matrixStats.benchmarks

colMedians() and rowMedians() benchmarks on subsetted computation

This report benchmark the performance of colMedians() and rowMedians() 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  5247785 280.3    8529671 455.6  8529671 455.6
Vcells 10124522  77.3   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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  5239184 279.9    8529671 455.6  8529671 455.6
Vcells 10096500  77.1   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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	colMedians_X_S	0.002163	0.002199	0.0024745	0.0022340	0.0023215	0.019472
2	colMedians(X, rows, cols)	0.002535	0.002617	0.0027482	0.0026785	0.0027815	0.005729
3	colMedians(X[rows, cols])	0.002998	0.003217	0.0034158	0.0033335	0.0034665	0.008748

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colMedians(X, rows, cols)	1.171983	1.190086	1.110587	1.198970	1.198148	0.2942173
3	colMedians(X[rows, cols])	1.386038	1.462938	1.380363	1.492166	1.493216	0.4492605

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians_X_S	0.002181	0.0022175	0.0023243	0.0022505	0.0023545	0.005164
2	rowMedians(X, cols, rows)	0.002533	0.0026210	0.0029240	0.0026630	0.0028205	0.021817
3	rowMedians(X[cols, rows])	0.003055	0.0032280	0.0034302	0.0033365	0.0034945	0.006212

	expr	min	lq	mean	median	uq	max
1	rowMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMedians(X, cols, rows)	1.161394	1.181962	1.257998	1.183293	1.197919	4.224826
3	rowMedians(X[cols, rows])	1.400734	1.455693	1.475774	1.482559	1.484179	1.202943

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	colMedians_X_S	2.163	2.1990	2.47453	2.2340	2.3215	19.472
2	rowMedians_X_S	2.181	2.2175	2.32432	2.2505	2.3545	5.164

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
2	rowMedians_X_S	1.008322	1.008413	0.9392976	1.007386	1.014215	0.2652013

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5237789 279.8    8529671 455.6  8529671 455.6
Vcells 9764735  74.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5237765 279.8    8529671 455.6  8529671 455.6
Vcells 9769788  74.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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	colMedians(X, rows, cols)	0.069116	0.072851	0.0793460	0.077139	0.0862925	0.104431
1	colMedians_X_S	0.069252	0.071934	0.0797361	0.078661	0.0867320	0.098567
3	colMedians(X[rows, cols])	0.078479	0.082545	0.0916573	0.090465	0.0992660	0.147848

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.0000000
1	colMedians_X_S	1.001968	0.9874127	1.004917	1.019731	1.005093	0.9438481
3	colMedians(X[rows, cols])	1.135468	1.1330661	1.155161	1.172753	1.150343	1.4157482

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians(X, cols, rows)	0.069257	0.0738550	0.0805676	0.0787260	0.0866245	0.127741
1	rowMedians_X_S	0.070610	0.0735400	0.0812061	0.0796825	0.0882810	0.111361
3	rowMedians(X[cols, rows])	0.080528	0.0840335	0.0924440	0.0897890	0.0999170	0.123347

	expr	min	lq	mean	median	uq	max
2	rowMedians(X, cols, rows)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.0000000
1	rowMedians_X_S	1.019536	0.9957349	1.007925	1.012150	1.019123	0.8717718
3	rowMedians(X[cols, rows])	1.162742	1.1378173	1.147409	1.140525	1.153450	0.9656023

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	colMedians_X_S	69.252	71.934	79.73608	78.6610	86.732	98.567
2	rowMedians_X_S	70.610	73.540	81.20607	79.6825	88.281	111.361

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.00000	1.000000	1.000000	1.000000	1.00000	1.0000
2	rowMedians_X_S	1.01961	1.022326	1.018436	1.012986	1.01786	1.1298

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5238531 279.8    8529671 455.6  8529671 455.6
Vcells 9768787  74.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5238507 279.8    8529671 455.6  8529671 455.6
Vcells 9773840  74.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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
1	colMedians_X_S	0.054543	0.0594295	0.0631123	0.0629970	0.0673695	0.079262
2	colMedians(X, rows, cols)	0.056625	0.0595910	0.0645022	0.0632955	0.0679385	0.086290
3	colMedians(X[rows, cols])	0.063995	0.0669875	0.0736701	0.0727865	0.0788835	0.124442

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colMedians(X, rows, cols)	1.038172	1.002717	1.022022	1.004738	1.008446	1.088668
3	colMedians(X[rows, cols])	1.173294	1.127176	1.167285	1.155396	1.170908	1.570008

