matrixStats.benchmarks

---

colCumprods() and rowCumprods() benchmarks

This report benchmark the performance of colCumprods() and rowCumprods() against alternative methods.

Alternative methods

• apply() + cumprod()

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, range = c(-1, 1))

Results

10x10 integer matrix

> X <- data[["10x10"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5218434 278.7    7916910 422.9  7916910 422.9
Vcells 9906905  75.6   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204744 278.0    7916910 422.9  7916910 422.9
Vcells 9861448  75.3   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.002276	0.0025275	0.0032295	0.0028850	0.003557	0.015081
2	apply+cumprod	0.042929	0.0449480	0.0477027	0.0459065	0.047163	0.162532

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.0000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	18.8616	17.78358	14.77102	15.91213	13.25921	10.77727

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.002377	0.0028930	0.0035815	0.003685	0.0038685	0.013845
2	apply+cumprod	0.045675	0.0470545	0.0489029	0.047617	0.0480500	0.130832

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.0000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumprod	19.2154	16.26495	13.65418	12.92185	12.42083	9.449765

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	colCumprods	2.276	2.5275	3.22948	2.885	3.5570	15.081
2	rowCumprods	2.377	2.8930	3.58153	3.685	3.8685	13.845

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowCumprods	1.044376	1.144609	1.109011	1.277296	1.087574	0.9180426

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5203306 277.9    7916910 422.9  7916910 422.9
Vcells 9477850  72.4   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5203300 277.9    7916910 422.9  7916910 422.9
Vcells 9482893  72.4   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.026066	0.0277180	0.0303940	0.0289365	0.0322705	0.050303
2	apply+cumprod	0.256745	0.2694895	0.3040831	0.2967080	0.3323485	0.488569

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.00000	1.00000	1.00000	1.000000
2	apply+cumprod	9.849804	9.722545	10.00471	10.25376	10.29883	9.712522

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.032413	0.0343935	0.0386037	0.0361505	0.0402575	0.062581
2	apply+cumprod	0.248389	0.2592440	0.3038023	0.2847105	0.3224585	0.579472

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.000000	1.0000	1.000000	1.000000
2	apply+cumprod	7.663252	7.537587	7.869765	7.8757	8.009899	9.259552

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	colCumprods	26.066	27.7180	30.39400	28.9365	32.2705	50.303
2	rowCumprods	32.413	34.3935	38.60373	36.1505	40.2575	62.581

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.00000	1.000000	1.000000	1.000000
2	rowCumprods	1.243497	1.240836	1.27011	1.249305	1.247502	1.244081

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5204038 278.0    7916910 422.9  7916910 422.9
Vcells 9481366  72.4   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204032 278.0    7916910 422.9  7916910 422.9
Vcells 9486409  72.4   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.024857	0.0266135	0.0289418	0.0285575	0.0301910	0.060870
2	apply+cumprod	0.157447	0.1673045	0.1842770	0.1833200	0.1960545	0.311474

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumprod	6.334111	6.286452	6.367162	6.419329	6.493806	5.117036

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.033903	0.0363210	0.0396467	0.0390005	0.042471	0.057180
2	apply+cumprod	0.166161	0.1724105	0.1887558	0.1877015	0.200694	0.290792

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumprod	4.901071	4.746854	4.760942	4.812797	4.725436	5.085554

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	colCumprods	24.857	26.6135	28.94178	28.5575	30.191	60.87
2	rowCumprods	33.903	36.3210	39.64672	39.0005	42.471	57.18

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumprods	1.363922	1.364758	1.369878	1.365683	1.406744	0.939379

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5204226 278.0    7916910 422.9  7916910 422.9
Vcells 9482052  72.4   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204220 278.0    7916910 422.9  7916910 422.9
Vcells 9487095  72.4   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.021124	0.0226045	0.0269961	0.0253885	0.0292555	0.053620
2	apply+cumprod	0.909392	0.9494455	1.0832734	1.0568940	1.1696135	1.559529

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.0000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	43.05018	42.0025	40.12705	41.62885	39.97927	29.08484

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.024064	0.0252535	0.0296163	0.0275465	0.0317855	0.060211
2	apply+cumprod	0.922854	0.9723930	1.0861168	1.0374410	1.1854125	1.790418

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.0000	1.00000	1.00000	1.00000
2	apply+cumprod	38.34998	38.50528	36.6729	37.66145	37.29413	29.73573

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	colCumprods	21.124	22.6045	26.99609	25.3885	29.2555	53.620
2	rowCumprods	24.064	25.2535	29.61633	27.5465	31.7855	60.211

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.00000	1.000000	1.00000	1.000000
2	rowCumprods	1.139178	1.117189	1.09706	1.084999	1.08648	1.122921

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5204412 278.0    7916910 422.9  7916910 422.9
Vcells 9482539  72.4   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204400 278.0    7916910 422.9  7916910 422.9
Vcells 9532572  72.8   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.192213	0.218718	0.237096	0.233236	0.2516265	0.307654
2	apply+cumprod	1.857093	2.025908	2.603234	2.214641	2.4522365	19.043625

