Apply a function to each combination of columns - r

Question

I have a data frame with n columns and want to apply a function to each combination of columns. This is very similar to how the cor() function takes a data frame as input and produces a correlation matrix as output, for example:
X <- data.frame(A=rnorm(100), B=rnorm(100), C=rnorm(100))
cor(X)
Which will generate this output:
> cor(X)
A B C
A 1.00000000 -0.01199511 0.02337429
B -0.01199511 1.00000000 0.07918920
C 0.02337429 0.07918920 1.00000000
However, I have a custom function that I need to apply to each combination of columns. I am now using a solution that uses nested for loops, which works:
f <- function(x, y) sum((x+y)^2) # some placeholder function
out <- matrix(NA, ncol = ncol(X), nrow = ncol(X)) # pre-allocate
for(i in seq_along(X)) {
for(j in seq_along(X)) {
out[i, j] <- f(X[, i], X[, j]) # apply f() to each combination
}
}
Which produces:
> out
[,1] [,2] [,3]
[1,] 422.4447 207.0833 211.4198
[2,] 207.0833 409.1242 218.2430
[3,] 211.4198 218.2430 397.5321
I am currently trying to transition into the tidyverse and would prefer to avoid using for loops. Could someone show me a tidy solution for this situation? Thanks!

Answer 1

You could do
library(tidyverse)
f <- function(x, y) sum((x+y)^2)
X <- data.frame(A=rnorm(100), B=rnorm(100), C=rnorm(100))
as.list(X) %>%
expand.grid(., .) %>%
mutate(out = map2_dbl(Var1, Var2, f)) %>%
as_tibble()

Answer 2

This isn’t a tidyverse solution, but it does avoid using for loops. We use RcppAlgos (I am the author) to generate all pair-wise permutations of columns and apply your custom function to each of these. After that, we coerce to a matrix.
set.seed(42)
X <- data.frame(A=rnorm(100), B=rnorm(100), C=rnorm(100))
library(RcppAlgos)
matrix(permuteGeneral(ncol(X), 2, repetition = TRUE, FUN = function(y) {
sum((X[,y[1]] + X[,y[2]])^2)
}), ncol = ncol(X))
# [,1] [,2] [,3]
# [1,] 429.8549 194.4271 179.4449
# [2,] 194.4271 326.8032 197.2585
# [3,] 179.4449 197.2585 409.6313

Answer 3

Using base R you could do:
set.seed(42)
X <- data.frame(A=rnorm(100), B=rnorm(100), C=rnorm(100))
OUT = diag(colSums((X+X)^2))
OUT[lower.tri(OUT)] = combn(X, 2, function(x) sum(do.call('+', x)^2)) #combn(X,2,function(x)sum(rowSums(x)^2))
OUT[upper.tri(OUT)] = OUT[lower.tri(OUT)]
OUT
[,1] [,2] [,3]
[1,] 429.8549 194.4271 179.4449
[2,] 194.4271 326.8032 197.2585
[3,] 179.4449 197.2585 409.6313