matrixStats.benchmarks

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colMads() and rowMads() benchmarks on subsetted computation

This report benchmark the performance of colMads() and rowMads() on subsetted computation.

Data type “integer”

Data

> rmatrix <- function(nrow, ncol, mode = c("logical", "double", "integer", "index"), range = c(-100, 
+     +100), na_prob = 0) {
+     mode <- match.arg(mode)
+     n <- nrow * ncol
+     if (mode == "logical") {
+         x <- sample(c(FALSE, TRUE), size = n, replace = TRUE)
+     }     else if (mode == "index") {
+         x <- seq_len(n)
+         mode <- "integer"
+     }     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
+     dim(x) <- c(nrow, ncol)
+     x
+ }
> rmatrices <- function(scale = 10, seed = 1, ...) {
+     set.seed(seed)
+     data <- list()
+     data[[1]] <- rmatrix(nrow = scale * 1, ncol = scale * 1, ...)
+     data[[2]] <- rmatrix(nrow = scale * 10, ncol = scale * 10, ...)
+     data[[3]] <- rmatrix(nrow = scale * 100, ncol = scale * 1, ...)
+     data[[4]] <- t(data[[3]])
+     data[[5]] <- rmatrix(nrow = scale * 10, ncol = scale * 100, ...)
+     data[[6]] <- t(data[[5]])
+     names(data) <- sapply(data, FUN = function(x) paste(dim(x), collapse = "x"))
+     data
+ }
> data <- rmatrices(mode = mode)

Results

10x10 integer matrix

> X <- data[["10x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5230613 279.4    8529671 455.6  8529671 455.6
Vcells 10010013  76.4   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222666 279.0    8529671 455.6  8529671 455.6
Vcells 9983739  76.2   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+10x10 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.002897	0.0030155	0.0058568	0.0031005	0.0031965	0.275000
2	colMads(X, rows, cols)	0.003300	0.0034380	0.0035962	0.0035395	0.0036545	0.006543
3	colMads(X[rows, cols])	0.003731	0.0040170	0.0043862	0.0041550	0.0043645	0.018293

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.139109	1.140109	0.6140243	1.141590	1.143282	0.0237927
3	colMads(X[rows, cols])	1.287884	1.332117	0.7489081	1.340106	1.365400	0.0665200

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on integer+10x10 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.002952	0.003079	0.0032072	0.0031660	0.0032480	0.006710
2	rowMads(X, cols, rows)	0.003306	0.003475	0.0064096	0.0035395	0.0036735	0.270258
3	rowMads(X[cols, rows])	0.003782	0.004016	0.0042449	0.0041560	0.0042925	0.007147

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.119919	1.128613	1.998491	1.117972	1.131004	40.276900
3	rowMads(X[cols, rows])	1.281165	1.304320	1.323547	1.312697	1.321583	1.065127

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+10x10 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+10x10 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	2.897	3.0155	5.85682	3.1005	3.1965	275.00
2	rowMads_X_S	2.952	3.0790	3.20720	3.1660	3.2480	6.71

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000
2	rowMads_X_S	1.018985	1.021058	0.5476009	1.021126	1.016111	0.0244

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+10x10 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

100x100 integer matrix

> X <- data[["100x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5221596 278.9    8529671 455.6  8529671 455.6
Vcells 9652762  73.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5221572 278.9    8529671 455.6  8529671 455.6
Vcells 9657815  73.7   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+100x100 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	0.133489	0.1427000	0.1643306	0.1620720	0.1762455	0.229778
1	colMads_X_S	0.133940	0.1420545	0.1653787	0.1640340	0.1782025	0.230007
3	colMads(X[rows, cols])	0.141483	0.1520570	0.1757110	0.1737415	0.1913060	0.269344

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	1.003379	0.9954765	1.006378	1.012106	1.011104	1.000997
3	colMads(X[rows, cols])	1.059885	1.0655711	1.069253	1.072002	1.085452	1.172192

