matrixStats.benchmarks

---

colVars() and rowVars() benchmarks on subsetted computation

This report benchmark the performance of colVars() and rowVars() 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  5313475 283.8    8529671 455.6  8529671 455.6
Vcells 10408382  79.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5304511 283.3    8529671 455.6  8529671 455.6
Vcells 10378278  79.2   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars_X_S	0.002451	0.0025125	0.0070175	0.0025795	0.0026850	0.436973
2	colVars(X, rows, cols)	0.002814	0.0029330	0.0030652	0.0030040	0.0031325	0.005606
3	colVars(X[rows, cols])	0.003282	0.0034870	0.0036752	0.0035845	0.0036990	0.007568

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
2	colVars(X, rows, cols)	1.148103	1.167363	0.4367996	1.164567	1.166667	0.0128292
3	colVars(X[rows, cols])	1.339045	1.387861	0.5237121	1.389610	1.377654	0.0173191

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars_X_S	0.002484	0.0025335	0.0026493	0.0025930	0.0026770	0.005196
2	rowVars(X, cols, rows)	0.002873	0.0029225	0.0073218	0.0029825	0.0031230	0.430308
3	rowVars(X[cols, rows])	0.003265	0.0035030	0.0037006	0.0036340	0.0037575	0.005864

	expr	min	lq	mean	median	uq	max
1	rowVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowVars(X, cols, rows)	1.156602	1.153542	2.763635	1.150212	1.166604	82.81524
3	rowVars(X[cols, rows])	1.314412	1.382672	1.396793	1.401466	1.403623	1.12856

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

Table: Benchmarking of colVars_X_S() and rowVars_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	colVars_X_S	2.451	2.5125	7.01752	2.5795	2.685	436.973
2	rowVars_X_S	2.484	2.5335	2.64934	2.5930	2.677	5.196

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.0000000	1.000000	1.0000000	1.0000000
2	rowVars_X_S	1.013464	1.008358	0.3775322	1.005234	0.9970205	0.0118909

Figure: Benchmarking of colVars_X_S() and rowVars_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  5303939 283.3    8529671 455.6  8529671 455.6
Vcells 10214460  78.0   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5303915 283.3    8529671 455.6  8529671 455.6
Vcells 10219513  78.0   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars(X, rows, cols)	0.027985	0.0286135	0.0303356	0.0302370	0.0309675	0.048198
1	colVars_X_S	0.028323	0.0287680	0.0306895	0.0308400	0.0313955	0.046575
3	colVars(X[rows, cols])	0.038464	0.0391175	0.0422214	0.0417525	0.0436855	0.077703

	expr	min	lq	mean	median	uq	max
2	colVars(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colVars_X_S	1.012078	1.005400	1.011667	1.019942	1.013821	0.9663264
3	colVars(X[rows, cols])	1.374451	1.367099	1.391811	1.380841	1.410689	1.6121623

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars(X, cols, rows)	0.026026	0.027455	0.0286493	0.0283570	0.0287885	0.063004
1	rowVars_X_S	0.028856	0.030070	0.0312815	0.0313595	0.0320725	0.046009
3	rowVars(X[cols, rows])	0.038393	0.040125	0.0418369	0.0418370	0.0431630	0.056781

	expr	min	lq	mean	median	uq	max
2	rowVars(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowVars_X_S	1.108737	1.095247	1.091877	1.105882	1.114073	0.7302552
3	rowVars(X[cols, rows])	1.475179	1.461482	1.460311	1.475368	1.499314	0.9012285

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

Table: Benchmarking of colVars_X_S() and rowVars_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	colVars_X_S	28.323	28.768	30.68953	30.8400	31.3955	46.575
2	rowVars_X_S	28.856	30.070	31.28148	31.3595	32.0725	46.009

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowVars_X_S	1.018819	1.045259	1.019288	1.016845	1.021564	0.9878476