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians_X_S	0.056406	0.0594995	0.0645912	0.0625805	0.0684625	0.086030
2	rowMedians(X, cols, rows)	0.057026	0.0604740	0.0656146	0.0656415	0.0696365	0.080560
3	rowMedians(X[cols, rows])	0.067574	0.0716700	0.0781866	0.0768110	0.0825960	0.133214

	expr	min	lq	mean	median	uq	max
1	rowMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowMedians(X, cols, rows)	1.010992	1.016378	1.015844	1.048913	1.017148	0.9364175
3	rowMedians(X[cols, rows])	1.197993	1.204548	1.210484	1.227395	1.206441	1.5484598

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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
2	rowMedians_X_S	56.406	59.4995	64.59124	62.5805	68.4625	86.030
1	colMedians_X_S	54.543	59.4295	63.11233	62.9970	67.3695	79.262

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.0000000	1.0000000	1.0000000	1.000000	1.0000000	1.0000000
1	colMedians_X_S	0.9669716	0.9988235	0.9771036	1.006655	0.9840351	0.9213298

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5238735 279.8    8529671 455.6  8529671 455.6
Vcells 9769665  74.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5238711 279.8    8529671 455.6  8529671 455.6
Vcells 9774718  74.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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
1	colMedians_X_S	0.057607	0.0638645	0.0694792	0.0687495	0.0734705	0.113717
2	colMedians(X, rows, cols)	0.059817	0.0649060	0.0703234	0.0692460	0.0760760	0.101284
3	colMedians(X[rows, cols])	0.068616	0.0777975	0.0825283	0.0823880	0.0875695	0.106415

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colMedians(X, rows, cols)	1.038363	1.016308	1.012152	1.007222	1.035463	0.8906672
3	colMedians(X[rows, cols])	1.191105	1.218165	1.187814	1.198380	1.191900	0.9357880

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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
1	rowMedians_X_S	0.057861	0.064206	0.0689257	0.0687080	0.072853	0.094408
2	rowMedians(X, cols, rows)	0.055081	0.065515	0.0705320	0.0691355	0.075734	0.118382
3	rowMedians(X[cols, rows])	0.065683	0.074714	0.0802904	0.0796345	0.085440	0.104847

	expr	min	lq	mean	median	uq	max
1	rowMedians_X_S	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMedians(X, cols, rows)	0.9519538	1.020388	1.023305	1.006222	1.039545	1.253940
3	rowMedians(X[cols, rows])	1.1351860	1.163661	1.164882	1.159028	1.172773	1.110573

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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
2	rowMedians_X_S	57.861	64.2060	68.92574	68.7080	72.8530	94.408
1	colMedians_X_S	57.607	63.8645	69.47915	68.7495	73.4705	113.717

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.0000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	colMedians_X_S	0.9956102	0.9946812	1.008029	1.000604	1.008476	1.204527

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5238948 279.8    8529671 455.6  8529671 455.6
Vcells 9792341  74.8   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5238924 279.8    8529671 455.6  8529671 455.6
Vcells 9842394  75.1   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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
2	colMedians(X, rows, cols)	0.635346	0.6738715	0.7030194	0.6914905	0.695738	1.094365
1	colMedians_X_S	0.644687	0.6738565	0.7190352	0.7011530	0.713199	1.084984
3	colMedians(X[rows, cols])	0.709922	0.7313225	0.7970094	0.7729150	0.795093	1.167164

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.0000000
1	colMedians_X_S	1.014702	0.9999777	1.022782	1.013973	1.025097	0.9914279
3	colMedians(X[rows, cols])	1.117379	1.0852551	1.133695	1.117752	1.142805	1.0665217

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians(X, cols, rows)	0.653285	0.6896480	0.7130112	0.7085320	0.7116845	1.109525
1	rowMedians_X_S	0.654745	0.6735305	0.7320690	0.7105690	0.7270165	1.116330
3	rowMedians(X[cols, rows])	0.718816	0.7586375	0.7996243	0.7812705	0.7928640	1.177174

	expr	min	lq	mean	median	uq	max
2	rowMedians(X, cols, rows)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	rowMedians_X_S	1.002235	0.9766294	1.026729	1.002875	1.021543	1.006133
3	rowMedians(X[cols, rows])	1.100310	1.1000358	1.121475	1.102661	1.114067	1.060971

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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
1	colMedians_X_S	644.687	673.8565	719.0353	701.153	713.1990	1084.984
2	rowMedians_X_S	654.745	673.5305	732.0690	710.569	727.0165	1116.330

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.000000	1.0000000	1.000000	1.000000	1.000000	1.000000
2	rowMedians_X_S	1.015601	0.9995162	1.018127	1.013429	1.019374	1.028891

