Is there a R function that applies a function to each pair of columns?

Question

I often need to apply a function to each pair of columns in a dataframe/matrix and return the results in a matrix. Now I always write a loop to do this. For instance, to make a matrix containing the p-values of correlations I write:

df <- data.frame(x=rnorm(100),y=rnorm(100),z=rnorm(100))

n <- ncol(df)

foo <- matrix(0,n,n)

for ( i in 1:n)
{
    for (j in i:n)
    {
        foo[i,j] <- cor.test(df[,i],df[,j])$p.value
    }
}

foo[lower.tri(foo)] <- t(foo)[lower.tri(foo)]

foo
          [,1]      [,2]      [,3]
[1,] 0.0000000 0.7215071 0.5651266
[2,] 0.7215071 0.0000000 0.9019746
[3,] 0.5651266 0.9019746 0.0000000

which works, but is quite slow for very large matrices. I can write a function for this in R (not bothering with cutting time in half by assuming a symmetrical outcome as above):

Papply <- function(x,fun)
{
n <- ncol(x)

foo <- matrix(0,n,n)
for ( i in 1:n)
{
    for (j in 1:n)
    {
        foo[i,j] <- fun(x[,i],x[,j])
    }
}
return(foo)
}

Or a function with Rcpp:

library("Rcpp")
library("inline")

src <- 
'
NumericMatrix x(xR);
Function f(fun);
NumericMatrix y(x.ncol(),x.ncol());

for (int i = 0; i < x.ncol(); i++)
{
    for (int j = 0; j < x.ncol(); j++)
    {
        y(i,j) = as<double>(f(wrap(x(_,i)),wrap(x(_,j))));
    }
}
return wrap(y);
'

Papply2 <- cxxfunction(signature(xR="numeric",fun="function"),src,plugin="Rcpp")

But both are quite slow even on a pretty small dataset of 100 variables ( I thought the Rcpp function would be faster, but I guess conversion between R and C++ all the time takes its toll):

> system.time(Papply(matrix(rnorm(100*300),300,100),function(x,y)cor.test(x,y)$p.value))
   user  system elapsed 
   3.73    0.00    3.73 
> system.time(Papply2(matrix(rnorm(100*300),300,100),function(x,y)cor.test(x,y)$p.value))
   user  system elapsed 
   3.71    0.02    3.75 

So my question is:

1. Due to the simplicity of these functions I assume this is already somewhere in R. Is there an apply or plyr function that does this? I have looked for it but haven't been able to find it.
2. If so, is it faster?

Answer 1

It wouldn't be faster, but you can use outer to simplify the code. It does require a vectorized function, so here I've used Vectorize to make a vectorized version of the function to get the correlation between two columns.

df <- data.frame(x=rnorm(100),y=rnorm(100),z=rnorm(100))
n <- ncol(df)

corpij <- function(i,j,data) {cor.test(data[,i],data[,j])$p.value}
corp <- Vectorize(corpij, vectorize.args=list("i","j"))
outer(1:n,1:n,corp,data=df)