matrixStats.benchmarks

---

colMads() and rowMads() benchmarks on subsetted computation

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

Data type “integer”

Data

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

Results

10x10 integer matrix

> X <- data[["10x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5243906 280.1    7916910 422.9  7916910 422.9
Vcells 10047688  76.7   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  5231495 279.4    7916910 422.9  7916910 422.9
Vcells 10006268  76.4   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.006461	0.0066115	0.0103122	0.0067700	0.0069370	0.322087
2	colMads(X, rows, cols)	0.006751	0.0069835	0.0078828	0.0072040	0.0074595	0.023508
3	colMads(X[rows, cols])	0.007859	0.0081680	0.0096296	0.0083655	0.0088925	0.022904

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.044885	1.056266	0.7644191	1.064106	1.075321	0.0729865
3	colMads(X[rows, cols])	1.216375	1.235423	0.9338008	1.235672	1.281894	0.0711112

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.005541	0.0056780	0.0061529	0.0057750	0.0058790	0.016646
2	rowMads(X, cols, rows)	0.005881	0.0059870	0.0095139	0.0061465	0.0063030	0.308944
3	rowMads(X[cols, rows])	0.006677	0.0069645	0.0075766	0.0071005	0.0072495	0.026886

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.061361	1.054421	1.546228	1.064329	1.072121	18.559654
3	rowMads(X[cols, rows])	1.205017	1.226576	1.231385	1.229524	1.233118	1.615163

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	5.541	5.6780	6.15294	5.775	5.879	16.646
1	colMads_X_S	6.461	6.6115	10.31221	6.770	6.937	322.087

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
1	colMads_X_S	1.166035	1.164406	1.675981	1.172294	1.179963	19.34921

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

100x100 integer matrix

> X <- data[["100x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5230452 279.4    7916910 422.9  7916910 422.9
Vcells 9675367  73.9   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5230446 279.4    7916910 422.9  7916910 422.9
Vcells 9680450  73.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.150744	0.1725660	0.1883551	0.1817665	0.2066325	0.290421
2	colMads(X, rows, cols)	0.155053	0.1769645	0.1906507	0.1871850	0.2014920	0.284946
3	colMads(X[rows, cols])	0.162317	0.1833385	0.2039483	0.1957515	0.2191250	0.321468

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.0000000	1.0000000
2	colMads(X, rows, cols)	1.028585	1.025489	1.012188	1.029810	0.9751225	0.9811481
3	colMads(X[rows, cols])	1.076772	1.062425	1.082786	1.076939	1.0604576	1.1069034

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.158667	0.1711335	0.1888072	0.179911	0.1994355	0.285859
2	rowMads(X, cols, rows)	0.164316	0.1754695	0.1928971	0.184062	0.2051630	0.276354
3	rowMads(X[cols, rows])	0.168787	0.1819430	0.2041112	0.191321	0.2107595	0.732824

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.035603	1.025337	1.021662	1.023073	1.028719	0.9667493
3	rowMads(X[cols, rows])	1.063781	1.063164	1.081056	1.063420	1.056780	2.5635855

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	158.667	171.1335	188.8072	179.9110	199.4355	285.859
1	colMads_X_S	150.744	172.5660	188.3551	181.7665	206.6325	290.421

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.0000000	1.000000	1.0000000	1.000000	1.000000	1.000000
1	colMads_X_S	0.9500652	1.008371	0.9976055	1.010313	1.036087	1.015959

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

1000x10 integer matrix

> X <- data[["1000x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231194 279.4    7916910 422.9  7916910 422.9
Vcells 9679412  73.9   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231188 279.4    7916910 422.9  7916910 422.9
Vcells 9684495  73.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.132375	0.145282	0.1571632	0.1544420	0.1685910	0.218577
2	colMads(X, rows, cols)	0.136071	0.144580	0.1607086	0.1546965	0.1698660	0.227247
3	colMads(X[rows, cols])	0.142876	0.151133	0.1712344	0.1625450	0.1852135	0.309634

