matrixStats.benchmarks

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colCumsums() and rowCumsums() benchmarks

This report benchmark the performance of colCumsums() and rowCumsums() against alternative methods.

Alternative methods

• apply() + cumsum()

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"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5213650 278.5    8529671 455.6  8529671 455.6
Vcells 9925088  75.8   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204441 278.0    8529671 455.6  8529671 455.6
Vcells 9894840  75.5   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.001911	0.0022615	0.0028634	0.0026425	0.0032065	0.011830
2	apply+cumsum	0.040984	0.0430095	0.0450429	0.0436840	0.0443830	0.134853

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	21.44636	19.01813	15.73078	16.53131	13.84157	11.39924

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.002019	0.0023745	0.0030955	0.0031475	0.0033615	0.012904
2	apply+cumsum	0.041296	0.0430055	0.0453320	0.0439765	0.0448645	0.127759

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumsum	20.45369	18.11139	14.64467	13.97188	13.34657	9.900728

Figure: Benchmarking of colCumsums() and apply+cumsum() on integer+10x10 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	1.911	2.2615	2.86336	2.6425	3.2065	11.830
2	rowCumsums	2.019	2.3745	3.09546	3.1475	3.3615	12.904

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.056515	1.049967	1.081059	1.191107	1.048339	1.090786

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

100x100 integer matrix

> X <- data[["100x100"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5203021 277.9    8529671 455.6  8529671 455.6
Vcells 9511362  72.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5202997 277.9    8529671 455.6  8529671 455.6
Vcells 9516375  72.7   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.030985	0.0331105	0.0356015	0.0341035	0.0369750	0.07321
2	apply+cumsum	0.233731	0.2475550	0.2683101	0.2554475	0.2792505	0.42647

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.000000	1.000000	1.00000	1.000000	1.000000
2	apply+cumsum	7.54336	7.476631	7.536484	7.49036	7.552414	5.825297

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.034552	0.0367395	0.0400708	0.038110	0.0411165	0.075774
2	apply+cumsum	0.231944	0.2421085	0.2662760	0.255937	0.2775260	0.437345

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumsum	6.712897	6.589869	6.645136	6.715744	6.749748	5.771703

Figure: Benchmarking of colCumsums() and apply+cumsum() on integer+100x100 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	30.985	33.1105	35.60150	34.1035	36.9750	73.210
2	rowCumsums	34.552	36.7395	40.07081	38.1100	41.1165	75.774

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.11512	1.109603	1.125537	1.117481	1.112008	1.035022

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

1000x10 integer matrix

> X <- data[["1000x10"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5203753 278.0    8529671 455.6  8529671 455.6
Vcells 9514872  72.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5203729 278.0    8529671 455.6  8529671 455.6
Vcells 9519885  72.7   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.031286	0.0334150	0.0412783	0.0358795	0.0393105	0.383971
2	apply+cumsum	0.145744	0.1545035	0.1875465	0.1641285	0.1866940	0.641418

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumsum	4.658442	4.623777	4.543462	4.574437	4.749215	1.670486

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.039003	0.0403455	0.0440631	0.043102	0.0463195	0.065613
2	apply+cumsum	0.150331	0.1564150	0.1698952	0.167528	0.1779855	0.270237

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.00000	1.000000	1.00000
2	apply+cumsum	3.854344	3.876888	3.855721	3.88678	3.842561	4.11865

Figure: Benchmarking of colCumsums() and apply+cumsum() on integer+1000x10 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	31.286	33.4150	41.27832	35.8795	39.3105	383.971
2	rowCumsums	39.003	40.3455	44.06314	43.1020	46.3195	65.613

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowCumsums	1.24666	1.207407	1.067465	1.201299	1.178298	0.1708801

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

10x1000 integer matrix

> X <- data[["10x1000"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5203941 278.0    8529671 455.6  8529671 455.6
Vcells 9515562  72.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5203917 278.0    8529671 455.6  8529671 455.6
Vcells 9520575  72.7   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.026868	0.0285480	0.0320503	0.0299965	0.0349415	0.052815
2	apply+cumsum	0.900702	0.9357485	1.0189601	0.9755480	1.0908195	1.451818

