matrixStats.benchmarks

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 5226503 279.2    7916910 422.9  7916910 422.9
Vcells 9961868  76.1   33191153 253.3 53339345 407.0
> 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 5212610 278.4    7916910 422.9  7916910 422.9
Vcells 9915729  75.7   33191153 253.3 53339345 407.0
> 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	0.002278	0.002707	0.0034123	0.003059	0.0038905	0.013835
2	apply+cumsum	0.044732	0.045870	0.0475668	0.046364	0.0468820	0.138939

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	19.63652	16.94496	13.93988	15.15659	12.05038	10.04257

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	0.002422	0.0029325	0.0040383	0.0037390	0.0040845	0.014181
2	apply+cumsum	0.042963	0.0443370	0.0538542	0.0460005	0.0498390	0.146758

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	17.73865	15.11918	13.33603	12.30289	12.20198	10.34892

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	2.278	2.7070	3.41228	3.059	3.8905	13.835
2	rowCumsums	2.422	2.9325	4.03825	3.739	4.0845	14.181

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.063213	1.083303	1.183446	1.222295	1.049865	1.025009

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 5211172 278.4    7916910 422.9  7916910 422.9
Vcells 9532221  72.8   33191153 253.3 53339345 407.0
> 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 5211166 278.4    7916910 422.9  7916910 422.9
Vcells 9537264  72.8   33191153 253.3 53339345 407.0
> 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	0.022061	0.023750	0.0266040	0.0246580	0.026556	0.090221
2	apply+cumsum	0.232339	0.245513	0.2698124	0.2549345	0.278076	0.477796

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	10.53166	10.33739	10.14181	10.33882	10.47131	5.29584

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	0.033106	0.035911	0.0397424	0.038665	0.0408545	0.076372
2	apply+cumsum	0.244971	0.255562	0.2916267	0.284571	0.3080375	0.543506

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumsum	7.399595	7.116538	7.337922	7.359912	7.539867	7.116561

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	22.061	23.750	26.60396	24.658	26.5560	90.221
2	rowCumsums	33.106	35.911	39.74241	38.665	40.8545	76.372

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowCumsums	1.500657	1.512042	1.493853	1.568051	1.538428	0.8464992

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 5211904 278.4    7916910 422.9  7916910 422.9
Vcells 9535729  72.8   33191153 253.3 53339345 407.0
> 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 5211898 278.4    7916910 422.9  7916910 422.9
Vcells 9540772  72.8   33191153 253.3 53339345 407.0
> 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	0.023164	0.0262155	0.0288144	0.0275415	0.0289715	0.060915
2	apply+cumsum	0.153739	0.1716840	0.1853298	0.1799110	0.1937875	0.314449

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.000000	1.00000	1.000000	1.000000
2	apply+cumsum	6.63698	6.54895	6.431839	6.53236	6.688901	5.162095

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	0.034434	0.0365650	0.0411813	0.038978	0.0417915	0.072976
2	apply+cumsum	0.148096	0.1534955	0.1759504	0.171227	0.1783725	0.384864

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumsum	4.300865	4.197881	4.272578	4.392914	4.268153	5.273843

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	23.164	26.2155	28.81443	27.5415	28.9715	60.915
2	rowCumsums	34.434	36.5650	41.18133	38.9780	41.7915	72.976

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.486531	1.394786	1.429191	1.415246	1.442504	1.197997

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 5212092 278.4    7916910 422.9  7916910 422.9
Vcells 9536418  72.8   33191153 253.3 53339345 407.0
> 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 5212086 278.4    7916910 422.9  7916910 422.9
Vcells 9541461  72.8   33191153 253.3 53339345 407.0
> 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	0.018293	0.0195380	0.0223278	0.0211385	0.024441	0.041329
2	apply+cumsum	0.876124	0.9043695	1.0088345	0.9613105	1.104437	1.434505

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.0000
2	apply+cumsum	47.89395	46.28772	45.18299	45.47676	45.18788	34.7094

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	0.023917	0.0252630	0.0290411	0.0270525	0.031964	0.049488
2	apply+cumsum	0.893217	0.9071915	1.0250141	0.9846725	1.133282	1.487310

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	37.34653	35.90989	35.29527	36.39858	35.45497	30.05395

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
1	colCumsums	18.293	19.538	22.32775	21.1385	24.441	41.329
2	rowCumsums	23.917	25.263	29.04112	27.0525	31.964	49.488

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.30744	1.293019	1.300674	1.279774	1.307802	1.197416

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 5212278 278.4    7916910 422.9  7916910 422.9
Vcells 9536905  72.8   33191153 253.3 53339345 407.0
> 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 5212266 278.4    7916910 422.9  7916910 422.9
Vcells 9586938  73.2   33191153 253.3 53339345 407.0
> 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	0.165376	0.1728155	0.208861	0.1952225	0.220419	0.31994
2	apply+cumsum	1.702645	1.7484045	2.124853	1.8557210	2.164325	16.71682