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.00000	1.000000	1.000000	1.00000
2	apply+cumprod	9.661641	9.262649	10.97966	9.495282	9.745541	61.89949

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.233535	0.2666795	0.2892378	0.2857985	0.3083355	0.406547
2	apply+cumprod	1.877209	2.0892115	2.6503312	2.2804735	2.4822040	19.068182

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumprod	8.038234	7.834166	9.163157	7.979305	8.050335	46.90277

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	colCumprods	192.213	218.7180	237.0960	233.2360	251.6265	307.654
2	rowCumprods	233.535	266.6795	289.2378	285.7985	308.3355	406.547

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.000000	1.000000	1.000000	1.00000	1.000000
2	rowCumprods	1.21498	1.219285	1.219918	1.225362	1.22537	1.321442

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5204605 278.0    7916910 422.9  7916910 422.9
Vcells 9483099  72.4   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204599 278.0    7916910 422.9  7916910 422.9
Vcells 9533142  72.8   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.188189	0.210303	0.2285379	0.2252015	0.2403785	0.349567
2	apply+cumprod	1.060915	1.159491	1.4324526	1.2974905	1.3982185	7.410537

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.0000	1.000000	1.000000	1.00000
2	apply+cumprod	5.637497	5.513433	6.2679	5.761465	5.816737	21.19919

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.242658	0.2768575	0.2976501	0.2971445	0.309726	0.412638
2	apply+cumprod	1.032783	1.1748890	1.4189550	1.2837250	1.386918	7.382424

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.00000	1.000000	1.000000	1.000000	1.0000
2	apply+cumprod	4.256126	4.24366	4.767191	4.320205	4.477887	17.8908

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	colCumprods	188.189	210.3030	228.5379	225.2015	240.3785	349.567
2	rowCumprods	242.658	276.8575	297.6501	297.1445	309.7260	412.638

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.00000	1.00000	1.000000	1.000000	1.000000
2	rowCumprods	1.289438	1.31647	1.30241	1.319461	1.288493	1.180426

Figure: Benchmarking of colCumprods() and rowCumprods() 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, range = c(-1, 1))

Results

10x10 double matrix

> X <- data[["10x10"]]
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204805 278.0    7916910 422.9  7916910 422.9
Vcells 9599476  73.3   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204790 278.0    7916910 422.9  7916910 422.9
Vcells 9599604  73.3   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.001963	0.0021960	0.0027747	0.0025365	0.0031060	0.013481
2	apply+cumprod	0.037692	0.0387235	0.0408208	0.0394760	0.0402135	0.134046

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.0000	1.00000	1.00000	1.000000
2	apply+cumprod	19.20122	17.63365	14.7117	15.56318	12.94704	9.943328

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.002208	0.0026775	0.0033424	0.003423	0.003610	0.015228
2	apply+cumprod	0.045010	0.0459455	0.0474587	0.046297	0.046759	0.122212

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumprod	20.38496	17.15985	14.19885	13.52527	12.95263	8.025479

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	colCumprods	1.963	2.1960	2.77472	2.5365	3.106	13.481
2	rowCumprods	2.208	2.6775	3.34243	3.4230	3.610	15.228

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowCumprods	1.124809	1.219262	1.204601	1.349497	1.162267	1.12959

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5204980 278.0    7916910 422.9  7916910 422.9
Vcells 9599583  73.3   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5204974 278.0    7916910 422.9  7916910 422.9
Vcells 9609626  73.4   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.013744	0.0150235	0.0170667	0.0163440	0.0177015	0.036787
2	apply+cumprod	0.236768	0.2559470	0.2833312	0.2734325	0.2986060	0.492447

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	17.22701	17.03644	16.60143	16.72984	16.86897	13.38644

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.012419	0.0132775	0.0150558	0.0139935	0.0149275	0.045979
2	apply+cumprod	0.234897	0.2496335	0.2808525	0.2729390	0.3032490	0.449333

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.0000	1.00000	1.00000
2	apply+cumprod	18.91432	18.80124	18.65411	19.5047	20.31479	9.77257

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	rowCumprods	12.419	13.2775	15.05580	13.9935	14.9275	45.979
1	colCumprods	13.744	15.0235	17.06668	16.3440	17.7015	36.787

	expr	min	lq	mean	median	uq	max
2	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
1	colCumprods	1.106691	1.131501	1.133562	1.167971	1.185831	0.8000826

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5205172 278.0    7916910 422.9  7916910 422.9
Vcells 9600470  73.3   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205166 278.0    7916910 422.9  7916910 422.9
Vcells 9610513  73.4   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.027122	0.0320995	0.0371901	0.0344585	0.0405005	0.085127
2	apply+cumprod	0.412845	0.4747850	0.5193167	0.5002615	0.5624670	0.715780

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.0000	1.0000	1.000000
2	apply+cumprod	15.22178	14.79104	13.96385	14.5178	13.8879	8.408378

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.025907	0.0310365	0.0340336	0.0327145	0.0352570	0.069214
2	apply+cumprod	0.412143	0.4502965	0.4934302	0.4859855	0.5216145	0.679230

