matrixStats.benchmarks

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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 5205811 278.1    8529671 455.6  8529671 455.6
Vcells 9870675  75.4   31876688 243.2 60562128 462.1
> 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 5196805 277.6    8529671 455.6  8529671 455.6
Vcells 9841105  75.1   31876688 243.2 60562128 462.1
> 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	0.001949	0.0022965	0.0030256	0.0026615	0.0033695	0.012399
2	apply+cumprod	0.044139	0.0460580	0.0479272	0.0466245	0.0472950	0.132437

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	22.647	20.05574	15.84036	17.51813	14.03621	10.68126

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	0.002060	0.0024415	0.0031550	0.0031155	0.0033620	0.013542
2	apply+cumprod	0.044074	0.0461700	0.0489976	0.0469145	0.0476405	0.131468

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumprod	21.39515	18.91051	15.53028	15.05842	14.17029	9.708167

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	1.949	2.2965	3.02564	2.6615	3.3695	12.399
2	rowCumprods	2.060	2.4415	3.15497	3.1155	3.3620	13.542

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.00000	1.000000	1.000000	1.0000000	1.000000
2	rowCumprods	1.056952	1.06314	1.042745	1.170581	0.9977742	1.092185

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 5195385 277.5    8529671 455.6  8529671 455.6
Vcells 9457537  72.2   31876688 243.2 60562128 462.1
> 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 5195361 277.5    8529671 455.6  8529671 455.6
Vcells 9462550  72.2   31876688 243.2 60562128 462.1
> 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	0.034171	0.0365015	0.0395443	0.0378660	0.0407970	0.063975
2	apply+cumprod	0.249824	0.2666890	0.2909338	0.2794035	0.3068755	0.479452

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumprod	7.310995	7.306248	7.357162	7.378743	7.522011	7.494365

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	0.034235	0.0368590	0.0398965	0.0381275	0.0416085	0.058114
2	apply+cumprod	0.247888	0.2661715	0.2912208	0.2784865	0.3015130	0.502095

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumprod	7.240777	7.221343	7.299401	7.304085	7.246428	8.639829

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	34.171	36.5015	39.54429	37.8660	40.7970	63.975
2	rowCumprods	34.235	36.8590	39.89653	38.1275	41.6085	58.114

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.0000000
2	rowCumprods	1.001873	1.009794	1.008908	1.006906	1.019891	0.9083861

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 5196117 277.6    8529671 455.6  8529671 455.6
Vcells 9461044  72.2   31876688 243.2 60562128 462.1
> 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 5196093 277.6    8529671 455.6  8529671 455.6
Vcells 9466057  72.3   31876688 243.2 60562128 462.1
> 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	0.035570	0.0381615	0.0411372	0.0406135	0.0436800	0.059271
2	apply+cumprod	0.162312	0.1748130	0.1899283	0.1890485	0.2021335	0.290299

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumprod	4.563171	4.580873	4.616951	4.654819	4.627598	4.897825

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	0.038940	0.0401195	0.0435610	0.0418435	0.0462225	0.074072
2	apply+cumprod	0.162627	0.1649235	0.1834179	0.1796835	0.1962705	0.306611

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.000000	1.00000	1.000000	1.000000
2	apply+cumprod	4.176348	4.110806	4.210599	4.29418	4.246211	4.139364

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	35.57	38.1615	41.13716	40.6135	43.6800	59.271
2	rowCumprods	38.94	40.1195	43.56100	41.8435	46.2225	74.072

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumprods	1.094743	1.051308	1.058921	1.030285	1.058207	1.249717

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 5196305 277.6    8529671 455.6  8529671 455.6
Vcells 9461731  72.2   31876688 243.2 60562128 462.1
> 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 5196281 277.6    8529671 455.6  8529671 455.6
Vcells 9466744  72.3   31876688 243.2 60562128 462.1
> 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	0.029683	0.0310620	0.0365562	0.0335665	0.040015	0.059939
2	apply+cumprod	0.950867	0.9810315	1.0957693	1.0387115	1.193547	1.534638

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	32.03406	31.58301	29.97493	30.94489	29.82748	25.60333

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	0.026171	0.0279540	0.0321708	0.0302045	0.033187	0.060131
2	apply+cumprod	0.957065	0.9888725	1.0968540	1.0296575	1.174174	1.894367

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.000
2	apply+cumprod	36.56968	35.37499	34.09465	34.08954	35.38056	31.504

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
2	rowCumprods	26.171	27.954	32.17085	30.2045	33.187	60.131
1	colCumprods	29.683	31.062	36.55619	33.5665	40.015	59.939

	expr	min	lq	mean	median	uq	max
2	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colCumprods	1.134194	1.111183	1.136314	1.111308	1.205743	0.996807