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colMads(X, rows, cols)	1.027921	0.995168	1.022559	1.001648	1.007563	1.039666
3	colMads(X[rows, cols])	1.079328	1.040273	1.089532	1.052466	1.098597	1.416590

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.133105	0.1412965	0.1575030	0.1494015	0.1704670	0.263786
2	rowMads(X, cols, rows)	0.138331	0.1486965	0.1668694	0.1651235	0.1814835	0.220752
3	rowMads(X[cols, rows])	0.145450	0.1533105	0.1759290	0.1682140	0.1897590	0.269146

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.039262	1.052372	1.059468	1.105233	1.064625	0.8368602
3	rowMads(X[cols, rows])	1.092746	1.085027	1.116988	1.125919	1.113171	1.0203195

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	133.105	141.2965	157.5030	149.4015	170.467	263.786
1	colMads_X_S	132.375	145.2820	157.1632	154.4420	168.591	218.577

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.0000000	1.000000	1.0000000	1.000000	1.0000000	1.0000000
1	colMads_X_S	0.9945156	1.028207	0.9978423	1.033738	0.9889949	0.8286149

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

10x1000 integer matrix

> X <- data[["10x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231398 279.4    7916910 422.9  7916910 422.9
Vcells 9680244  73.9   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231392 279.4    7916910 422.9  7916910 422.9
Vcells 9685327  73.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.116337	0.1250735	0.1341516	0.1331330	0.1417995	0.203789
2	colMads(X, rows, cols)	0.122930	0.1317790	0.1402742	0.1381900	0.1449090	0.175553
3	colMads(X[rows, cols])	0.129010	0.1411950	0.1485621	0.1472825	0.1560985	0.185881

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.00000	1.000000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.056672	1.053613	1.04564	1.037985	1.021929	0.8614449
3	colMads(X[rows, cols])	1.108934	1.128896	1.10742	1.106281	1.100840	0.9121248

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.108344	0.1189930	0.1282284	0.1246955	0.1343735	0.166795
2	rowMads(X, cols, rows)	0.111563	0.1243335	0.1351196	0.1306870	0.1416940	0.199874
3	rowMads(X[cols, rows])	0.118255	0.1307120	0.1409377	0.1370545	0.1507270	0.203455

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.029711	1.044881	1.053742	1.048049	1.054479	1.198321
3	rowMads(X[cols, rows])	1.091477	1.098485	1.099115	1.099113	1.121702	1.219791

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	108.344	118.9930	128.2284	124.6955	134.3735	166.795
1	colMads_X_S	116.337	125.0735	134.1516	133.1330	141.7995	203.789

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.0000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	1.073774	1.0511	1.046193	1.067665	1.055264	1.221793

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

100x1000 integer matrix

> X <- data[["100x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231611 279.4    7916910 422.9  7916910 422.9
Vcells 9702906  74.1   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231605 279.4    7916910 422.9  7916910 422.9
Vcells 9752989  74.5   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.400372	1.486560	1.569583	1.524242	1.559886	2.352329
2	colMads(X, rows, cols)	1.413594	1.505658	1.573534	1.540343	1.567050	2.504831
3	colMads(X[rows, cols])	1.469610	1.557375	1.654098	1.597702	1.650988	2.449214

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colMads(X, rows, cols)	1.009442	1.012847	1.002517	1.010563	1.004592	1.064830
3	colMads(X[rows, cols])	1.049443	1.047637	1.053846	1.048194	1.058403	1.041187

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.394227	1.417390	1.525045	1.479062	1.539834	2.349436
2	rowMads(X, cols, rows)	1.414948	1.459517	1.538112	1.511899	1.560473	2.234901
3	rowMads(X[cols, rows])	1.462044	1.506732	1.585514	1.552474	1.627152	2.141753

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.014862	1.029721	1.008568	1.022201	1.013403	0.951250
3	rowMads(X[cols, rows])	1.048641	1.063032	1.039651	1.049634	1.056706	0.911603

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.394227	1.41739	1.525045	1.479062	1.539834	2.349436
1	colMads_X_S	1.400372	1.48656	1.569583	1.524242	1.559886	2.352329