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on integer+100x100 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	0.134054	0.1444445	0.1645099	0.1610480	0.176094	0.242336
1	rowMads_X_S	0.137631	0.1461835	0.1689280	0.1673675	0.183561	0.224565
3	rowMads(X[cols, rows])	0.145598	0.1560775	0.1765251	0.1731375	0.190183	0.239563

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowMads_X_S	1.026683	1.012039	1.026856	1.039240	1.042404	0.9266679
3	rowMads(X[cols, rows])	1.086115	1.080536	1.073036	1.075068	1.080008	0.9885572

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+100x100 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+100x100 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	133.940	142.0545	165.3787	164.0340	178.2025	230.007
2	rowMads_X_S	137.631	146.1835	168.9280	167.3675	183.5610	224.565

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.00000	1.0000000
2	rowMads_X_S	1.027557	1.029066	1.021462	1.020322	1.03007	0.9763399

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+100x100 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

1000x10 integer matrix

> X <- data[["1000x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222338 279.0    8529671 455.6  8529671 455.6
Vcells 9656804  73.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222314 279.0    8529671 455.6  8529671 455.6
Vcells 9661857  73.8   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+1000x10 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	0.117453	0.1247245	0.1396233	0.1364435	0.1481360	0.186024
1	colMads_X_S	0.115756	0.1296875	0.1410565	0.1382630	0.1474685	0.207656
3	colMads(X[rows, cols])	0.123733	0.1314120	0.1472302	0.1438235	0.1582085	0.228173

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	0.9855517	1.039792	1.010265	1.013335	0.995494	1.116286
3	colMads(X[rows, cols])	1.0534682	1.053618	1.054481	1.054088	1.067995	1.226578

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on integer+1000x10 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.119852	0.1342820	0.1505124	0.1431685	0.1527535	0.251675
2	rowMads(X, cols, rows)	0.117795	0.1277995	0.1474039	0.1459425	0.1574675	0.239278
3	rowMads(X[cols, rows])	0.129588	0.1424825	0.1649833	0.1585315	0.1696535	0.289764

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.0000000	1.0000000	1.0000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	0.9828372	0.9517247	0.9793474	1.019376	1.030860	0.950742
3	rowMads(X[cols, rows])	1.0812335	1.0610692	1.0961446	1.107307	1.110636	1.151342

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+1000x10 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+1000x10 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	115.756	129.6875	141.0565	138.2630	147.4685	207.656
2	rowMads_X_S	119.852	134.2820	150.5124	143.1685	152.7535	251.675

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.00000	1.000000	1.00000
2	rowMads_X_S	1.035385	1.035427	1.067036	1.03548	1.035838	1.21198

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+1000x10 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

10x1000 integer matrix

> X <- data[["10x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222542 279.0    8529671 455.6  8529671 455.6
Vcells 9657625  73.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222518 279.0    8529671 455.6  8529671 455.6
Vcells 9662678  73.8   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+10x1000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	0.097614	0.1059500	0.1156218	0.1127260	0.1201080	0.166373
1	colMads_X_S	0.094198	0.1038435	0.1150566	0.1131975	0.1245320	0.180748
3	colMads(X[rows, cols])	0.107073	0.1175900	0.1261233	0.1231830	0.1342685	0.166177

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
1	colMads_X_S	0.965005	0.980118	0.9951123	1.004183	1.036833	1.0864022
3	colMads(X[rows, cols])	1.096902	1.109863	1.0908267	1.092765	1.117898	0.9988219

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on integer+10x1000 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	0.102962	0.1091030	0.1166636	0.1124835	0.1200705	0.195332
1	rowMads_X_S	0.107028	0.1115420	0.1203751	0.1161365	0.1277905	0.155609
3	rowMads(X[cols, rows])	0.116490	0.1212795	0.1314804	0.1262820	0.1395350	0.187189

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowMads_X_S	1.039490	1.022355	1.031813	1.032476	1.064296	0.7966385
3	rowMads(X[cols, rows])	1.131388	1.111606	1.127004	1.122671	1.162109	0.9583120

