# Iterate over cartesian product of vectors

I have the following nested loop:

```for (x in xs) {
for (y in ys) {
# Do something with x and y
}
}
```

Which I’d like to flatten so I thought of building a Cartesian product of the two vectors xs and ys and iterating over the result. In Python, this would be trivial:

```for xy in product(xs, ys):
# x, y = xy[0], xy[1]
```

But in R, the simplest equivalent I’ve found looks daunting:

```xys <- expand.grid(xs, ys)
for (i in 1 : nrow(xys)) {
xy <- as.vector(xys[i, ])
# x <- xy[1], y <- xy[2]
}
```

Surely there must be a better way, no? (To clarify, I don’t want to iterate over an index … I think there must be a way to directly iterate over the tuples in the product.)

You can use the apply function to apply a function to each row of your data frame. Just replace "your function" with your actual function.

```# example data
xs <- rnorm(10)
ys <- rnorm(10)

apply(expand.grid(xs, ys), 1, FUN = function(x) {"your function"})
```

This is a very basic example. Here, the sum of both values in a row is calculated:

```apply(expand.grid(xs, ys), 1, FUN = function(x) {x[1] + x[2]})
```

Here is a variant that uses named arguments (xs, ys) instead of indices (x[1], x[2]):

```myfun <- function(xs, ys) xs + ys
arguments <- expand.grid(xs = rnorm(10), ys = rnorm(10))
apply(arguments, 1, function(x)do.call(myfun, as.list(x)))
```

R has a different paradigm than Python, so don't expect it to have generators or tuples -- we have vectors and indices for that.

This way, to map a function on a Cartesian product simply call

```outer(xs,ys,function(x,y) ...)
```

and undim the result if you wish.

EDIT: In case xs or ys are something more complex than base vectors, one option is to use indices, i.e.

```outer(seq(a=xs),seq(a=ys),function(xi,yi) ... xs[[xi]]/ys[xi,]/etc. ...)
```

or map a function on a bit hand-crafted product using mapply

```mapply(function(x,y) ...,xs,rep(ys,each=length(xs)))
```