Figure: Benchmarking of colVars_X_S() and rowVars_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  5304664 283.3    8529671 455.6  8529671 455.6
Vcells 10218477  78.0   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5304658 283.3    8529671 455.6  8529671 455.6
Vcells 10223560  78.0   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars_X_S	0.028019	0.0292240	0.0302776	0.030340	0.0315175	0.034922
2	colVars(X, rows, cols)	0.029855	0.0307185	0.0320918	0.032063	0.0329080	0.044749
3	colVars(X[rows, cols])	0.038693	0.0391380	0.0419313	0.041079	0.0436910	0.072446

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colVars(X, rows, cols)	1.065527	1.051139	1.059917	1.056790	1.044118	1.281399
3	colVars(X[rows, cols])	1.380956	1.339242	1.384895	1.353955	1.386246	2.074509

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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
2	rowVars(X, cols, rows)	0.029057	0.0303490	0.0321784	0.0320585	0.0330030	0.047128
1	rowVars_X_S	0.030924	0.0319015	0.0335245	0.0330375	0.0344330	0.046180
3	rowVars(X[cols, rows])	0.042868	0.0446260	0.0471752	0.0461325	0.0482645	0.082476

	expr	min	lq	mean	median	uq	max
2	rowVars(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowVars_X_S	1.064253	1.051155	1.041832	1.030538	1.043329	0.9798846
3	rowVars(X[cols, rows])	1.475307	1.470427	1.466050	1.439010	1.462428	1.7500424

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

Table: Benchmarking of colVars_X_S() and rowVars_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	colVars_X_S	28.019	29.2240	30.27761	30.3400	31.5175	34.922
2	rowVars_X_S	30.924	31.9015	33.52450	33.0375	34.4330	46.180

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.00000	1.00000	1.000000	1.000000	1.000000	1.000000
2	rowVars_X_S	1.10368	1.09162	1.107237	1.088909	1.092504	1.322376

Figure: Benchmarking of colVars_X_S() and rowVars_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  5304887 283.4    8529671 455.6  8529671 455.6
Vcells 10219326  78.0   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5304863 283.4    8529671 455.6  8529671 455.6
Vcells 10224379  78.1   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars_X_S	0.024115	0.0252590	0.0264496	0.0262930	0.0272620	0.046359
2	colVars(X, rows, cols)	0.026724	0.0277995	0.0290717	0.0287825	0.0293585	0.043846
3	colVars(X[rows, cols])	0.036762	0.0384355	0.0400454	0.0395665	0.0412865	0.056059

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colVars(X, rows, cols)	1.108190	1.100578	1.099136	1.094683	1.076902	0.9457926
3	colVars(X[rows, cols])	1.524445	1.521656	1.514024	1.504830	1.514434	1.2092366

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars(X, cols, rows)	0.025886	0.0266785	0.0284970	0.0276275	0.028616	0.052249
1	rowVars_X_S	0.026625	0.0274760	0.0289053	0.0289415	0.030196	0.039186
3	rowVars(X[cols, rows])	0.037645	0.0381920	0.0407808	0.0407245	0.042712	0.056766

	expr	min	lq	mean	median	uq	max
2	rowVars(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowVars_X_S	1.028548	1.029893	1.014329	1.047561	1.055214	0.7499856
3	rowVars(X[cols, rows])	1.454261	1.431565	1.431055	1.474057	1.492592	1.0864514

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

Table: Benchmarking of colVars_X_S() and rowVars_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	colVars_X_S	24.115	25.259	26.44962	26.2930	27.262	46.359
2	rowVars_X_S	26.625	27.476	28.90532	28.9415	30.196	39.186

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.00000	1.000000	1.0000000
2	rowVars_X_S	1.104085	1.087771	1.092844	1.10073	1.107622	0.8452728

Figure: Benchmarking of colVars_X_S() and rowVars_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  5305097 283.4    8529671 455.6  8529671 455.6
Vcells 10241990  78.2   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5305073 283.4    8529671 455.6  8529671 455.6
Vcells 10292043  78.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars(X, rows, cols)	0.170699	0.1713820	0.1943607	0.1804095	0.2148900	0.320984
1	colVars_X_S	0.180924	0.1814310	0.2063428	0.1918895	0.2278745	0.319186
3	colVars(X[rows, cols])	0.246783	0.2497795	0.2871655	0.2778190	0.3137455	0.382359

	expr	min	lq	mean	median	uq	max
2	colVars(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colVars_X_S	1.059901	1.058635	1.061649	1.063633	1.060424	0.9943985
3	colVars(X[rows, cols])	1.445720	1.457443	1.477488	1.539935	1.460028	1.1912089