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+10x1000 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+10x1000 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	94.198	103.8435	115.0566	113.1975	124.5320	180.748
2	rowMads_X_S	107.028	111.5420	120.3751	116.1365	127.7905	155.609

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowMads_X_S	1.136203	1.074136	1.046225	1.025964	1.026166	0.8609169

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+10x1000 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

100x1000 integer matrix

> X <- data[["100x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222755 279.0    8529671 455.6  8529671 455.6
Vcells 9680296  73.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222731 279.0    8529671 455.6  8529671 455.6
Vcells 9730349  74.3   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+100x1000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.417719	1.630202	1.691884	1.665612	1.692498	2.364768
2	colMads(X, rows, cols)	1.483859	1.632983	1.737114	1.687781	1.754010	2.278443
3	colMads(X[rows, cols])	1.498354	1.715013	1.818983	1.776871	1.818416	2.565856

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.046652	1.001706	1.026734	1.013310	1.036344	0.9634954
3	colMads(X[rows, cols])	1.056877	1.052024	1.075123	1.066798	1.074397	1.0850350

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on integer+100x1000 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	1.506947	1.553424	1.652926	1.599171	1.653604	2.224853
1	rowMads_X_S	1.564443	1.585908	1.705902	1.634154	1.723385	2.317330
3	rowMads(X[cols, rows])	1.632498	1.655447	1.795700	1.700440	1.755014	4.476681

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	rowMads_X_S	1.038154	1.020911	1.032050	1.021876	1.042199	1.041565
3	rowMads(X[cols, rows])	1.083315	1.065676	1.086377	1.063326	1.061327	2.012124

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+100x1000 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+100x1000 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.564443	1.585908	1.705902	1.634154	1.723385	2.317330
1	colMads_X_S	1.417719	1.630202	1.691884	1.665612	1.692498	2.364768

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.0000000	1.00000	1.0000000	1.00000	1.000000	1.000000
1	colMads_X_S	0.9062133	1.02793	0.9917825	1.01925	0.982078	1.020471

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+100x1000 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

1000x100 integer matrix

> X <- data[["1000x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222965 279.0    8529671 455.6  8529671 455.6
Vcells 9681071  73.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5222941 279.0    8529671 455.6  8529671 455.6
Vcells 9731124  74.3   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+1000x100 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.085066	1.149720	1.208804	1.185625	1.226300	1.643439
1	colMads_X_S	1.089497	1.184171	1.214995	1.198657	1.223488	1.847442
3	colMads(X[rows, cols])	1.154745	1.205556	1.264744	1.261588	1.296334	1.804970

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.0000000	1.000000
1	colMads_X_S	1.004084	1.029964	1.005122	1.010991	0.9977069	1.124132
3	colMads(X[rows, cols])	1.064216	1.048564	1.046277	1.064070	1.0571104	1.098288

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on integer+1000x100 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	1.105407	1.170870	1.214940	1.201795	1.207318	1.882349
1	rowMads_X_S	1.127465	1.203342	1.238002	1.229418	1.237796	1.591996
3	rowMads(X[cols, rows])	1.198161	1.268891	1.305387	1.301751	1.312086	1.874509

	expr	min	lq	mean	median	uq	max
2	rowMads(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowMads_X_S	1.019955	1.027733	1.018981	1.022984	1.025245	0.8457496
3	rowMads(X[cols, rows])	1.083909	1.083716	1.074445	1.083172	1.086778	0.9958350

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on integer+1000x100 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+1000x100 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.089497	1.184171	1.214995	1.198657	1.223488	1.847442
2	rowMads_X_S	1.127465	1.203342	1.238002	1.229418	1.237796	1.591996

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.00000	1.000000	1.000000	1.000000	1.0000000
2	rowMads_X_S	1.034849	1.01619	1.018935	1.025663	1.011695	0.8617299

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on integer+1000x100 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

Data type “double”