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	1.004407	1.048801	1.029204	1.030546	1.013022	1.001231

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

1000x100 integer matrix

> X <- data[["1000x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231821 279.5    7916910 422.9  7916910 422.9
Vcells 9703676  74.1   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5231815 279.5    7916910 422.9  7916910 422.9
Vcells 9753759  74.5   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.068531	1.103423	1.263605	1.190616	1.350091	2.042932
2	colMads(X, rows, cols)	1.082369	1.130214	1.305716	1.267970	1.382912	2.163751
3	colMads(X[rows, cols])	1.131169	1.179632	1.356598	1.344891	1.445767	2.318192

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colMads(X, rows, cols)	1.012951	1.024280	1.033326	1.064970	1.024311	1.059140
3	colMads(X[rows, cols])	1.058621	1.069066	1.073594	1.129576	1.070866	1.134738

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.069824	1.125537	1.162773	1.131031	1.144457	1.634217
2	rowMads(X, cols, rows)	1.084957	1.143484	1.188054	1.148244	1.179420	1.846898
3	rowMads(X[cols, rows])	1.139413	1.198958	1.242890	1.201920	1.237421	1.880642

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.014145	1.015945	1.021742	1.015219	1.030549	1.130142
3	rowMads(X[cols, rows])	1.065047	1.065232	1.068902	1.062676	1.081230	1.150791

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.069824	1.125537	1.162773	1.131031	1.144457	1.634217
1	colMads_X_S	1.068531	1.103423	1.263605	1.190616	1.350091	2.042932

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.0000000	1.0000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	0.9987914	0.9803525	1.086717	1.052682	1.179678	1.250098

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

Data type “double”

Data

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

Results

10x10 double matrix

> X <- data[["10x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232039 279.5    7916910 422.9  7916910 422.9
Vcells 9794766  74.8   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232024 279.5    7916910 422.9  7916910 422.9
Vcells 9794934  74.8   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.006820	0.007030	0.0080161	0.0071670	0.007302	0.043344
2	colMads(X, rows, cols)	0.007211	0.007546	0.0077459	0.0076925	0.007850	0.011437
3	colMads(X[rows, cols])	0.008061	0.008479	0.0087793	0.0085880	0.008812	0.013953

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.0000000	1.000000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.057331	1.073400	0.9662843	1.073322	1.075048	0.2638658
3	colMads(X[rows, cols])	1.181965	1.206117	1.0951979	1.198270	1.206793	0.3219131

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.005948	0.0062135	0.0064334	0.0063220	0.0064810	0.014349
2	rowMads(X, cols, rows)	0.006447	0.0066480	0.0071979	0.0067475	0.0068950	0.041921
3	rowMads(X[cols, rows])	0.007092	0.0074300	0.0076489	0.0075585	0.0077265	0.012075

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.083894	1.069928	1.118843	1.067305	1.063879	2.9215276
3	rowMads(X[cols, rows])	1.192334	1.195783	1.188941	1.195587	1.192177	0.8415221

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	5.948	6.2135	6.43337	6.322	6.481	14.349
1	colMads_X_S	6.820	7.0300	8.01614	7.167	7.302	43.344

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.000000	1.00000	1.000000	1.000000
1	colMads_X_S	1.146604	1.131407	1.246025	1.13366	1.126678	3.020698

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

100x100 double matrix

> X <- data[["100x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232237 279.5    7916910 422.9  7916910 422.9
Vcells 9800702  74.8   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232231 279.5    7916910 422.9  7916910 422.9
Vcells 9810785  74.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.181034	0.1857450	0.2217456	0.2159095	0.2376490	0.306645
2	colMads(X, rows, cols)	0.185944	0.1943390	0.2270757	0.2206815	0.2441455	0.313599
3	colMads(X[rows, cols])	0.192420	0.1978665	0.2360815	0.2273085	0.2600040	0.361669

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colMads(X, rows, cols)	1.027122	1.046268	1.024037	1.022102	1.027337	1.022678
3	colMads(X[rows, cols])	1.062894	1.065259	1.064650	1.052795	1.094067	1.179439