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.0000	1.00000	1.00000	1.000000	1.000000	1.00000
2	apply+cumsum	10.2956	10.11717	10.17353	9.505672	9.819138	52.24986

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	0.233452	0.239689	0.266635	0.2497895	0.2809225	0.413261
2	apply+cumsum	1.706766	1.778274	2.161816	1.8427445	2.1507855	16.897307

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.00000	1.000000	1.00000
2	apply+cumsum	7.310993	7.419091	8.107771	7.37719	7.656153	40.88774

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	165.376	172.8155	208.861	195.2225	220.4190	319.940
2	rowCumsums	233.452	239.6890	266.635	249.7895	280.9225	413.261

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.411644	1.386965	1.276615	1.279512	1.274493	1.291683

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 5212471 278.4    7916910 422.9  7916910 422.9
Vcells 9537470  72.8   33191153 253.3 53339345 407.0
> 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 5212465 278.4    7916910 422.9  7916910 422.9
Vcells 9587513  73.2   33191153 253.3 53339345 407.0
> 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	0.157979	0.1611115	0.1896346	0.188222	0.206122	0.285872
2	apply+cumsum	0.933707	1.0044370	1.2173664	1.156057	1.250851	7.971091

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumsum	5.910323	6.234421	6.419536	6.141989	6.068498	27.88343

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	0.240847	0.2528475	0.2834285	0.271229	0.311126	0.410411
2	apply+cumsum	0.938000	0.9535505	1.2044704	1.081750	1.226506	7.897673

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumsum	3.894589	3.771247	4.249644	3.988327	3.942154	19.24333

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	157.979	161.1115	189.6346	188.222	206.122	285.872
2	rowCumsums	240.847	252.8475	283.4285	271.229	311.126	410.411

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumsums	1.524551	1.569395	1.494603	1.441006	1.509427	1.435646

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 5212671 278.4    7916910 422.9  7916910 422.9
Vcells 9653182  73.7   33191153 253.3 53339345 407.0
> 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 5212656 278.4    7916910 422.9  7916910 422.9
Vcells 9653310  73.7   33191153 253.3 53339345 407.0
> 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	0.002246	0.0025490	0.0033277	0.0029560	0.0037935	0.016422
2	apply+cumsum	0.044421	0.0458615	0.0486451	0.0464835	0.0472070	0.161339

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumsum	19.77783	17.99196	14.61832	15.72514	12.44418	9.824565

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	0.002213	0.0026925	0.0034486	0.003605	0.0037530	0.015736
2	apply+cumsum	0.044530	0.0457105	0.0474352	0.046100	0.0465115	0.149849

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumsum	20.12201	16.97697	13.75492	12.78779	12.39315	9.522687

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	2.246	2.5490	3.32768	2.956	3.7935	16.422
2	rowCumsums	2.213	2.6925	3.44860	3.605	3.7530	15.736

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.0000000	1.000000	1.000000	1.000000	1.0000000	1.0000000
2	rowCumsums	0.9853072	1.056297	1.036338	1.219553	0.9893238	0.9582268

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 5212846 278.4    7916910 422.9  7916910 422.9
Vcells 9654002  73.7   33191153 253.3 53339345 407.0
> 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 5212840 278.4    7916910 422.9  7916910 422.9
Vcells 9664045  73.8   33191153 253.3 53339345 407.0
> 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	0.013719	0.0152435	0.0190947	0.0161920	0.0183730	0.109809
2	apply+cumsum	0.230781	0.2427330	0.2941777	0.2674925	0.3097775	0.684934

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumsum	16.822	15.92371	15.40622	16.52004	16.86047	6.237503

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	0.010698	0.0121060	0.0138545	0.0127970	0.0141175	0.025811
2	apply+cumsum	0.232530	0.2462635	0.2829568	0.2670155	0.3001925	0.596969

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	21.73584	20.34227	20.42342	20.86548	21.26386	23.12847

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
2	rowCumsums	10.698	12.1060	13.85453	12.797	14.1175	25.811
1	colCumsums	13.719	15.2435	19.09473	16.192	18.3730	109.809

	expr	min	lq	mean	median	uq	max
2	rowCumsums	1.000000	1.000000	1.00000	1.000000	1.000000	1.000000
1	colCumsums	1.282389	1.259169	1.37823	1.265297	1.301434	4.254349

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 5213038 278.5    7916910 422.9  7916910 422.9
Vcells 9654907  73.7   33191153 253.3 53339345 407.0
> 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 5213032 278.5    7916910 422.9  7916910 422.9
Vcells 9664950  73.8   33191153 253.3 53339345 407.0
> 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	0.016662	0.0187350	0.0207255	0.019895	0.021390	0.05948
2	apply+cumsum	0.152046	0.1639515	0.1848770	0.180297	0.196685	0.30003