Data

> rmatrix <- function(nrow, ncol, mode = c("logical", "double", "integer", "index"), range = c(-100, 
+     +100), na_prob = 0) {
+     mode <- match.arg(mode)
+     n <- nrow * ncol
+     if (mode == "logical") {
+         x <- sample(c(FALSE, TRUE), size = n, replace = TRUE)
+     }     else if (mode == "index") {
+         x <- seq_len(n)
+         mode <- "integer"
+     }     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
+     dim(x) <- c(nrow, ncol)
+     x
+ }
> rmatrices <- function(scale = 10, seed = 1, ...) {
+     set.seed(seed)
+     data <- list()
+     data[[1]] <- rmatrix(nrow = scale * 1, ncol = scale * 1, ...)
+     data[[2]] <- rmatrix(nrow = scale * 10, ncol = scale * 10, ...)
+     data[[3]] <- rmatrix(nrow = scale * 100, ncol = scale * 1, ...)
+     data[[4]] <- t(data[[3]])
+     data[[5]] <- rmatrix(nrow = scale * 10, ncol = scale * 100, ...)
+     data[[6]] <- t(data[[5]])
+     names(data) <- sapply(data, FUN = function(x) paste(dim(x), collapse = "x"))
+     data
+ }
> data <- rmatrices(mode = mode)

Results

10x10 double matrix

> X <- data[["10x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223183 279.0    8529671 455.6  8529671 455.6
Vcells 9772162  74.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223150 279.0    8529671 455.6  8529671 455.6
Vcells 9772300  74.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+10x10 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.003726	0.0038045	0.0042544	0.0038940	0.0040430	0.026198
2	colMads(X, rows, cols)	0.004155	0.0043660	0.0046214	0.0044525	0.0045435	0.011127
3	colMads(X[rows, cols])	0.004658	0.0049150	0.0051246	0.0050410	0.0051965	0.011186

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.115137	1.147588	1.086266	1.143426	1.123794	0.4247271
3	colMads(X[rows, cols])	1.250134	1.291891	1.204549	1.294556	1.285308	0.4269792

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on double+10x10 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.003594	0.0036745	0.0038523	0.0038010	0.0039325	0.006779
2	rowMads(X, cols, rows)	0.003975	0.0042030	0.0045456	0.0043055	0.0044020	0.024302
3	rowMads(X[cols, rows])	0.004466	0.0047335	0.0050846	0.0048645	0.0049875	0.019734

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.106010	1.143829	1.179974	1.132728	1.119390	3.584894
3	rowMads(X[cols, rows])	1.242627	1.288202	1.319877	1.279795	1.268277	2.911049

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+10x10 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on double+10x10 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	3.594	3.6745	3.85229	3.801	3.9325	6.779
1	colMads_X_S	3.726	3.8045	4.25439	3.894	4.0430	26.198

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.00000	1.000000	1.000000	1.000000
1	colMads_X_S	1.036728	1.035379	1.10438	1.024467	1.028099	3.864582

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on double+10x10 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

100x100 double matrix

> X <- data[["100x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223381 279.0    8529671 455.6  8529671 455.6
Vcells 9778099  74.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223357 279.0    8529671 455.6  8529671 455.6
Vcells 9788152  74.7   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+100x100 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.185069	0.1922325	0.2081775	0.2033905	0.2202775	0.252736
2	colMads(X, rows, cols)	0.185441	0.1947715	0.2096435	0.2038805	0.2210425	0.280302
3	colMads(X[rows, cols])	0.195130	0.2025730	0.2222310	0.2150940	0.2420335	0.303092

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colMads(X, rows, cols)	1.002010	1.013208	1.007042	1.002409	1.003473	1.109070
3	colMads(X[rows, cols])	1.054364	1.053792	1.067507	1.057542	1.098766	1.199243

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on double+100x100 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.183997	0.1996895	0.2176960	0.212422	0.2309220	0.317659
2	rowMads(X, cols, rows)	0.185518	0.2023970	0.2163835	0.215181	0.2294845	0.281491
3	rowMads(X[cols, rows])	0.194266	0.2109260	0.2262418	0.223656	0.2390645	0.300976

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.008266	1.013559	0.9939712	1.012988	0.993775	0.8861421
3	rowMads(X[cols, rows])	1.055811	1.056270	1.0392560	1.052885	1.035261	0.9474814