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars(X, cols, rows)	0.176198	0.1771145	0.1991892	0.1815065	0.2190860	0.340945
1	rowVars_X_S	0.199158	0.1996755	0.2363779	0.2266205	0.2590505	0.364469
3	rowVars(X[cols, rows])	0.262288	0.2645515	0.3063157	0.2876855	0.3367670	0.448063

	expr	min	lq	mean	median	uq	max
2	rowVars(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	rowVars_X_S	1.130308	1.127381	1.186701	1.248553	1.182415	1.068996
3	rowVars(X[cols, rows])	1.488598	1.493675	1.537813	1.584987	1.537145	1.314180

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

Table: Benchmarking of colVars_X_S() and rowVars_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	colVars_X_S	180.924	181.4310	206.3428	191.8895	227.8745	319.186
2	rowVars_X_S	199.158	199.6755	236.3779	226.6205	259.0505	364.469

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowVars_X_S	1.100783	1.100559	1.145559	1.180995	1.136812	1.14187

Figure: Benchmarking of colVars_X_S() and rowVars_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  5305310 283.4    8529671 455.6  8529671 455.6
Vcells 10242762  78.2   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5305286 283.4    8529671 455.6  8529671 455.6
Vcells 10292815  78.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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
1	colVars_X_S	0.178698	0.1792615	0.2049866	0.188912	0.2250750	0.313021
2	colVars(X, rows, cols)	0.170253	0.1712710	0.2008434	0.195449	0.2151080	0.288070
3	colVars(X[rows, cols])	0.242082	0.2438890	0.2862163	0.272755	0.3163155	0.461182

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.0000000	1.0000000	1.0000000	1.000000	1.000000	1.0000000
2	colVars(X, rows, cols)	0.9527415	0.9554255	0.9797881	1.034603	0.955717	0.9202897
3	colVars(X[rows, cols])	1.3546990	1.3605208	1.3962681	1.443820	1.405378	1.4733261

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars(X, cols, rows)	0.180915	0.182972	0.2118343	0.1986295	0.230347	0.368540
1	rowVars_X_S	0.203932	0.204951	0.2357006	0.2190045	0.263383	0.342913
3	rowVars(X[cols, rows])	0.270652	0.272308	0.3132944	0.2891600	0.353193	0.459817

	expr	min	lq	mean	median	uq	max
2	rowVars(X, cols, rows)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	rowVars_X_S	1.127225	1.120122	1.112665	1.102578	1.143418	0.9304635
3	rowVars(X[cols, rows])	1.496018	1.488250	1.478960	1.455776	1.533308	1.2476719

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

Table: Benchmarking of colVars_X_S() and rowVars_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	colVars_X_S	178.698	179.2615	204.9866	188.9120	225.075	313.021
2	rowVars_X_S	203.932	204.9510	235.7006	219.0045	263.383	342.913

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.00000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowVars_X_S	1.14121	1.143307	1.149834	1.159294	1.170201	1.095495

Figure: Benchmarking of colVars_X_S() and rowVars_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  5305527 283.4    8529671 455.6  8529671 455.6
Vcells 10333858  78.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5305494 283.4    8529671 455.6  8529671 455.6
Vcells 10333996  78.9   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars_X_S	0.002423	0.0025035	0.0027823	0.0025600	0.0026405	0.019923
2	colVars(X, rows, cols)	0.002790	0.0029340	0.0030901	0.0030425	0.0031570	0.005115
3	colVars(X[rows, cols])	0.003314	0.0035325	0.0037636	0.0036705	0.0038240	0.008721