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumsum	9.125315	8.751081	8.920278	9.062428	9.195185	5.044217

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	0.013276	0.0144580	0.0169073	0.015806	0.017651	0.052774
2	apply+cumsum	0.145198	0.1517435	0.1751258	0.170163	0.185089	0.368591

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumsum	10.93688	10.49547	10.35798	10.76572	10.48603	6.984329

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
2	rowCumsums	13.276	14.458	16.90733	15.806	17.651	52.774
1	colCumsums	16.662	18.735	20.72547	19.895	21.390	59.480

	expr	min	lq	mean	median	uq	max
2	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
1	colCumsums	1.255047	1.295822	1.225828	1.258699	1.211829	1.12707

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 5213226 278.5    7916910 422.9  7916910 422.9
Vcells 9655032  73.7   33191153 253.3 53339345 407.0
> 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 5213220 278.5    7916910 422.9  7916910 422.9
Vcells 9665075  73.8   33191153 253.3 53339345 407.0
> 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	0.008864	0.0111405	0.0142059	0.013116	0.0151935	0.033082
2	apply+cumsum	0.865354	0.9370735	1.0609918	1.045918	1.1338155	1.774160

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	97.62568	84.11413	74.68681	79.74367	74.62504	53.62916

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	0.007737	0.0097975	0.0126345	0.0111965	0.0137065	0.042369
2	apply+cumsum	0.860312	0.9016980	1.0196333	0.9785475	1.0969060	1.778533

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.0000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	111.1945	92.03348	80.70237	87.39762	80.02816	41.97722

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	7.737	9.7975	12.63449	11.1965	13.7065	42.369
1	colCumsums	8.864	11.1405	14.20588	13.1160	15.1935	33.082

	expr	min	lq	mean	median	uq	max
2	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colCumsums	1.145664	1.137076	1.124373	1.171437	1.108489	0.7808067

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 5213412 278.5    7916910 422.9  7916910 422.9
Vcells 9656087  73.7   33191153 253.3 53339345 407.0
> 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 5213400 278.5    7916910 422.9  7916910 422.9
Vcells 9756120  74.5   33191153 253.3 53339345 407.0
> 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	0.093477	0.1151905	0.1383346	0.1265555	0.146074	0.428721
2	apply+cumsum	1.624217	1.9158050	2.4034007	2.0877540	2.351233	16.458542

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	17.37558	16.63162	17.37383	16.49675	16.09617	38.38987

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	0.069672	0.0827205	0.0948781	0.091741	0.1043975	0.178666
2	apply+cumsum	1.664966	1.8916655	2.3568622	2.064633	2.2148785	16.044517

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.0000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	23.8972	22.86816	24.84094	22.50501	21.21582	89.80174

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
2	rowCumsums	69.672	82.7205	94.87815	91.7410	104.3975	178.666
1	colCumsums	93.477	115.1905	138.33456	126.5555	146.0740	428.721

	expr	min	lq	mean	median	uq	max
2	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.00000	1.000000
1	colCumsums	1.341672	1.392527	1.458023	1.379487	1.39921	2.399567

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 5213605 278.5    7916910 422.9  7916910 422.9
Vcells 9656213  73.7   33191153 253.3 53339345 407.0
> 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 5213599 278.5    7916910 422.9  7916910 422.9
Vcells 9756256  74.5   33191153 253.3 53339345 407.0
> 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	0.119729	0.1302805	0.1451242	0.1392615	0.150550	0.237169
2	apply+cumsum	1.016016	1.1154795	1.3228116	1.1700515	1.238112	7.165728

	expr	min	lq	mean	median	uq	max
1	colCumsums	1.000000	1.000000	1.000000	1.00000	1.000000	1.00000
2	apply+cumsum	8.485964	8.562137	9.115031	8.40183	8.223926	30.21359

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	0.085070	0.0943095	0.1145056	0.104183	0.117703	0.306502
2	apply+cumsum	1.170405	1.2400040	1.5206206	1.341770	1.490292	8.052489

	expr	min	lq	mean	median	uq	max
1	rowCumsums	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumsum	13.75814	13.14824	13.27989	12.87897	12.66146	26.27222

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
2	rowCumsums	85.070	94.3095	114.5055	104.1830	117.703	306.502
1	colCumsums	119.729	130.2805	145.1242	139.2615	150.550	237.169

	expr	min	lq	mean	median	uq	max
2	rowCumsums	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colCumsums	1.407417	1.381414	1.267399	1.336701	1.279067	0.7737927

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_0.60.0     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 24.88 secs.

Reproducibility

To reproduce this report, do:

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