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5239158 279.9    8529671 455.6  8529671 455.6
Vcells 9793150  74.8   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5239134 279.8    8529671 455.6  8529671 455.6
Vcells 9843203  75.1   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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	colMedians(X, rows, cols)	0.542375	0.5586685	0.6134581	0.5899005	0.6108425	0.897709
1	colMedians_X_S	0.548545	0.5801265	0.6199907	0.5974650	0.6132550	0.919849
3	colMedians(X[rows, cols])	0.613835	0.6391615	0.6827193	0.6663900	0.6871140	1.060343

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMedians_X_S	1.011376	1.038409	1.010649	1.012823	1.003950	1.024663
3	colMedians(X[rows, cols])	1.131754	1.144080	1.112903	1.129665	1.124863	1.181166

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians(X, cols, rows)	0.562586	0.5799270	0.6204745	0.6098665	0.6151765	0.987498
1	rowMedians_X_S	0.563336	0.5812390	0.6226931	0.6109915	0.6181360	0.911761
3	rowMedians(X[cols, rows])	0.630449	0.6649245	0.7000485	0.6858585	0.6996220	1.046044

	expr	min	lq	mean	median	uq	max
2	rowMedians(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowMedians_X_S	1.001333	1.002262	1.003576	1.001845	1.004811	0.9233041
3	rowMedians(X[cols, rows])	1.120627	1.146566	1.128247	1.124604	1.137270	1.0592872

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	colMedians_X_S	548.545	580.1265	619.9907	597.4650	613.255	919.849
2	rowMedians_X_S	563.336	581.2390	622.6931	610.9915	618.136	911.761

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.000000	1.000000	1.000000	1.00000	1.000000	1.0000000
2	rowMedians_X_S	1.026964	1.001918	1.004359	1.02264	1.007959	0.9912073

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5239376 279.9    8529671 455.6  8529671 455.6
Vcells 9884275  75.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5239343 279.9    8529671 455.6  8529671 455.6
Vcells 9884413  75.5   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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	colMedians_X_S	0.002490	0.0025895	0.0028466	0.0026545	0.002736	0.018644
2	colMedians(X, rows, cols)	0.002917	0.0030090	0.0031242	0.0030645	0.003159	0.005872
3	colMedians(X[rows, cols])	0.003429	0.0036395	0.0038189	0.0037195	0.003856	0.008036

	expr	min	lq	mean	median	uq	max
1	colMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colMedians(X, rows, cols)	1.171486	1.162000	1.097493	1.154455	1.154605	0.3149539
3	colMedians(X[rows, cols])	1.377108	1.405484	1.341542	1.401206	1.409357	0.4310234

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians_X_S	0.002556	0.0025905	0.0027087	0.0026310	0.0027155	0.005601
2	rowMedians(X, cols, rows)	0.002897	0.0030335	0.0033404	0.0031045	0.0032295	0.021598
3	rowMedians(X[cols, rows])	0.003444	0.0036960	0.0038254	0.0037505	0.0038540	0.006482

	expr	min	lq	mean	median	uq	max
1	rowMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMedians(X, cols, rows)	1.133412	1.171010	1.233222	1.179970	1.189284	3.856097
3	rowMedians(X[cols, rows])	1.347418	1.426752	1.412292	1.425504	1.419260	1.157293

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	rowMedians_X_S	2.556	2.5905	2.70866	2.6310	2.7155	5.601
1	colMedians_X_S	2.490	2.5895	2.84665	2.6545	2.7360	18.644

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMedians_X_S	0.9741784	0.999614	1.050944	1.008932	1.007549	3.328691

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5239574 279.9    8529671 455.6  8529671 455.6
Vcells 9890242  75.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5239550 279.9    8529671 455.6  8529671 455.6
Vcells 9900295  75.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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
2	colMedians(X, rows, cols)	0.101925	0.1117655	0.1212787	0.1171620	0.1295415	0.151337
1	colMedians_X_S	0.103978	0.1112645	0.1234687	0.1188605	0.1317415	0.161438
3	colMedians(X[rows, cols])	0.115783	0.1256555	0.1383609	0.1321245	0.1517625	0.198398

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	colMedians_X_S	1.020142	0.9955174	1.018057	1.014497	1.016983	1.066745
3	colMedians(X[rows, cols])	1.135963	1.1242781	1.140851	1.127708	1.171536	1.310968

