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Insert grid - expand.grid to concatenate rows

If we want to get all combinations of two vectors, we can use the rep / recycling rules:

 x <- 1:4 y <- 1:2 cbind(rep(x, each = length(y)), rep(y, length(x))) # [,1] [,2] # [1,] 1 1 # [2,] 1 2 # [3,] 2 1 # [4,] 2 2 # [5,] 3 1 # [6,] 3 2 # [7,] 4 1 # [8,] 4 2

But expand.grid much nicer - it handles all the repetitions for us.

 expand.grid(x, y) # Var1 Var2 # 1 1 1 # 2 2 1 # 3 3 1 # 4 4 1 # 5 1 2 # 6 2 2 # 7 3 2 # 8 4 2

Is there a simple version for string concatenation? How to paste.grid ? I have a named object where many objects have names like x_y_z , where x , y and z change as x and y above.

For example, suppose x can be "avg" or "median" , y can be "male" or "female" , and z can be "height" or "weight" . How can we get all 8 combinations of three?

Using rep is pain:

 x <- c("avg", "median") y <- c("male", "female") z <- c("height", "weight") paste(rep(x, each = length(y) * length(z)), rep(rep(y, each = length(z)), length(x)), rep(z, length(x) * length(y)), sep = "_")

And expand.grid bit awkward (and probably inefficient):

 apply(expand.grid(x, y, z), 1, paste, collapse = "_")

Am I missing something? Is there a better way to do this?

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4 answers

Yes, this is what interaction does

 levels(interaction(x,y,z,sep='_'))

The implementation pretty much matches your rep code.

Outputs:

  [1] "avg_female_height" "median_female_height" "avg_male_height" "median_male_height" "avg_female_weight"   
 [6] "median_female_weight" "avg_male_weight" "median_male_weight"
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Using the data.table CJ cross connect function:

 library(data.table) CJ(x,y,z)[, paste(V1,V2,V3, sep = "_")] #[1] "avg_female_height" "avg_female_weight" "avg_male_height" "avg_male_weight" #[5] "median_female_height" "median_female_weight" "median_male_height" "median_male_weight"

Or a variant of your apply approach:

 do.call(paste, c(expand.grid(x, y, z), sep = "_")) #[1] "avg_male_height" "median_male_height" "avg_female_height" "median_female_height" #[5] "avg_male_weight" "median_male_weight" "avg_female_weight" "median_female_weight"
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The rudimentary ( microbenchmark::microbenchmark ) benchmarking shows quite significant acceleration using:

 library(tidyr) library(magrittr) df <- data.frame(x, y, z) df %>% complete(x, y, z) %>% unite("combo", x, y, z, sep = "_")

A bit slower, but perhaps a more straightforward and vectorized apply option:

 df <- expand.grid(x, y, z) df$combo <- paste(df$Var1, df$Var1, df$Var3, sep = "_")

Someone should listen using the data.table approach ...

Benchmarking: small grid (256 elements)

 set.seed(21034) x <- sample(letters, 4, TRUE) y <- sample(letters, 4, TRUE) z <- sample(letters, 4, TRUE) a <- sample(letters, 4, TRUE) library(data.table) library(microbenchmark) library(magrittr) library(tidyr) microbenchmark(times = 25L, DT1 = CJ(x, y, z, a)[ , paste(V1, V2, V3, V4, sep = "_")], DT2 = CJ(x, y, z, a)[ , do.call(paste, c(.SD, sep = "_"))], app1 = do.call(paste, c(expand.grid(x, y, z, a), sep = "_")), app2 = paste((df <- expand.grid(x, y, z, a))$Var1, df$Var2, df$Var3, sep = "_"), magg_outer = outer(x, y, paste, sep = "_") %>% outer(z, paste, sep = "_") %>% outer(a, paste, sep = "_") %>% as.vector, magg_tidy = data.frame(x, y, z, a) %>% complete(x, y, z, a) %>% unite("combo", x, y, z, a, sep = "_"), interaction = levels(interaction(x, y, z, a, sep = "_")), original = apply(expand.grid(x, y, z, a), 1, paste, collapse = "_"), rep = paste(rep(x, each = (ny <- length(y)) * (nz <- length(z)) * (na <- length(a))), rep(rep(y, each = nz * na), (nx <- length(x))), rep(rep(z, each = na), nx * ny), sep = "_"), Reduce = Reduce(function(x, y) paste(rep(x, each = length(y)), rep(y, length(x)), sep = "_"), list(x, y, z, a))) # Unit: microseconds # expr min lq mean median uq max neval cld # DT1 529.578 576.6400 624.00002 589.8270 604.9845 5449.287 1000 d # DT2 561.028 606.4220 639.94659 620.4335 636.2735 5484.514 1000 d # app1 201.043 225.4475 240.36960 233.4795 243.7090 4244.687 1000 b # app2 196.692 225.6130 244.33543 234.0455 243.7925 4110.605 1000 b # magg_outer 164.352 194.1395 205.30300 204.4220 211.1990 456.122 1000 b # magg_tidy 1872.228 2038.1560 2150.98234 2067.8770 2126.1025 21891.884 1000 f # interaction 254.885 295.1935 313.54392 306.6680 316.8095 4196.465 1000 c # original 852.018 935.4960 976.24388 954.5115 972.5550 4973.724 1000 e # rep 50.737 54.1515 60.22671 55.3660 56.9220 3823.655 1000 a # Reduce 58.395 65.3860 68.46049 66.8920 68.5640 158.184 1000 a