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+100x100 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on double+100x100 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	185.069	192.2325	208.1775	203.3905	220.2775	252.736
2	rowMads_X_S	183.997	199.6895	217.6960	212.4220	230.9220	317.659

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads_X_S	0.9942076	1.038792	1.045723	1.044405	1.048323	1.256881

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on double+100x100 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

1000x10 double matrix

> X <- data[["1000x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223580 279.0    8529671 455.6  8529671 455.6
Vcells 9779494  74.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223556 279.0    8529671 455.6  8529671 455.6
Vcells 9789547  74.7   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+1000x10 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	0.175997	0.1773025	0.2077430	0.1962025	0.2291455	0.291108
3	colMads(X[rows, cols])	0.183437	0.1847305	0.2166757	0.2032115	0.2393360	0.332860
1	colMads_X_S	0.172278	0.1781660	0.2096855	0.2047495	0.2254340	0.284149

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.0000000	1.0000000
3	colMads(X[rows, cols])	1.042273	1.041894	1.042999	1.035723	1.0444717	1.1434244
1	colMads_X_S	0.978869	1.004870	1.009351	1.043562	0.9838029	0.9760948

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on double+1000x10 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.172019	0.1766200	0.2047788	0.1916175	0.2220000	0.293810
2	rowMads(X, cols, rows)	0.175103	0.1777085	0.2124895	0.2085635	0.2366575	0.289278
3	rowMads(X[cols, rows])	0.183978	0.1897030	0.2214018	0.2181130	0.2410750	0.340425

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.017928	1.006163	1.037654	1.088437	1.066025	0.9845751
3	rowMads(X[cols, rows])	1.069521	1.074074	1.081175	1.138273	1.085923	1.1586570

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+1000x10 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on double+1000x10 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	172.019	176.620	204.7788	191.6175	222.000	293.810
1	colMads_X_S	172.278	178.166	209.6855	204.7495	225.434	284.149

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colMads_X_S	1.001506	1.008753	1.023961	1.068532	1.015469	0.9671182

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on double+1000x10 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

10x1000 double matrix

> X <- data[["10x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223784 279.0    8529671 455.6  8529671 455.6
Vcells 9779629  74.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223760 279.0    8529671 455.6  8529671 455.6
Vcells 9789682  74.7   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+10x1000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	0.141589	0.1505660	0.1690891	0.1650760	0.1825165	0.246319
1	colMads_X_S	0.138516	0.1474945	0.1739136	0.1754285	0.1910490	0.262605
3	colMads(X[rows, cols])	0.151591	0.1656825	0.1886651	0.1861745	0.2011445	0.290701

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.0000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	0.9782963	0.9796003	1.028532	1.062714	1.046749	1.066118
3	colMads(X[rows, cols])	1.0706411	1.1003978	1.115773	1.127811	1.102062	1.180181

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on double+10x1000 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.137422	0.1501845	0.1723559	0.1694125	0.185415	0.236189
2	rowMads(X, cols, rows)	0.140753	0.1505595	0.1718368	0.1725220	0.182812	0.271620
3	rowMads(X[cols, rows])	0.148459	0.1593680	0.1851883	0.1840025	0.201822	0.248958

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.0000000	1.000000
2	rowMads(X, cols, rows)	1.024239	1.002497	0.996988	1.018355	0.9859612	1.150011
3	rowMads(X[cols, rows])	1.080315	1.061148	1.074453	1.086121	1.0884880	1.054063

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+10x1000 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on double+10x1000 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	137.422	150.1845	172.3559	169.4125	185.415	236.189
1	colMads_X_S	138.516	147.4945	173.9135	175.4285	191.049	262.605

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	1.007961	0.9820887	1.009038	1.035511	1.030386	1.111843

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on double+10x1000 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