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colVars(X, rows, cols)	1.151465	1.171959	1.110621	1.188477	1.195607	0.2567384
3	colVars(X[rows, cols])	1.367726	1.411025	1.352713	1.433789	1.448211	0.4377353

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars_X_S	0.002438	0.002495	0.0026244	0.0025585	0.0026630	0.005217
2	rowVars(X, cols, rows)	0.002836	0.002919	0.0032354	0.0030095	0.0031415	0.020951
3	rowVars(X[cols, rows])	0.003357	0.003563	0.0037771	0.0036510	0.0037745	0.009268

	expr	min	lq	mean	median	uq	max
1	rowVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowVars(X, cols, rows)	1.163249	1.169940	1.232799	1.176275	1.179685	4.01591
3	rowVars(X[cols, rows])	1.376948	1.428056	1.439219	1.427008	1.417386	1.77650

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

Table: Benchmarking of colVars_X_S() and rowVars_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	rowVars_X_S	2.438	2.4950	2.62441	2.5585	2.6630	5.217
1	colVars_X_S	2.423	2.5035	2.78229	2.5600	2.6405	19.923

	expr	min	lq	mean	median	uq	max
2	rowVars_X_S	1.0000000	1.000000	1.000000	1.000000	1.0000000	1.000000
1	colVars_X_S	0.9938474	1.003407	1.060158	1.000586	0.9915509	3.818861

Figure: Benchmarking of colVars_X_S() and rowVars_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  5305724 283.4    8529671 455.6  8529671 455.6
Vcells 10339798  78.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5305700 283.4    8529671 455.6  8529671 455.6
Vcells 10349851  79.0   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars(X, rows, cols)	0.027517	0.0283115	0.0297297	0.0294775	0.0307375	0.034834
1	colVars_X_S	0.028107	0.0286775	0.0301949	0.0299240	0.0311230	0.034625
3	colVars(X[rows, cols])	0.042798	0.0433775	0.0465208	0.0459590	0.0477750	0.077095

	expr	min	lq	mean	median	uq	max
2	colVars(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colVars_X_S	1.021441	1.012928	1.015645	1.015147	1.012542	0.9940001
3	colVars(X[rows, cols])	1.555329	1.532151	1.564788	1.559121	1.554290	2.2132112

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars(X, cols, rows)	0.027510	0.0285280	0.0302492	0.0300195	0.0308850	0.055849
1	rowVars_X_S	0.027792	0.0283365	0.0301394	0.0303665	0.0311465	0.045532
3	rowVars(X[cols, rows])	0.042626	0.0430955	0.0456128	0.0455615	0.0467870	0.058819

	expr	min	lq	mean	median	uq	max
2	rowVars(X, cols, rows)	1.000000	1.0000000	1.0000000	1.000000	1.000000	1.0000000
1	rowVars_X_S	1.010251	0.9932873	0.9963688	1.011559	1.008467	0.8152697
3	rowVars(X[cols, rows])	1.549473	1.5106387	1.5078994	1.517730	1.514878	1.0531791

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

Table: Benchmarking of colVars_X_S() and rowVars_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	colVars_X_S	28.107	28.6775	30.19486	29.9240	31.1230	34.625
2	rowVars_X_S	27.792	28.3365	30.13938	30.3665	31.1465	45.532

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.0000000	1.0000000	1.0000000	1.000000	1.000000	1.000000
2	rowVars_X_S	0.9887928	0.9881091	0.9981626	1.014787	1.000755	1.315004

Figure: Benchmarking of colVars_X_S() and rowVars_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  5305924 283.4    8529671 455.6  8529671 455.6
Vcells 10341197  78.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5305900 283.4    8529671 455.6  8529671 455.6
Vcells 10351250  79.0   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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
1	colVars_X_S	0.028114	0.0292890	0.0303046	0.0303190	0.0307595	0.045685
2	colVars(X, rows, cols)	0.028809	0.0309165	0.0322758	0.0321100	0.0328970	0.044336
3	colVars(X[rows, cols])	0.042581	0.0438735	0.0467559	0.0455775	0.0473600	0.081429

