Cartesian product data frame

Question

I have three or more independent variables represented as R vectors, like so:

A <- c(1,2,3) B <- factor(c('x','y')) C <- c(0.1,0.5) 

and I want to take the Cartesian product of all of them and put the result into a data frame, like this:

A B C 1 x 0.1 1 x 0.5 1 y 0.1 1 y 0.5 2 x 0.1 2 x 0.5 2 y 0.1 2 y 0.5 3 x 0.1 3 x 0.5 3 y 0.1 3 y 0.5 

I can do this by manually writing out calls to rep:

d <- data.frame(A = rep(A, times=length(B)*length(C)),                 B = rep(B, times=length(A), each=length(C)),                 C = rep(C, each=length(A)*length(B)) 

but there must be a more elegant way to do it, yes? product in itertools does part of the job, but I can't find any way to absorb the output of an iterator and put it into a data frame. Any suggestions?

p.s. The next step in this calculation looks like

d$D <- f(d$A, d$B, d$C) 

so if you know a way to do both steps at once, that would also be helpful.

Answer 1

You can use expand.grid(A, B, C)

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EDIT: an alternative to using do.call to achieve the second part, is the function mdply from the package plyr:

library(plyr)  d = expand.grid(x = A, y = B, z = C) d = mdply(d, f) 

To illustrate its usage using a trivial function 'paste', you can try

d = mdply(d, 'paste', sep = '+'); 

Answer 2

There's a function manipulating dataframe, which is helpful in this case.

It can produce various join(in SQL terminology), while Cartesian product is a special case.

You have to convert the varibles to data frames first, because it take data frame as parameters.

so something like this will do:

A.B=merge(data.frame(A=A), data.frame(B=B),by=NULL); A.B.C=merge(A.B, data.frame(C=C),by=NULL); 

The only thing to care about is that rows are not sorted as you depicted. You may sort them manually as you wish.

merge(x, y, by = intersect(names(x), names(y)),       by.x = by, by.y = by, all = FALSE, all.x = all, all.y = all,       sort = TRUE, suffixes = c(".x",".y"),       incomparables = NULL, ...) 

"If by or both by.x and by.y are of length 0 (a length zero vector or NULL), the result, r, is the Cartesian product of x and y"

see this url for detail: http://stat.ethz.ch/R-manual/R-patched/library/base/html/merge.html