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.180731	0.1869020	0.2265100	0.2222905	0.2551420	0.309529
2	rowMads(X, cols, rows)	0.185157	0.1957525	0.2300699	0.2278440	0.2462805	0.345742
3	rowMads(X[cols, rows])	0.191981	0.2089810	0.2381580	0.2344965	0.2535245	0.324251

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.0000000	1.000000
2	rowMads(X, cols, rows)	1.024489	1.047354	1.015716	1.024983	0.9652684	1.116994
3	rowMads(X[cols, rows])	1.062247	1.118131	1.051424	1.054910	0.9936604	1.047563

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

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	181.034	185.745	221.7457	215.9095	237.649	306.645
2	rowMads_X_S	180.731	186.902	226.5100	222.2905	255.142	309.529

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads_X_S	0.9983263	1.006229	1.021486	1.029554	1.073609	1.009405

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

1000x10 double matrix

> X <- data[["1000x10"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232436 279.5    7916910 422.9  7916910 422.9
Vcells 9802098  74.8   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232430 279.5    7916910 422.9  7916910 422.9
Vcells 9812181  74.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	0.185844	0.2026050	0.2234706	0.2167915	0.235308	0.293963
1	colMads_X_S	0.180837	0.1986070	0.2244415	0.2170095	0.238893	0.317030
3	colMads(X[rows, cols])	0.192272	0.2089135	0.2324122	0.2212985	0.248980	0.345589

	expr	min	lq	mean	median	uq	max
2	colMads(X, rows, cols)	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colMads_X_S	0.973058	0.980267	1.004344	1.001006	1.015235	1.078469
3	colMads(X[rows, cols])	1.034588	1.031137	1.040012	1.020790	1.058103	1.175621

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.172049	0.1858410	0.2198896	0.2028665	0.223965	0.382953
2	rowMads(X, cols, rows)	0.175466	0.1821025	0.2244618	0.2156545	0.240009	0.378661
3	rowMads(X[cols, rows])	0.184379	0.1902135	0.2355515	0.2248160	0.251848	0.471076

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.0000000	1.000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.019861	0.9798833	1.020793	1.063036	1.071636	0.9887924
3	rowMads(X[cols, rows])	1.071666	1.0235282	1.071226	1.108197	1.124497	1.2301144

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	172.049	185.841	219.8896	202.8665	223.965	382.953
1	colMads_X_S	180.837	198.607	224.4415	217.0095	238.893	317.030

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colMads_X_S	1.051079	1.068693	1.020701	1.069716	1.066653	0.8278562

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

10x1000 double matrix

> X <- data[["10x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232640 279.5    7916910 422.9  7916910 422.9
Vcells 9802233  74.8   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232634 279.5    7916910 422.9  7916910 422.9
Vcells 9812316  74.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	0.150915	0.1690890	0.1867714	0.179132	0.2088355	0.262401
2	colMads(X, rows, cols)	0.159292	0.1758265	0.1938986	0.184998	0.2054650	0.306824
3	colMads(X[rows, cols])	0.165582	0.1879530	0.2060520	0.195646	0.2228385	0.311156

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.0000000	1.000000
2	colMads(X, rows, cols)	1.055508	1.039846	1.038160	1.032747	0.9838605	1.169294
3	colMads(X[rows, cols])	1.097187	1.111563	1.103231	1.092189	1.0670528	1.185803

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	0.150267	0.1699290	0.1893758	0.1769815	0.207537	0.242933
2	rowMads(X, cols, rows)	0.159441	0.1732380	0.1945342	0.1850940	0.216090	0.290576
3	rowMads(X[cols, rows])	0.162003	0.1830045	0.2048999	0.2029095	0.228913	0.305179

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.061051	1.019473	1.027239	1.045838	1.041212	1.196116
3	rowMads(X[cols, rows])	1.078101	1.076947	1.081975	1.146501	1.102998	1.256227

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	150.267	169.929	189.3758	176.9815	207.5370	242.933
1	colMads_X_S	150.915	169.089	186.7714	179.1320	208.8355	262.401

