vectorization - R - Vectorized implementation of ternary function -


i have 3 vectors x, y , z of equal length n. need create n x n x n array of function f(x[i],y[j],z[k]). straightforward way sequentially loop through each element of each of 3 vectors. however, time required compute array grows exponentially n. there way implement using vectorized operations?

edit: mentioned in comments, have added simple example of what's needed.

set.seed(1) x = rnorm(10) y = seq(11,20) z = seq(21,30)  f = array(0, dim=c( length(x),length(y),length(z) ) ) (i in 1:length(x))   (j in 1:length(y))     (k in 1:length(z))       f[i,j,k] = x[i] * (y[j] + z[k])

thanks.

you can use nested outer : 

set.seed(1) x = rnorm(10) y = seq(11,20) z = seq(21,30)  f = array(0, dim = c( length(x),length(y),length(z) ) ) (i in 1:length(x))   (j in 1:length(y))     (k in 1:length(z))       f[i,j,k] = x[i] * (y[j] + z[k])  f2 <- outer(x, outer(y, z, "+"), "*")  > identical(f, f2) [1] true

a microbenchmark including expand.grid solution proposed nick k :

x = rnorm(100) y = seq(1:100) z = seq(101:200)  forloop <- function(x, y, z) {   f = array(0, dim = c( length(x),length(y),length(z) ) )   (i in 1:length(x))     (j in 1:length(y))       (k in 1:length(z))         f[i,j,k] = x[i] * (y[j] + z[k])   return(f) }  nestedouter <- function(x, y, z) {   outer(x, outer(y, z, "+"), "*") }  expandgrid <- function(x, y, z) {   df <- expand.grid(x = x, y = y, z = z)   g <- df$x * (df$y + df$z)   dim(g) <- c(length(x), length(y), length(z))   return(g) }  library(microbenchmark) mbm <- microbenchmark(   forloop = f1 <- forloop(x, y, z),    nestedouter = f2 <- nestedouter(x, y, z),    expandgrid = f3 <- expandgrid(x, y, z),    times = 50l)  > mbm unit: milliseconds expr         min         lq        mean      median          uq        max neval forloop 3261.872552 3339.37383 3458.812265 3388.721159 3524.651971 4074.40422    50 nestedouter    3.293461    3.36810    9.874336    3.541637    5.126789   54.24087    50 expandgrid   53.907789   57.15647   85.612048   88.286431  103.516819  235.45443    50

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