How to map a function over two lists, first one and than the other?
For example, assuming I have two lists {a,b,c} and {d,e,f}:
[#1 + #2] & /@ {{a,b,c},{d,e,f}}
That maps the expression simultaneously, but I want a result looking like:
{{a+d},{a+e},{a+f},{b+d},{b+e},...}
You can use Outer or Tuples as follows:
Join @@ Outer[List @* Plus, {a, b, c}, {d, e, f}]
{{a + d}, {a + e}, {a + f}, {b + d}, {b + e}, {b + f}, {c + d}, {c + e}, {c + f}}
Map[List @* Total] @ Tuples[ {{a, b, c}, {d, e, f}}]
{{a + d}, {a + e}, {a + f}, {b + d}, {b + e}, {b + f}, {c + d}, {c + e}, {c + f}}
Also
List /@ Total /@ Tuples[ {{a, b, c}, {d, e, f}}] (* or *)
Tuples[foo[{a, b, c}, {d, e, f}]] /. foo -> List @* Plus
{{a + d}, {a + e}, {a + f}, {b + d}, {b + e}, {b + f}, {c + d}, {c + e}, {c + f}}
{{a, b, c}, {d, e, f}} // Tuples // Map[Total /* List]
$\endgroup$
– Gustavo Delfino
Aug 8 at 13:13
Try using Distribute:
Distribute[{{a, b, c}, {d, e, f}}, List]
(*{{a, d}, {a, e}, {a, f}, {b, d}, {b, e}, {b, f}, {c, d}, {c, e}, {c,f}}*)
As with other solutions, you have to do some cleaning up afterword, but you can use Table with lists defining the iterators:
Flatten[Table[{i + j}, {i, {a, b, c}}, {j, {d, e, f}}], 1]
If you really want to map it onto the lists, you can use the following, but the result is the same:
Flatten[Table[{i + j}, {i, #1}, {j, #2}], 1] & @@ {{a, b, c}, {d, e, f}}
either option outputs:
{{a + d}, {a + e}, {a + f}, {b + d}, {b + e}, {b + f}, {c + d}, {c + e}, {c + f}}
{{a, b, c}, {d, e, f}} // Total? p.s.[#1 + #2] & /@is not a valid syntax. $\endgroup$ – Kuba♦ Aug 8 at 10:01