R generate all possible interaction variables

Question

I have a dataframe with variables, say a,b,c,d

dat <- data.frame(a=runif(1e5), b=runif(1e5), c=runif(1e5), d=runif(1e5))

and would like to g

Answer 1

Assuming that the expected output would be the combinations of column names (from the comments it should be a_b, a_c etc), we can use combn on the column names of the dataset and specify the m as 2.

combn(colnames(dat), 2, FUN=paste, collapse='_')
#[1] "a_b" "a_c" "a_d" "b_c" "b_d" "c_d"

If we need to multiply the combinations of columns in 'dat', we subset the dataset using each element of the combn output of column names (dat[,x[1]], dat[,x[2]]), multiply (*) it, convert to 'data.frame' (data.frame(), set the column names (setNames) by pasteing the combination of column names. We create the output in a list and cbind the list elements with do.call(cbind.

do.call(cbind, combn(colnames(dat), 2, FUN= function(x) 
                list(setNames(data.frame(dat[,x[1]]*dat[,x[2]]), 
                 paste(x, collapse="_")) )))
#         a_b        a_c        a_d        b_c        b_d        c_d
#1 0.26929788 0.17697473 0.26453066 0.55676619 0.83221898 0.54691008
#2 0.06291005 0.08337501 0.04455453 0.10370775 0.05542008 0.07344851
#3 0.53789990 0.47301970 0.03112880 0.51305076 0.03376319 0.02969076
#4 0.41596384 0.34920860 0.25992717 0.53948322 0.40155468 0.33711187
#5 0.16878584 0.21232357 0.09196025 0.08162171 0.03535148 0.04447027

Benchmarks

set.seed(494)
dat <- data.frame(a=runif(1e6), b=runif(1e6), c=runif(1e6), d=runif(1e6))

greg <- function()model.matrix( ~.^2, data=dat)
akrun <- function() {do.call(cbind, combn(colnames(dat), 2, FUN= function(x) 
           list(setNames(data.frame(dat[,x[1]]*dat[,x[2]]), 
            paste(x, collapse="_")) )))}

system.time(greg())
#  user  system elapsed 
#  1.159   0.024   1.182 

system.time(akrun())
#  user  system elapsed 
#  0.013   0.000   0.013 

library(microbenchmark)
microbenchmark(greg(), akrun(), times=20L, unit='relative')
# Unit: relative
#   expr      min       lq     mean   median       uq      max neval cld
# greg() 39.63122 38.53662 10.23198 18.81274 6.568741 4.642702    20   b
# akrun()  1.00000  1.00000  1.00000  1.00000 1.000000 1.000000    20  a 

NOTE: The benchmarks differ with number of columns, number of rows. Here, I am using the number of columns as showed in the OP's post.

data

set.seed(24)
dat <- data.frame(a=runif(5), b=runif(5), c=runif(5), d=runif(5))