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumprod	15.90856	14.50861	14.49832	14.85535	14.79464	9.813477

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	rowCumprods	25.907	31.0365	34.03362	32.7145	35.2570	69.214
1	colCumprods	27.122	32.0995	37.19009	34.4585	40.5005	85.127

	expr	min	lq	mean	median	uq	max
2	rowCumprods	1.000000	1.00000	1.000000	1.00000	1.000000	1.00000
1	colCumprods	1.046898	1.03425	1.092746	1.05331	1.148722	1.22991

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5205360 278.0    7916910 422.9  7916910 422.9
Vcells 9601512  73.3   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205354 278.0    7916910 422.9  7916910 422.9
Vcells 9611555  73.4   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.009387	0.0119355	0.0141167	0.0131270	0.014437	0.038537
2	apply+cumprod	0.897687	0.9131300	1.0391664	0.9775385	1.136804	1.786624

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	95.63087	76.50538	73.61277	74.46778	78.74243	46.36126

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.008247	0.0115815	0.0138269	0.012521	0.014407	0.037626
2	apply+cumprod	0.878591	0.9197755	1.0632066	1.012345	1.127908	2.487850

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.0000	1.00000	1.00000	1.00000	1.00000	1.0000
2	apply+cumprod	106.5346	79.41765	76.89384	80.85177	78.28889	66.1205

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	rowCumprods	8.247	11.5815	13.82694	12.521	14.407	37.626
1	colCumprods	9.387	11.9355	14.11666	13.127	14.437	38.537

	expr	min	lq	mean	median	uq	max
2	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colCumprods	1.138232	1.030566	1.020953	1.048399	1.002082	1.024212

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5205546 278.1    7916910 422.9  7916910 422.9
Vcells 9601639  73.3   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205534 278.1    7916910 422.9  7916910 422.9
Vcells 9701672  74.1   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.104298	0.1213275	0.273692	0.1322565	0.1474345	13.07530
2	apply+cumprod	1.817213	2.0556005	2.424008	2.1965345	2.5138735	15.43967

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.000000	1.00000	1.00000	1.000000
2	apply+cumprod	17.42328	16.94258	8.856703	16.60814	17.05078	1.180827

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.070852	0.082701	0.0979202	0.096008	0.1078345	0.166844
2	apply+cumprod	1.711892	1.993286	2.4320129	2.129755	2.3170945	15.179939

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.0000	1.00000	1.00000
2	apply+cumprod	24.16152	24.10232	24.83669	22.1831	21.48751	90.98283

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	rowCumprods	70.852	82.7010	97.92018	96.0080	107.8345	166.844
1	colCumprods	104.298	121.3275	273.69196	132.2565	147.4345	13075.299

	expr	min	lq	mean	median	uq	max
2	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
1	colCumprods	1.472054	1.467062	2.795052	1.377557	1.367229	78.36841

Figure: Benchmarking of colCumprods() and rowCumprods() 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 5205739 278.1    7916910 422.9  7916910 422.9
Vcells 9602856  73.3   33191153 253.3 53339345 407.0
> colStats <- microbenchmark(colCumprods = colCumprods(X), `apply+cumprod` = apply(X, MARGIN = 2L, 
+     FUN = cumprod), unit = "ms")
> X <- t(X)
> gc()
          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 5205733 278.1    7916910 422.9  7916910 422.9
Vcells 9702899  74.1   33191153 253.3 53339345 407.0
> rowStats <- microbenchmark(rowCumprods = rowCumprods(X), `apply+cumprod` = apply(X, MARGIN = 1L, 
+     FUN = cumprod), unit = "ms")

Table: Benchmarking of colCumprods() and apply+cumprod() 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	colCumprods	0.239273	0.2436585	0.2621753	0.2541975	0.2654105	0.431607
2	apply+cumprod	3.586672	3.6197690	3.9729681	3.6671295	3.9296190	10.165060

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.0000	1.00000	1.00000
2	apply+cumprod	14.98987	14.85591	15.15386	14.4263	14.80582	23.55166

Table: Benchmarking of rowCumprods() and apply+cumprod() 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	rowCumprods	0.210453	0.216730	0.2336882	0.2255365	0.237798	0.362024
2	apply+cumprod	3.628790	3.655593	4.0744468	3.6975880	4.065031	10.928963

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.0000	1.00000	1.00000	1.0000
2	apply+cumprod	17.24276	16.86704	17.4354	16.39463	17.09447	30.1885

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

Table: Benchmarking of colCumprods() and rowCumprods() 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	rowCumprods	210.453	216.7300	233.6882	225.5365	237.7980	362.024
1	colCumprods	239.273	243.6585	262.1753	254.1975	265.4105	431.607

	expr	min	lq	mean	median	uq	max
2	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colCumprods	1.136943	1.124249	1.121902	1.127079	1.116118	1.192206

Figure: Benchmarking of colCumprods() and rowCumprods() 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 25.21 secs.

Reproducibility

To reproduce this report, do:

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

---

Copyright Henrik Bengtsson. Last updated on 2021-08-25 22:14:21 (+0200 UTC). Powered by RSP.