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.0000000	1.0000000	1.000000	1.000000	1.000000
1	colMads_X_S	1.004312	0.9950568	0.9862478	1.012151	1.006257	1.080137

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

100x1000 double matrix

> X <- data[["100x1000"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232853 279.5    7916910 422.9  7916910 422.9
Vcells 9847683  75.2   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5232847 279.5    7916910 422.9  7916910 422.9
Vcells 9947766  75.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.835194	1.938079	2.028240	1.974273	2.022076	3.370790
2	colMads(X, rows, cols)	1.865895	1.972180	2.051073	2.019049	2.062898	3.155397
3	colMads(X[rows, cols])	1.925984	2.043358	2.156455	2.076226	2.133806	3.724922

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.00000	1.000000	1.0000000
2	colMads(X, rows, cols)	1.016729	1.017595	1.011258	1.02268	1.020188	0.9361001
3	colMads(X[rows, cols])	1.049472	1.054321	1.063215	1.05164	1.055255	1.1050591

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.826397	1.880685	1.980898	1.912635	1.965585	3.078375
2	rowMads(X, cols, rows)	1.871696	1.925647	2.004012	1.967893	2.015769	2.957353
3	rowMads(X[cols, rows])	1.934569	1.991013	2.091519	2.034030	2.082826	3.001702

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowMads(X, cols, rows)	1.024802	1.023908	1.011669	1.028891	1.025531	0.9606864
3	rowMads(X[cols, rows])	1.059227	1.058664	1.055844	1.063470	1.059647	0.9750930

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

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

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.826397	1.880685	1.980898	1.912635	1.965585	3.078375
1	colMads_X_S	1.835194	1.938079	2.028240	1.974273	2.022076	3.370790

	expr	min	lq	mean	median	uq	max
2	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
1	colMads_X_S	1.004817	1.030518	1.023899	1.032226	1.028741	1.09499

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

1000x100 double matrix

> X <- data[["1000x100"]]
> rows <- sample.int(nrow(X), size = nrow(X) * 0.7)
> cols <- sample.int(ncol(X), size = ncol(X) * 0.7)
> X_S <- X[rows, cols]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5233063 279.5    7916910 422.9  7916910 422.9
Vcells 9847824  75.2   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colMads_X_S = colMads(X_S, na.rm = FALSE), `colMads(X, rows, cols)` = colMads(X, 
+     rows = rows, cols = cols, na.rm = FALSE), `colMads(X[rows, cols])` = colMads(X[rows, cols], na.rm = FALSE), 
+     unit = "ms")
> X <- t(X)
> X_S <- t(X_S)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5233057 279.5    7916910 422.9  7916910 422.9
Vcells 9947907  75.9   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowMads_X_S = rowMads(X_S, na.rm = FALSE), `rowMads(X, cols, rows)` = rowMads(X, 
+     rows = cols, cols = rows, na.rm = FALSE), `rowMads(X[cols, rows])` = rowMads(X[cols, rows], na.rm = FALSE), 
+     unit = "ms")

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.662577	1.764182	1.881925	1.812294	1.962526	2.706855
2	colMads(X, rows, cols)	1.698820	1.795595	1.928039	1.838185	1.986263	2.907189
3	colMads(X[rows, cols])	1.761786	1.857565	1.979535	1.897971	2.022568	2.775815

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	colMads(X, rows, cols)	1.021799	1.017806	1.024503	1.014286	1.012095	1.074010
3	colMads(X[rows, cols])	1.059672	1.052933	1.051867	1.047275	1.030594	1.025476

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

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.675134	1.816307	1.982094	1.892659	2.108662	2.734573
2	rowMads(X, cols, rows)	1.708224	1.859171	2.086072	1.934903	2.267864	3.254756
3	rowMads(X[cols, rows])	1.783076	1.935579	2.138052	2.032256	2.269516	3.282786

	expr	min	lq	mean	median	uq	max
1	rowMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowMads(X, cols, rows)	1.019754	1.023599	1.052459	1.022320	1.075499	1.190225
3	rowMads(X[cols, rows])	1.064438	1.065667	1.078683	1.073757	1.076283	1.200475