100x1000 double matrix

> X <- data[["100x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223997  279    8529671 455.6  8529671 455.6
Vcells 9825073   75   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5223973 279.0    8529671 455.6  8529671 455.6
Vcells 9925126  75.8   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+100x1000 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.875287	2.024370	2.060110	2.032348	2.040499	3.241494
2	colMads(X, rows, cols)	1.872633	2.021563	2.045685	2.033446	2.038120	3.172565
3	colMads(X[rows, cols])	1.969665	2.132613	2.175704	2.138631	2.146966	3.166726

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.0000000	1.0000000	1.000000	1.000000	1.0000000	1.0000000
2	colMads(X, rows, cols)	0.9985847	0.9986131	0.992998	1.000540	0.9988339	0.9787354
3	colMads(X[rows, cols])	1.0503272	1.0534695	1.056111	1.052296	1.0521772	0.9769341

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on double+100x1000 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.863827	2.015923	2.076716	2.021421	2.054693	3.223811
2	rowMads(X, cols, rows)	1.882677	2.040559	2.054763	2.045401	2.058898	2.997697
3	rowMads(X[cols, rows])	1.972272	2.126524	2.168128	2.134272	2.152099	2.893971

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.010114	1.012221	0.9894288	1.011863	1.002047	0.9298613
3	rowMads(X[cols, rows])	1.058184	1.054864	1.0440176	1.055828	1.047407	0.8976863

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+100x1000 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on double+100x1000 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.863827	2.015923	2.076716	2.021421	2.054693	3.223811
1	colMads_X_S	1.875287	2.024370	2.060110	2.032348	2.040499	3.241494

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.00000	1.0000000	1.000000	1.0000000	1.000000
1	colMads_X_S	1.006149	1.00419	0.9920035	1.005406	0.9930919	1.005485

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on double+100x1000 data (original and transposed). Outliers are displayed as crosses. Times are in milliseconds.

1000x100 double matrix

> X <- data[["1000x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5224207 279.1    8529671 455.6  8529671 455.6
Vcells 9825214  75.0   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5224183 279.1    8529671 455.6  8529671 455.6
Vcells 9925267  75.8   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+1000x100 data. The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.706926	1.850517	1.887975	1.854982	1.903505	2.812716
2	colMads(X, rows, cols)	1.714144	1.852256	1.896291	1.859166	1.911118	2.640585
3	colMads(X[rows, cols])	1.801265	1.944529	1.966103	1.956179	2.001884	2.847237

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.004229	1.000940	1.004405	1.002255	1.003999	0.9388026
3	colMads(X[rows, cols])	1.055268	1.050803	1.041382	1.054554	1.051683	1.0122732

Table: Benchmarking of rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on double+1000x100 data (transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.701636	1.838294	1.866937	1.846607	1.897780	2.446870
2	rowMads(X, cols, rows)	1.723853	1.863206	1.907139	1.871997	1.912233	2.926454
3	rowMads(X[cols, rows])	1.802261	1.950943	1.978890	1.961919	2.003583	2.957204

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.013056	1.013552	1.021534	1.013750	1.007616	1.195999
3	rowMads(X[cols, rows])	1.059134	1.061280	1.059966	1.062445	1.055751	1.208566

Figure: Benchmarking of colMads_X_S(), colMads(X, rows, cols)() and colMads(X[rows, cols])() on double+1000x100 data as well as rowMads_X_S(), rowMads(X, cols, rows)() and rowMads(X[cols, rows])() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colMads_X_S() and rowMads_X_S() on double+1000x100 data (original and transposed). The top panel shows times in milliseconds and the bottom panel shows relative times.

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.701636	1.838294	1.866937	1.846607	1.897780	2.446870
1	colMads_X_S	1.706926	1.850517	1.887975	1.854982	1.903505	2.812716

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	1.003109	1.006649	1.011269	1.004536	1.003017	1.149516

Figure: Benchmarking of colMads_X_S() and rowMads_X_S() on double+1000x100 data (original and transposed). 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 26.63 secs.

Reproducibility

To reproduce this report, do:

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

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Copyright Dongcan Jiang. Last updated on 2021-08-25 18:56:41 (+0200 UTC). Powered by RSP.