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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
2	rowMedians(X, cols, rows)	0.100047	0.1098685	0.1210682	0.1172750	0.1301320	0.174698
1	rowMedians_X_S	0.100199	0.1109900	0.1219336	0.1179545	0.1356425	0.157060
3	rowMedians(X[cols, rows])	0.112576	0.1235160	0.1345665	0.1313620	0.1411585	0.173878

	expr	min	lq	mean	median	uq	max
2	rowMedians(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowMedians_X_S	1.001519	1.010208	1.007148	1.005794	1.042345	0.8990372
3	rowMedians(X[cols, rows])	1.125231	1.124217	1.111493	1.120119	1.084733	0.9953062

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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
2	rowMedians_X_S	100.199	110.9900	121.9335	117.9545	135.6425	157.060
1	colMedians_X_S	103.978	111.2645	123.4687	118.8605	131.7415	161.438

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.000000	1.000000	1.00000	1.000000	1.0000000	1.000000
1	colMedians_X_S	1.037715	1.002473	1.01259	1.007681	0.9712406	1.027875

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5239773 279.9    8529671 455.6  8529671 455.6
Vcells 9891676  75.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5239749 279.9    8529671 455.6  8529671 455.6
Vcells 9901729  75.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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	colMedians(X, rows, cols)	0.104012	0.1111355	0.1220537	0.1161530	0.1321765	0.155425
1	colMedians_X_S	0.103607	0.1135510	0.1246139	0.1190045	0.1382310	0.170538
3	colMedians(X[rows, cols])	0.115903	0.1236835	0.1368437	0.1283180	0.1482930	0.196038

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMedians_X_S	0.9961062	1.021735	1.020976	1.024550	1.045806	1.097237
3	colMedians(X[rows, cols])	1.1143233	1.112907	1.121176	1.104733	1.121932	1.261303

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians_X_S	0.100210	0.1097955	0.1186854	0.1135725	0.1251785	0.184877
2	rowMedians(X, cols, rows)	0.101310	0.1083490	0.1209355	0.1163735	0.1318075	0.156862
3	rowMedians(X[cols, rows])	0.114796	0.1225060	0.1361408	0.1302300	0.1452115	0.213212

	expr	min	lq	mean	median	uq	max
1	rowMedians_X_S	1.000000	1.0000000	1.000000	1.000000	1.000000	1.0000000
2	rowMedians(X, cols, rows)	1.010977	0.9868255	1.018959	1.024663	1.052956	0.8484668
3	rowMedians(X[cols, rows])	1.145554	1.1157652	1.147073	1.146668	1.160035	1.1532641

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	rowMedians_X_S	100.210	109.7955	118.6854	113.5725	125.1785	184.877
1	colMedians_X_S	103.607	113.5510	124.6139	119.0045	138.2310	170.538

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colMedians_X_S	1.033899	1.034204	1.049952	1.047829	1.104271	0.9224403

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5239977 279.9    8529671 455.6  8529671 455.6
Vcells 9891811  75.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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 5239953 279.9    8529671 455.6  8529671 455.6
Vcells 9901864  75.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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	colMedians(X, rows, cols)	0.088462	0.09563	0.1030767	0.0992875	0.1069560	0.147320
1	colMedians_X_S	0.090052	0.09560	0.1060133	0.1038405	0.1167395	0.147353
3	colMedians(X[rows, cols])	0.105745	0.11218	0.1228702	0.1206255	0.1320260	0.153536

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	colMedians_X_S	1.017974	0.9996863	1.028489	1.045857	1.091472	1.000224
3	colMedians(X[rows, cols])	1.195372	1.1730628	1.192027	1.214911	1.234395	1.042194

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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
2	rowMedians(X, cols, rows)	0.088831	0.0944575	0.1032622	0.0994000	0.1096750	0.155342
1	rowMedians_X_S	0.089726	0.0944270	0.1036007	0.0997180	0.1111390	0.129735
3	rowMedians(X[cols, rows])	0.102564	0.1072990	0.1181547	0.1148835	0.1272235	0.144642

	expr	min	lq	mean	median	uq	max
2	rowMedians(X, cols, rows)	1.000000	1.0000000	1.000000	1.000000	1.000000	1.0000000
1	rowMedians_X_S	1.010075	0.9996771	1.003278	1.003199	1.013348	0.8351573
3	rowMedians(X[cols, rows])	1.154597	1.1359500	1.144220	1.155770	1.160005	0.9311197

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	rowMedians_X_S	89.726	94.427	103.6007	99.7180	111.1390	129.735
1	colMedians_X_S	90.052	95.600	106.0133	103.8405	116.7395	147.353

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000
1	colMedians_X_S	1.003633	1.012422	1.023287	1.041342	1.050392	1.1358

