Implement cross join (cartesian product)

[kevinanewman]

• Describe what feature you would like to see implemented.
  Implement cross join (cartesian product) - every row of the left Frame combined with every row of the right Frame.

For example, in pandas:
cross_df = pd.merge(left_df, right_df, how='cross')

conceptually, this works but is very slow:
cross_dt = dt.rbind([dt.cbind(left_dt[i, :], right_dt[j, :]) for i in range(left_dt.nrows) for j in range(right_dt.nrows)])

• If possible, give an example of how it may look in the code and what result
  will be produced.

  left_dt = dt.Frame({'left_col': [1, 2, 3]})
  right_dt = dt.Frame({'right_col': [4, 5, 6]})
  
  cross_dt = left_dt[:, :, join(right_dt, how='cross')]  # something like this, I'm guessing
  
  print(cross_dt)
     | left_col  right_col
     |    int32      int32
  -- + --------  ---------
   0 |        1          4
   1 |        1          5
   2 |        1          6
   3 |        2          4
   4 |        2          5
   5 |        2          6
   6 |        3          4
   7 |        3          5
   8 |        3          6
  [9 rows x 2 columns]

• Click "Preview" to check that there are no formatting problems, that the
  request is stated clearly, and that it is not overbroad in scope.

• Thanks for contributing. We appreciate your input!

[samukweku]

any specific use case for this, @kevinanewman ?

[kevinanewman]

In my case, I use this to create the full-factorial combination of two dataframes. Each (relatively small and manageable) dataframe essentially contains sweeps of independent variables. It's easy to work with the small dataframes and then kick off a cross-join to combine them to create the much larger combined dataframe.

Hope this helps, thank you!