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	33.52322	32.77808	31.79257	32.52206	31.21845	27.48874

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.027042	0.0281790	0.0317528	0.0298610	0.033192	0.052271
2	apply+cumsum	0.896643	0.9348615	1.0179929	0.9697105	1.096916	1.433608

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.0000	1.00000
2	apply+cumsum	33.15742	33.17582	32.05995	32.47415	33.0476	27.42645

Figure: Benchmarking of colCumsums() and apply+cumsum() on integer+10x1000 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	rowCumsums	27.042	28.179	31.75279	29.8610	33.1920	52.271
1	colCumsums	26.868	28.548	32.05026	29.9965	34.9415	52.815

	expr	min	lq	mean	median	uq	max
2	rowCumsums	1.0000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colCumsums	0.9935656	1.013095	1.009368	1.004538	1.052709	1.010407

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

100x1000 integer matrix

> X <- data[["100x1000"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204103 278.0    8529671 455.6  8529671 455.6
Vcells 9516010  72.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204097  278    8529671 455.6  8529671 455.6
Vcells 9566053   73   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.242814	0.264977	0.2843808	0.2699675	0.2952235	0.737059
2	apply+cumsum	1.713847	1.839176	2.1032246	1.8978890	1.9780215	16.359792

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumsum	7.058271	6.940889	7.395804	7.030065	6.700081	22.19604

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.260093	0.279325	0.2935745	0.289555	0.298858	0.432349
2	apply+cumsum	1.699208	1.849131	2.1100754	1.905066	1.987033	16.991866

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumsum	6.533079	6.619996	7.187531	6.579287	6.648755	39.30127

Figure: Benchmarking of colCumsums() and apply+cumsum() on integer+100x1000 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	242.814	264.977	284.3808	269.9675	295.2235	737.059
2	rowCumsums	260.093	279.325	293.5745	289.5550	298.8580	432.349

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowCumsums	1.071162	1.054148	1.032329	1.072555	1.012311	0.5865867

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

1000x100 integer matrix

> X <- data[["1000x100"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204320 278.0    8529671 455.6  8529671 455.6
Vcells 9516617  72.7   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204296  278    8529671 455.6  8529671 455.6
Vcells 9566630   73   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.234917	0.247979	0.2704248	0.259225	0.288763	0.417261
2	apply+cumsum	0.938419	1.001057	1.1879427	1.046571	1.183283	8.001552

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumsum	3.994683	4.036862	4.392876	4.037305	4.097764	19.17637

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.268693	0.2808735	0.3055827	0.2935385	0.3265135	0.417652
2	apply+cumsum	0.947420	1.0135190	1.1753059	1.0573140	1.1840970	8.044296

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.00000	1.000000	1.00000
2	apply+cumsum	3.526032	3.608454	3.846114	3.60196	3.626487	19.26076

Figure: Benchmarking of colCumsums() and apply+cumsum() on integer+1000x100 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	234.917	247.9790	270.4248	259.2250	288.7630	417.261
2	rowCumsums	268.693	280.8735	305.5827	293.5385	326.5135	417.652

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.00000	1.00000	1.00000	1.000000	1.000000
2	rowCumsums	1.143778	1.13265	1.13001	1.13237	1.130732	1.000937

Figure: Benchmarking of colCumsums() and rowCumsums() 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"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204520 278.0    8529671 455.6  8529671 455.6
Vcells 9632330  73.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204487 278.0    8529671 455.6  8529671 455.6
Vcells 9632428  73.5   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.001778	0.0021550	0.0027174	0.0024265	0.0030855	0.012622
2	apply+cumsum	0.041617	0.0429945	0.0451775	0.0442875	0.0447965	0.121619

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.0000	1.00000	1.000000
2	apply+cumsum	23.40664	19.95104	16.62504	18.2516	14.51839	9.635478