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5240190 279.9    8529671 455.6  8529671 455.6
Vcells 9937299  75.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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  5240166 279.9    8529671 455.6  8529671 455.6
Vcells 10037352  76.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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
2	colMedians(X, rows, cols)	0.921789	0.979211	1.010901	1.002326	1.012625	1.589265
1	colMedians_X_S	0.938714	0.997927	1.037205	1.022477	1.028766	1.570415
3	colMedians(X[rows, cols])	1.036626	1.099875	1.152640	1.126634	1.149837	1.637606

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colMedians_X_S	1.018361	1.019113	1.026020	1.020104	1.015940	0.9881392
3	colMedians(X[rows, cols])	1.124581	1.123225	1.140211	1.124019	1.135502	1.0304172

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians_X_S	0.940216	0.994695	1.049102	1.020496	1.036348	1.649330
2	rowMedians(X, cols, rows)	0.946835	1.002986	1.032128	1.028485	1.034212	1.581807
3	rowMedians(X[cols, rows])	1.042311	1.109849	1.161684	1.131268	1.153399	1.743448

	expr	min	lq	mean	median	uq	max
1	rowMedians_X_S	1.000000	1.000000	1.0000000	1.000000	1.0000000	1.0000000
2	rowMedians(X, cols, rows)	1.007040	1.008335	0.9838207	1.007828	0.9979389	0.9590603
3	rowMedians(X[cols, rows])	1.108587	1.115768	1.1073129	1.108546	1.1129456	1.0570644

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	rowMedians_X_S	940.216	994.695	1049.102	1020.496	1036.349	1649.330
1	colMedians_X_S	938.714	997.927	1037.205	1022.477	1028.766	1570.415

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.0000000	1.000000	1.00000	1.000000	1.0000000	1.0000000
1	colMedians_X_S	0.9984025	1.003249	0.98866	1.001941	0.9926834	0.9521533

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 5240400 279.9    8529671 455.6  8529671 455.6
Vcells 9937440  75.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colMedians_X_S = colMedians(X_S, na.rm = FALSE), `colMedians(X, rows, cols)` = colMedians(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMedians(X[rows, cols])` = colMedians(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  5240376 279.9    8529671 455.6  8529671 455.6
Vcells 10037493  76.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowMedians_X_S = rowMedians(X_S, na.rm = FALSE), `rowMedians(X, cols, rows)` = rowMedians(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMedians(X[cols, rows])` = rowMedians(X[cols, rows], 
+     na.rm = FALSE), unit = "ms")

Table: Benchmarking of colMedians_X_S(), colMedians(X, rows, cols)() and colMedians(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
2	colMedians(X, rows, cols)	0.845679	0.8987655	0.9485350	0.920911	0.946645	1.420834
1	colMedians_X_S	0.865912	0.9361000	0.9665304	0.940565	0.965938	1.436688
3	colMedians(X[rows, cols])	0.957878	1.0109785	1.0527629	1.040747	1.069799	1.683818

	expr	min	lq	mean	median	uq	max
2	colMedians(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMedians_X_S	1.023925	1.041540	1.018972	1.021342	1.020380	1.011158
3	colMedians(X[rows, cols])	1.132673	1.124852	1.109883	1.130128	1.130095	1.185091

Table: Benchmarking of rowMedians_X_S(), rowMedians(X, cols, rows)() and rowMedians(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	rowMedians_X_S	0.862445	0.9155875	0.9573673	0.9401565	0.9662345	1.345372
2	rowMedians(X, cols, rows)	0.874553	0.9244920	0.9689037	0.9509190	0.9777455	1.561815
3	rowMedians(X[cols, rows])	0.959739	1.0286375	1.0703545	1.0536875	1.0793480	1.603569

	expr	min	lq	mean	median	uq	max
1	rowMedians_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMedians(X, cols, rows)	1.014039	1.009725	1.012050	1.011448	1.011913	1.160880
3	rowMedians(X[cols, rows])	1.112812	1.123473	1.118019	1.120758	1.117066	1.191915

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

Table: Benchmarking of colMedians_X_S() and rowMedians_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	rowMedians_X_S	862.445	915.5875	957.3673	940.1565	966.2345	1345.372
1	colMedians_X_S	865.912	936.1000	966.5304	940.5650	965.9380	1436.688

	expr	min	lq	mean	median	uq	max
2	rowMedians_X_S	1.00000	1.000000	1.000000	1.000000	1.0000000	1.000000
1	colMedians_X_S	1.00402	1.022404	1.009571	1.000434	0.9996931	1.067874

Figure: Benchmarking of colMedians_X_S() and rowMedians_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 25.15 secs.

Reproducibility

To reproduce this report, do:

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