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 5196467 277.6    8529671 455.6  8529671 455.6
Vcells 9462190  72.2   31876688 243.2 60562128 462.1
> 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 5196461 277.6    8529671 455.6  8529671 455.6
Vcells 9512233  72.6   31876688 243.2 60562128 462.1
> 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	0.267970	0.283156	0.3159124	0.305977	0.340631	0.455423
2	apply+cumprod	1.841431	1.923039	2.4845013	2.059309	2.420221	16.867736

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumprod	6.87178	6.791445	7.864527	6.730272	7.105109	37.03751

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	0.259049	0.2735335	0.3083633	0.289524	0.338052	0.458297
2	apply+cumprod	1.849302	1.9293140	2.5010254	2.092738	2.394850	17.265979

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	apply+cumprod	7.138812	7.053301	8.110646	7.228202	7.084265	37.67421

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
2	rowCumprods	259.049	273.5335	308.3633	289.524	338.052	458.297
1	colCumprods	267.970	283.1560	315.9124	305.977	340.631	455.423

	expr	min	lq	mean	median	uq	max
2	rowCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
1	colCumprods	1.034437	1.035179	1.024481	1.056828	1.007629	0.993729

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 5196684 277.6    8529671 455.6  8529671 455.6
Vcells 9462788  72.2   31876688 243.2 60562128 462.1
> 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 5196660 277.6    8529671 455.6  8529671 455.6
Vcells 9512801  72.6   31876688 243.2 60562128 462.1
> 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	0.260132	0.282246	0.3090793	0.303985	0.331859	0.445887
2	apply+cumprod	1.043017	1.146822	1.4105415	1.275292	1.381757	7.273948

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.0000	1.000000	1.000000	1.000000	1.00000
2	apply+cumprod	4.009568	4.0632	4.563689	4.195248	4.163689	16.31343

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	0.268310	0.3105955	0.3315711	0.3313445	0.350803	0.452780
2	apply+cumprod	1.052907	1.2035340	1.4515562	1.3271340	1.423838	7.597945

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.000000	1.0000	1.000000	1.00000
2	apply+cumprod	3.924218	3.874924	4.377813	4.0053	4.058795	16.78066

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	260.132	282.2460	309.0793	303.9850	331.859	445.887
2	rowCumprods	268.310	310.5955	331.5711	331.3445	350.803	452.780

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.00000	1.000000	1.000000	1.000000
2	rowCumprods	1.031438	1.100442	1.07277	1.090003	1.057084	1.015459

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 5196884 277.6    8529671 455.6  8529671 455.6
Vcells 9579162  73.1   31876688 243.2 60562128 462.1
> 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 5196851 277.6    8529671 455.6  8529671 455.6
Vcells 9579260  73.1   31876688 243.2 60562128 462.1
> 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	0.001968	0.0021225	0.0027960	0.0024555	0.0032630	0.012197
2	apply+cumprod	0.044528	0.0451800	0.0467777	0.0455225	0.0459955	0.125619

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	22.62602	21.28622	16.73051	18.53899	14.09608	10.29917

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	0.001921	0.0023785	0.0032358	0.003202	0.0033980	0.017820
2	apply+cumprod	0.042933	0.0451680	0.0466741	0.045943	0.0464395	0.119135

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.0000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumprod	22.3493	18.99012	14.42436	14.34822	13.66672	6.685466

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	1.968	2.1225	2.79595	2.4555	3.263	12.197
2	rowCumprods	1.921	2.3785	3.23578	3.2020	3.398	17.820

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.0000000	1.000000	1.00000	1.000000	1.000000	1.000000
2	rowCumprods	0.9761179	1.120613	1.15731	1.304011	1.041373	1.461015

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 5197059 277.6    8529671 455.6  8529671 455.6
Vcells 9579269  73.1   31876688 243.2 60562128 462.1
> 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 5197035 277.6    8529671 455.6  8529671 455.6
Vcells 9589282  73.2   31876688 243.2 60562128 462.1
> 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	0.018862	0.0201150	0.0219743	0.0212320	0.0234195	0.039722
2	apply+cumprod	0.235690	0.2489555	0.2757524	0.2725015	0.2913320	0.432350

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.0000
2	apply+cumprod	12.49549	12.37661	12.54888	12.83447	12.43972	10.8844

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	0.025778	0.0276110	0.0301306	0.0293440	0.0321305	0.044823
2	apply+cumprod	0.230967	0.2484535	0.2757140	0.2706595	0.2942805	0.446062

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.000000	1.000000	1.000000	1.000000	1.000000
2	apply+cumprod	8.95985	8.998352	9.150628	9.223674	9.158914	9.951632

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
1	colCumprods	18.862	20.115	21.97426	21.232	23.4195	39.722
2	rowCumprods	25.778	27.611	30.13061	29.344	32.1305	44.823

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumprods	1.366663	1.372657	1.371177	1.382065	1.371955	1.128418

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 5197251 277.6    8529671 455.6  8529671 455.6
Vcells 9580157  73.1   31876688 243.2 60562128 462.1
> 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 5197227 277.6    8529671 455.6  8529671 455.6
Vcells 9590170  73.2   31876688 243.2 60562128 462.1
> 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	0.028609	0.0327970	0.0367245	0.035979	0.0386805	0.063028
2	apply+cumprod	0.395913	0.4377725	0.4955622	0.485877	0.5336655	0.697110