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.001775	0.0021740	0.0031530	0.0029935	0.0032695	0.014764
2	apply+cumsum	0.040890	0.0426805	0.0476445	0.0440535	0.0451975	0.131418

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumsum	23.03662	19.63224	15.11104	14.71639	13.82398	8.901246

Figure: Benchmarking of colCumsums() and apply+cumsum() on double+10x10 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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
1	colCumsums	1.778	2.155	2.71744	2.4265	3.0855	12.622
2	rowCumsums	1.775	2.174	3.15296	2.9935	3.2695	14.764

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.0000000	1.000000	1.000000	1.00000	1.000000	1.000000
2	rowCumsums	0.9983127	1.008817	1.160268	1.23367	1.059634	1.169704

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

100x100 double matrix

> X <- data[["100x100"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204695 278.0    8529671 455.6  8529671 455.6
Vcells 9633150  73.5   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204671 278.0    8529671 455.6  8529671 455.6
Vcells 9643163  73.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.022690	0.0237980	0.0258113	0.024590	0.0271775	0.047038
2	apply+cumsum	0.230441	0.2418455	0.2624985	0.251979	0.2717825	0.423725

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumsum	10.15606	10.16243	10.16993	10.24721	10.00028	9.008142

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.025000	0.0267900	0.0289336	0.0277845	0.030582	0.043531
2	apply+cumsum	0.220881	0.2424455	0.2613835	0.2514460	0.272351	0.438277

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.000000	1.00000	1.000000	1.000000	1.00000
2	apply+cumsum	8.83524	9.049851	9.03391	9.049866	8.905598	10.06816

Figure: Benchmarking of colCumsums() and apply+cumsum() on double+100x100 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	22.69	23.798	25.81125	24.5900	27.1775	47.038
2	rowCumsums	25.00	26.790	28.93359	27.7845	30.5820	43.531

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowCumsums	1.101807	1.125725	1.120968	1.129911	1.125269	0.9254433

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

1000x10 double matrix

> X <- data[["1000x10"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204887 278.0    8529671 455.6  8529671 455.6
Vcells 9634052  73.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204863 278.0    8529671 455.6  8529671 455.6
Vcells 9644065  73.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.022242	0.0236490	0.0258394	0.0252725	0.027014	0.045889
2	apply+cumsum	0.142931	0.1497305	0.1635912	0.1607945	0.173429	0.258434

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.00000	1.00000	1.000000	1.00000
2	apply+cumsum	6.426176	6.331367	6.33109	6.36243	6.419967	5.63172

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.028172	0.029650	0.0322225	0.0312810	0.0336665	0.050613
2	apply+cumsum	0.143565	0.149054	0.1639212	0.1617185	0.1730210	0.271444

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumsum	5.096017	5.027116	5.087167	5.169863	5.139263	5.363128

Figure: Benchmarking of colCumsums() and apply+cumsum() on double+1000x10 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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
1	colCumsums	22.242	23.649	25.83935	25.2725	27.0140	45.889
2	rowCumsums	28.172	29.650	32.22250	31.2810	33.6665	50.613

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.266613	1.253753	1.247032	1.237748	1.246261	1.102944

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

10x1000 double matrix

> X <- data[["10x1000"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205075 278.0    8529671 455.6  8529671 455.6
Vcells 9634177  73.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205051 278.0    8529671 455.6  8529671 455.6
Vcells 9644190  73.6   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.019951	0.021407	0.0249837	0.02325	0.028980	0.041578
2	apply+cumsum	0.872224	0.929991	1.0234031	0.97128	1.098561	1.619498

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	43.71831	43.44331	40.96288	41.77548	37.90754	38.95084

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.019277	0.0205675	0.0232597	0.0217955	0.024536	0.041653
2	apply+cumsum	0.899400	0.9333850	1.0144295	0.9709405	1.085459	1.433657

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	46.65664	45.38155	43.61312	44.54775	44.23944	34.41906