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	colVars(X, rows, cols)	1.024721	1.055567	1.065045	1.059072	1.069491	0.9704717
3	colVars(X[rows, cols])	1.514584	1.497951	1.542865	1.503265	1.539687	1.7824012

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars_X_S	0.027404	0.029216	0.0303824	0.0296630	0.031700	0.044171
2	rowVars(X, cols, rows)	0.029509	0.031362	0.0328319	0.0328285	0.034127	0.043699
3	rowVars(X[cols, rows])	0.044517	0.047763	0.0497608	0.0483685	0.051843	0.086874

	expr	min	lq	mean	median	uq	max
1	rowVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowVars(X, cols, rows)	1.076814	1.073453	1.080622	1.106715	1.076561	0.9893143
3	rowVars(X[cols, rows])	1.624471	1.634823	1.637817	1.630600	1.635426	1.9667655

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

Table: Benchmarking of colVars_X_S() and rowVars_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	rowVars_X_S	27.404	29.216	30.38238	29.663	31.7000	44.171
1	colVars_X_S	28.114	29.289	30.30461	30.319	30.7595	45.685

	expr	min	lq	mean	median	uq	max
2	rowVars_X_S	1.000000	1.000000	1.0000000	1.000000	1.0000000	1.000000
1	colVars_X_S	1.025909	1.002499	0.9974403	1.022115	0.9703312	1.034276

Figure: Benchmarking of colVars_X_S() and rowVars_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  5306129 283.4    8529671 455.6  8529671 455.6
Vcells 10341333  78.9   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5306105 283.4    8529671 455.6  8529671 455.6
Vcells 10351386  79.0   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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
1	colVars_X_S	0.022560	0.0230830	0.0248897	0.0246065	0.0255495	0.046647
2	colVars(X, rows, cols)	0.024435	0.0254435	0.0271204	0.0267215	0.0278235	0.049176
3	colVars(X[rows, cols])	0.040151	0.0410115	0.0434201	0.0438420	0.0449765	0.051028

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colVars(X, rows, cols)	1.083112	1.102261	1.089624	1.085953	1.089004	1.054216
3	colVars(X[rows, cols])	1.779743	1.776697	1.744498	1.781724	1.760367	1.093918

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars_X_S	0.022952	0.0244625	0.0254638	0.0254965	0.0261215	0.038473
2	rowVars(X, cols, rows)	0.024120	0.0259270	0.0274347	0.0267445	0.0276475	0.053115
3	rowVars(X[cols, rows])	0.038254	0.0402460	0.0420541	0.0417415	0.0432995	0.057531

	expr	min	lq	mean	median	uq	max
1	rowVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowVars(X, cols, rows)	1.050889	1.059867	1.077401	1.048948	1.058419	1.380579
3	rowVars(X[cols, rows])	1.666696	1.645212	1.651524	1.637146	1.657619	1.495360

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

Table: Benchmarking of colVars_X_S() and rowVars_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
1	colVars_X_S	22.560	23.0830	24.88972	24.6065	25.5495	46.647
2	rowVars_X_S	22.952	24.4625	25.46378	25.4965	26.1215	38.473

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowVars_X_S	1.017376	1.059763	1.023064	1.036169	1.022388	0.824769

Figure: Benchmarking of colVars_X_S() and rowVars_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  5306339 283.4    8529671 455.6  8529671 455.6
Vcells 10386780  79.3   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5306315 283.4    8529671 455.6  8529671 455.6
Vcells 10486833  80.1   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars(X, rows, cols)	0.169359	0.1701765	0.1952870	0.1838380	0.2132940	0.351037
1	colVars_X_S	0.179704	0.1802660	0.2073025	0.1907365	0.2266135	0.318807
3	colVars(X[rows, cols])	0.274232	0.2768420	0.3249188	0.3157020	0.3540155	0.463902

	expr	min	lq	mean	median	uq	max
2	colVars(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colVars_X_S	1.061083	1.059288	1.061527	1.037525	1.062447	0.9081863
3	colVars(X[rows, cols])	1.619235	1.626793	1.663802	1.717284	1.659754	1.3215188