Benchmarking: large grid (1,000,000 elements)

 set.seed(21034) x <- sprintf("%03d", sample(100)) y <- sprintf("%03d", sample(100)) z <- sprintf("%02d", sample(10)) a <- sprintf("%02d", sample(10)) library(data.table) library(microbenchmark) library(magrittr) library(tidyr) microbenchmark(times = 25L, DT1 = CJ(x, y, z, a)[ , paste(V1, V2, V3, V4, sep = "_")], DT2 = CJ(x, y, z, a)[ , do.call(paste, c(.SD, sep = "_"))], app1 = do.call(paste, c(expand.grid(x, y, z, a), sep = "_")), app2 = paste((df <- expand.grid(x, y, z, a))$Var1, df$Var2, df$Var3, sep = "_"), magg_outer = outer(x, y, paste, sep = "_") %>% outer(z, paste, sep = "_") %>% outer(a, paste, sep = "_") %>% as.vector, magg_tidy = data.frame(x, y, z, a) %>% complete(x, y, z, a) %>% unite("combo", x, y, z, a, sep = "_"), interaction = levels(interaction(x, y, z, a, sep = "_")), original = apply(expand.grid(x, y, z, a), 1, paste, collapse = "_"), rep = paste(rep(x, each = (ny <- length(y)) * (nz <- length(z)) * (na <- length(a))), rep(rep(y, each = nz * na), (nx <- length(x))), rep(rep(z, each = na), nx * ny), sep = "_"), Reduce = Reduce(function(x, y) paste(rep(x, each = length(y)), rep(y, length(x)), sep = "_"), list(x, y, z, a))) # Unit: milliseconds # expr min lq mean median uq max neval cld # DT1 360.6528 467.8408 517.4579 520.1484 549.1756 861.1567 25 ab # DT2 355.0438 504.9642 572.0732 551.9106 615.6621 927.3210 25 b # app1 727.4513 766.3053 926.1888 910.3998 957.7610 1690.1540 25 c # app2 472.5724 567.1121 633.5304 600.3779 634.3158 1135.7535 25 b # magg_outer 384.0112 475.5070 600.6317 525.8936 676.7134 927.6736 25 b # magg_tidy 520.6428 602.5028 695.5500 680.8821 748.8746 1180.1107 25 bc # interaction 353.7317 481.4732 531.0035 518.7084 585.0872 693.5171 25 ab # original 4965.1156 5358.8704 5914.3560 5780.6609 6074.7470 9024.6476 25 d # rep 206.0964 236.5811 273.1093 252.8179 285.0910 455.1776 25 a # Reduce 322.0695 390.2595 446.3948 424.9185 508.5235 621.1878 25 ab
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How about using outer() ? Your two examples become

 x <- 1:4 y <- 1:2 as.vector(outer(x, y, paste, sep = "_")) ## [1] "1_1" "2_1" "3_1" "4_1" "1_2" "2_2" "3_2" "4_2" library(magrittr) x <- c("avg", "median") y <- c("male", "female") z <- c("height", "weight") outer(x, y, paste, sep = "_") %>% outer(z, paste, sep = "_") %>% as.vector ## [1] "avg_male_height" "median_male_height" "avg_female_height" "median_female_height" "avg_male_weight" ## [6] "median_male_weight" "avg_female_weight" "median_female_weight"

The second example can be simplified a bit with Reduce() :

 Reduce(function(a, b) outer(a, b, paste, sep = "_"), list(x, y, z)) %>% as.vector

It is inefficient. Using microbenchmark , I find that your solution using rep() about 10 times faster.

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