77019	30.72146	32.80154	46.24240
3	madDiff(x[idxs])	37.20858	39.89259	42.56868	40.85085	43.18691	55.18924
2	madDiff(x, idxs)	37.59856	40.26422	43.08320	41.20645	44.43903	54.45280

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
3	madDiff(x[idxs])	1.344640	1.339854	1.339894	1.329717	1.316612	1.193477
2	madDiff(x, idxs)	1.358733	1.352335	1.356089	1.341292	1.354785	1.177551

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on double+n = 1000000 data. Outliers are displayed as crosses. Times are in milliseconds.

n = 10000000 vector

> x <- data[["n = 10000000"]]
> idxs <- sample.int(length(x), size = length(x) * 0.7)
> x_S <- x[idxs]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5342427 285.4    7916910 422.9  7916910 422.9
Vcells 31932852 243.7   66913630 510.6 66909510 510.5
> stats <- microbenchmark(madDiff_x_S = madDiff(x_S), `madDiff(x, idxs)` = madDiff(x, idxs = idxs), 
+     `madDiff(x[idxs])` = madDiff(x[idxs]), unit = "ms")

Table: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() 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
1	madDiff_x_S	295.2065	315.0181	378.5460	324.6075	339.9018	770.2836
2	madDiff(x, idxs)	437.4005	488.3774	536.7878	506.2254	519.6453	920.3717
3	madDiff(x[idxs])	439.6459	493.2539	561.7259	508.0569	529.1599	940.5145

	expr	min	lq	mean	median	uq	max
1	madDiff_x_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	madDiff(x, idxs)	1.481677	1.550315	1.418025	1.559500	1.528810	1.194848
3	madDiff(x[idxs])	1.489283	1.565795	1.483904	1.565142	1.556802	1.220998

Figure: Benchmarking of madDiff_x_S(), madDiff(x, idxs)() and madDiff(x[idxs])() on double+n = 10000000 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 4.98 mins.

Reproducibility

To reproduce this report, do:

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

---

Copyright Dongcan Jiang. Last updated on 2021-08-25 22:40:28 (+0200 UTC). Powered by RSP.