Figure: Benchmarking of colCumsums() and apply+cumsum() on double+10x1000 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	rowCumsums	19.277	20.5675	23.25973	21.7955	24.536	41.653
1	colCumsums	19.951	21.4070	24.98367	23.2500	28.980	41.578

	expr	min	lq	mean	median	uq	max
2	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colCumsums	1.034964	1.040817	1.074117	1.066734	1.181122	0.9981994

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

100x1000 double matrix

> X <- data[["100x1000"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205237 278.0    8529671 455.6  8529671 455.6
Vcells 9635191  73.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205231 278.0    8529671 455.6  8529671 455.6
Vcells 9735234  74.3   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.169302	0.1869715	0.203835	0.1982765	0.2174725	0.296995
2	apply+cumsum	1.622244	1.7400535	2.168069	1.8591440	2.0870160	14.327352

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.00000	1.000000	1.000000	1.00000
2	apply+cumsum	9.581954	9.306517	10.63639	9.376522	9.596689	48.24105

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.183713	0.200637	0.3437208	0.2183715	0.239217	11.65280
2	apply+cumsum	1.644144	1.752021	2.1181943	1.9403660	2.160354	13.20317

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumsum	8.949525	8.732293	6.162543	8.885619	9.030938	1.133047

Figure: Benchmarking of colCumsums() and apply+cumsum() on double+100x1000 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	169.302	186.9715	203.8350	198.2765	217.4725	296.995
2	rowCumsums	183.713	200.6370	343.7208	218.3715	239.2170	11652.801

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.000000	1.00000	1.000000	1.000000	1.00000
2	rowCumsums	1.08512	1.073089	1.68627	1.101348	1.099987	39.23568

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

1000x100 double matrix

> X <- data[["1000x100"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205442 278.1    8529671 455.6  8529671 455.6
Vcells 9635337  73.6   31876688 243.2 60562128 462.1
> colStats <- microbenchmark(colCumsums = colCumsums(X), `apply+cumsum` = apply(X, MARGIN = 2L, FUN = cumsum), 
+     unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205430 278.0    8529671 455.6  8529671 455.6
Vcells 9735370  74.3   31876688 243.2 60562128 462.1
> rowStats <- microbenchmark(rowCumsums = rowCumsums(X), `apply+cumsum` = apply(X, MARGIN = 1L, FUN = cumsum), 
+     unit = "ms")

Table: Benchmarking of colCumsums() and apply+cumsum() 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	colCumsums	0.159095	0.1759715	0.1929168	0.1885775	0.2040345	0.280967
2	apply+cumsum	0.938149	1.0150880	1.2239085	1.0942785	1.1882135	6.904004

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.00000	1.000000	1.000000	1.000000	1.0000
2	apply+cumsum	5.896785	5.76848	6.344231	5.802805	5.823591	24.5723

Table: Benchmarking of rowCumsums() and apply+cumsum() 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	rowCumsums	0.193541	0.2109785	0.3366797	0.2288495	0.2427325	5.595377
2	apply+cumsum	0.952226	1.0191530	1.1220076	1.1013460	1.1857660	1.776875

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	apply+cumsum	4.920022	4.830601	3.332566	4.812534	4.885073	0.3175613

Figure: Benchmarking of colCumsums() and apply+cumsum() on double+1000x100 data as well as rowCumsums() and apply+cumsum() on the same data transposed. Outliers are displayed as crosses. Times are in milliseconds.

Table: Benchmarking of colCumsums() and rowCumsums() 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	colCumsums	159.095	175.9715	192.9168	188.5775	204.0345	280.967
2	rowCumsums	193.541	210.9785	336.6797	228.8495	242.7325	5595.377

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowCumsums	1.216512	1.198936	1.745207	1.213557	1.189664	19.91471

Figure: Benchmarking of colCumsums() and rowCumsums() 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 23.34 secs.

Reproducibility

To reproduce this report, do:

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

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Copyright Henrik Bengtsson. Last updated on 2021-08-25 18:54:45 (+0200 UTC). Powered by RSP.