Cartesian product data frame

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

---

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 = '+');

With library tidyr one can use tidyr::crossing (order will be as in OP):

library(tidyr)
crossing(A,B,C)
# A tibble: 12 x 3
#        A B         C
#    <dbl> <fct> <dbl>
#  1     1 x       0.1
#  2     1 x       0.5
#  3     1 y       0.1
#  4     1 y       0.5
#  5     2 x       0.1
#  6     2 x       0.5
#  7     2 y       0.1
#  8     2 y       0.5
#  9     3 x       0.1
# 10     3 x       0.5
# 11     3 y       0.1
# 12     3 y       0.5 

The next step would be to use tidyverse and especially the purrr::pmap* family:

library(tidyverse)
crossing(A,B,C) %>% mutate(D = pmap_chr(.,paste,sep="_"))
# A tibble: 12 x 4
#        A B         C D      
#    <dbl> <fct> <dbl> <chr>  
#  1     1 x       0.1 1_1_0.1
#  2     1 x       0.5 1_1_0.5
#  3     1 y       0.1 1_2_0.1
#  4     1 y       0.5 1_2_0.5
#  5     2 x       0.1 2_1_0.1
#  6     2 x       0.5 2_1_0.5
#  7     2 y       0.1 2_2_0.1
#  8     2 y       0.5 2_2_0.5
#  9     3 x       0.1 3_1_0.1
# 10     3 x       0.5 3_1_0.5
# 11     3 y       0.1 3_2_0.1
# 12     3 y       0.5 3_2_0.5

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

Consider using the wonderful data.table library for expressiveness and speed. It handles many plyr use-cases (relational group by), along with transform, subset and relational join using a fairly simple uniform syntax.

library(data.table)
d <- CJ(x=A, y=B, z=C)  # Cross join
d[, w:=f(x,y,z)]  # Mutates the data.table

or in one line

d <- CJ(x=A, y=B, z=C)[, w:=f(x,y,z)]