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	13.83876	13.34794	13.49405	13.50446	13.79676	11.06032

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	0.036700	0.0420755	0.0466227	0.0456225	0.0510135	0.075046
2	apply+cumprod	0.392675	0.4344265	0.4875954	0.4846930	0.5209075	0.699991

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.000000
2	apply+cumprod	10.69959	10.32493	10.45833	10.62399	10.21117	9.327492

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
1	colCumprods	28.609	32.7970	36.72451	35.9790	38.6805	63.028
2	rowCumprods	36.700	42.0755	46.62270	45.6225	51.0135	75.046

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000
2	rowCumprods	1.282813	1.282907	1.269525	1.268031	1.318843	1.190677

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 5197439 277.6    8529671 455.6  8529671 455.6
Vcells 9581190  73.1   31876688 243.2 60562128 462.1
> 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 5197415 277.6    8529671 455.6  8529671 455.6
Vcells 9591203  73.2   31876688 243.2 60562128 462.1
> 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	0.016459	0.0179895	0.0213786	0.0197340	0.0235935	0.038987
2	apply+cumprod	0.905260	0.9371045	1.0463409	0.9965325	1.1357045	1.489800

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	55.00091	52.09175	48.94342	50.49825	48.13633	38.21274

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	0.019238	0.020747	0.0241043	0.022805	0.0271085	0.042509
2	apply+cumprod	0.873590	0.936432	1.0400717	1.011245	1.1205125	1.473388

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	45.40961	45.13578	43.14886	44.34313	41.33436	34.66061

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
1	colCumprods	16.459	17.9895	21.37858	19.734	23.5935	38.987
2	rowCumprods	19.238	20.7470	24.10427	22.805	27.1085	42.509

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.00000	1.000000	1.000000
2	rowCumprods	1.168844	1.153284	1.127496	1.15562	1.148982	1.090338

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 5197601 277.6    8529671 455.6  8529671 455.6
Vcells 9581277  73.1   31876688 243.2 60562128 462.1
> 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 5197595 277.6    8529671 455.6  8529671 455.6
Vcells 9681320  73.9   31876688 243.2 60562128 462.1
> 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	0.135504	0.1553185	0.1715657	0.168157	0.1834145	0.256995
2	apply+cumprod	1.654691	1.7620635	2.2401876	1.952727	2.1626990	14.064804

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	12.21138	11.34484	13.05732	11.61252	11.79132	54.72793

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	0.183357	0.2040805	0.2365675	0.2285705	0.2510835	0.543653
2	apply+cumprod	1.678561	1.8237780	2.3575583	2.0346840	2.2589225	14.962240

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.000000	1.000000	1.00000	1.000000	1.000000	1.00000
2	apply+cumprod	9.154606	8.936562	9.96569	8.901779	8.996698	27.52167

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
1	colCumprods	135.504	155.3185	171.5657	168.1570	183.4145	256.995
2	rowCumprods	183.357	204.0805	236.5675	228.5705	251.0835	543.653

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.00000	1.000000
2	rowCumprods	1.353148	1.313948	1.378874	1.359268	1.36894	2.115423

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 5197800 277.6    8529671 455.6  8529671 455.6
Vcells 9582511  73.2   31876688 243.2 60562128 462.1
> 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 5197794 277.6    8529671 455.6  8529671 455.6
Vcells 9682554  73.9   31876688 243.2 60562128 462.1
> 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	0.269808	0.272780	0.2922876	0.2808795	0.2958015	0.475241
2	apply+cumprod	3.581382	3.600439	3.9115260	3.6187035	3.7918445	9.503469

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
2	apply+cumprod	13.27382	13.19906	13.38246	12.88347	12.81888	19.99716

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	0.333468	0.33711	0.4114935	0.3428665	0.350023	6.193611
2	apply+cumprod	3.598688	3.62139	3.8873814	3.6361255	3.819939	9.682939

	expr	min	lq	mean	median	uq	max
1	rowCumprods	1.0000	1.00000	1.000000	1.00000	1.00000	1.000000
2	apply+cumprod	10.7917	10.74246	9.447005	10.60508	10.91339	1.563375

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
1	colCumprods	269.808	272.78	292.2876	280.8795	295.8015	475.241
2	rowCumprods	333.468	337.11	411.4935	342.8665	350.0230	6193.611

	expr	min	lq	mean	median	uq	max
1	colCumprods	1.000000	1.000000	1.000000	1.000000	1.000000	1.00000
2	rowCumprods	1.235946	1.235831	1.407838	1.220689	1.183304	13.03257

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_0.60.1     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 24.8 secs.

Reproducibility

To reproduce this report, do:

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

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Copyright Henrik Bengtsson. Last updated on 2021-08-25 18:53:57 (+0200 UTC). Powered by RSP.