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

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

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.662577	1.764182	1.881925	1.812294	1.962526	2.706855
2	rowMads_X_S	1.675134	1.816307	1.982094	1.892659	2.108662	2.734573

	expr	min	lq	mean	median	uq	max
1	colMads_X_S	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowMads_X_S	1.007553	1.029547	1.053227	1.044344	1.074463	1.01024

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

Appendix

Session information

R version 4.1.1 Patched (2021-08-10 r80727)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.5 LTS

Matrix products: default
BLAS:   /home/hb/software/R-devel/R-4-1-branch/lib/R/lib/libRblas.so
LAPACK: /home/hb/software/R-devel/R-4-1-branch/lib/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] microbenchmark_1.4-7   matrixStats_0.60.0     ggplot2_3.3.5         
[4] knitr_1.33             R.devices_2.17.0       R.utils_2.10.1        
[7] R.oo_1.24.0            R.methodsS3_1.8.1-9001 history_0.0.1-9000    

loaded via a namespace (and not attached):
 [1] Biobase_2.52.0          httr_1.4.2              splines_4.1.1          
 [4] bit64_4.0.5             network_1.17.1          assertthat_0.2.1       
 [7] highr_0.9               stats4_4.1.1            blob_1.2.2             
[10] GenomeInfoDbData_1.2.6  robustbase_0.93-8       pillar_1.6.2           
[13] RSQLite_2.2.8           lattice_0.20-44         glue_1.4.2             
[16] digest_0.6.27           XVector_0.32.0          colorspace_2.0-2       
[19] Matrix_1.3-4            XML_3.99-0.7            pkgconfig_2.0.3        
[22] zlibbioc_1.38.0         genefilter_1.74.0       purrr_0.3.4            
[25] ergm_4.1.2              xtable_1.8-4            scales_1.1.1           
[28] tibble_3.1.4            annotate_1.70.0         KEGGREST_1.32.0        
[31] farver_2.1.0            generics_0.1.0          IRanges_2.26.0         
[34] ellipsis_0.3.2          cachem_1.0.6            withr_2.4.2            
[37] BiocGenerics_0.38.0     mime_0.11               survival_3.2-13        
[40] magrittr_2.0.1          crayon_1.4.1            statnet.common_4.5.0   
[43] memoise_2.0.0           laeken_0.5.1            fansi_0.5.0            
[46] R.cache_0.15.0          MASS_7.3-54             R.rsp_0.44.0           
[49] progressr_0.8.0         tools_4.1.1             lifecycle_1.0.0        
[52] S4Vectors_0.30.0        trust_0.1-8             munsell_0.5.0          
[55] tabby_0.0.1-9001        AnnotationDbi_1.54.1    Biostrings_2.60.2      
[58] compiler_4.1.1          GenomeInfoDb_1.28.1     rlang_0.4.11           
[61] grid_4.1.1              RCurl_1.98-1.4          cwhmisc_6.6            
[64] rstudioapi_0.13         rappdirs_0.3.3          startup_0.15.0         
[67] labeling_0.4.2          bitops_1.0-7            base64enc_0.1-3        
[70] boot_1.3-28             gtable_0.3.0            DBI_1.1.1              
[73] markdown_1.1            R6_2.5.1                lpSolveAPI_5.5.2.0-17.7
[76] rle_0.9.2               dplyr_1.0.7             fastmap_1.1.0          
[79] bit_4.0.4               utf8_1.2.2              parallel_4.1.1         
[82] Rcpp_1.0.7              vctrs_0.3.8             png_0.1-7              
[85] DEoptimR_1.0-9          tidyselect_1.1.1        xfun_0.25              
[88] coda_0.19-4            

Total processing time was 28.5 secs.

Reproducibility

To reproduce this report, do:

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

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Copyright Dongcan Jiang. Last updated on 2021-08-25 22:17:15 (+0200 UTC). Powered by RSP.