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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
2	rowVars(X, cols, rows)	0.185157	0.1873580	0.2378642	0.2130875	0.2735040	0.424047
1	rowVars_X_S	0.178136	0.1936855	0.2526022	0.2286480	0.2974055	0.457705
3	rowVars(X[cols, rows])	0.272941	0.2953370	0.3768145	0.3430070	0.4457450	0.687151

	expr	min	lq	mean	median	uq	max
2	rowVars(X, cols, rows)	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	rowVars_X_S	0.9620808	1.033772	1.061960	1.073024	1.087390	1.079373
3	rowVars(X[cols, rows])	1.4741058	1.576324	1.584158	1.609700	1.629757	1.620459

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

Table: Benchmarking of colVars_X_S() and rowVars_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
1	colVars_X_S	179.704	180.2660	207.3025	190.7365	226.6135	318.807
2	rowVars_X_S	178.136	193.6855	252.6022	228.6480	297.4055	457.705

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.0000000	1.000000	1.00000	1.000000	1.000000	1.00000
2	rowVars_X_S	0.9912745	1.074443	1.21852	1.198764	1.312391	1.43568

Figure: Benchmarking of colVars_X_S() and rowVars_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  5306552 283.5    8529671 455.6  8529671 455.6
Vcells 10386924  79.3   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colVars_X_S = colVars(X_S, na.rm = FALSE), `colVars(X, rows, cols)` = colVars(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colVars(X[rows, cols])` = colVars(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  5306528 283.4    8529671 455.6  8529671 455.6
Vcells 10486977  80.1   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowVars_X_S = rowVars(X_S, na.rm = FALSE), `rowVars(X, cols, rows)` = rowVars(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowVars(X[cols, rows])` = rowVars(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

Table: Benchmarking of colVars_X_S(), colVars(X, rows, cols)() and colVars(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	colVars_X_S	0.178952	0.1793685	0.2051606	0.1906165	0.2189645	0.341077
2	colVars(X, rows, cols)	0.171817	0.1729900	0.2030784	0.1971150	0.2166705	0.305432
3	colVars(X[rows, cols])	0.272187	0.2754670	0.3221239	0.3077675	0.3538490	0.544893

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.000000	1.0000000	1.0000000	1.000000	1.0000000	1.0000000
2	colVars(X, rows, cols)	0.960129	0.9644391	0.9898507	1.034092	0.9895234	0.8954928
3	colVars(X[rows, cols])	1.521006	1.5357602	1.5701058	1.614590	1.6160108	1.5975659

Table: Benchmarking of rowVars_X_S(), rowVars(X, cols, rows)() and rowVars(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	rowVars_X_S	0.179657	0.1806765	0.2120898	0.2022000	0.2313065	0.334975
2	rowVars(X, cols, rows)	0.192060	0.1937910	0.2292665	0.2210560	0.2504780	0.442760
3	rowVars(X[cols, rows])	0.276550	0.2855770	0.3323317	0.3093595	0.3642020	0.471504

	expr	min	lq	mean	median	uq	max
1	rowVars_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowVars(X, cols, rows)	1.069037	1.072585	1.080988	1.093254	1.082884	1.32177
3	rowVars(X[cols, rows])	1.539322	1.580599	1.566938	1.529968	1.574543	1.40758

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

Table: Benchmarking of colVars_X_S() and rowVars_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
1	colVars_X_S	178.952	179.3685	205.1606	190.6165	218.9645	341.077
2	rowVars_X_S	179.657	180.6765	212.0898	202.2000	231.3065	334.975

	expr	min	lq	mean	median	uq	max
1	colVars_X_S	1.00000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowVars_X_S	1.00394	1.007292	1.033775	1.060769	1.056365	0.9821096

Figure: Benchmarking of colVars_X_S() and rowVars_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 23.44 secs.

Reproducibility

To reproduce this report, do:

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

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Copyright Dongcan Jiang. Last updated on 2021-08-25 19:10:31 (+0200 UTC). Powered by RSP.