How to apply or Map a function to a 2 variables nested list

Question

I tried to understand the mechanism of pure function tricks. Imaging I have a nested list generated by:

list=Table[{p, q}, {p, 1, 9, 2}, {q, -p, p, 2}]

Result:

>    {{{1, -1}, {1, 1}}, {{3, -3}, {3, -1}, {3, 1}, {3,     3}}, {{5,
> -5}, {5, -3}, {5, -1}, {5, 1}, {5, 3}, {5,     5}}, {{7, -7}, {7, -5}, {7, -3}, {7, -1}, {7, 1}, {7, 3}, {7,     5}, {7, 7}}, {{9, -9}, {9,
> -7}, {9, -5}, {9, -3}, {9, -1}, {9,     1}, {9, 3}, {9, 5}, {9, 7}, {9, 9}}}

And a function:

Fun[x_, y_] := Total[Sqrt[x^2 + y^2]]

I want the Fun to apply to each pair of the list to calculate the sum of all the result.

Should I use something like Fun[#1,#2]&/@list ? But it never works out, idk why.Thanks for your help!

Answer 1

Apply Fun at level 2 of list.

list = Table[{p, q}, {p, 1, 9, 2}, {q, -p, p, 2}];

Fun[x_, y_] := Total[Sqrt[x^2 + y^2]]

Apply[Fun, list, {2}]

Answer 2

Why not just re-define your function to

Fun2[{x_, y_}] := Total[Sqrt[x^2 + y^2]]

then

Map[Fun2, list, {2}]

Answer 3

You can solve your problem as follows:

llist = Flatten[list, 1]
Apply[Fun, llist, 1]

If the structure of list should be kept

Table[Apply[Fun, list[[i]], -1], {i, 1, Length[list]}]

Answer 4

If you wish to keep the structure of the list you can do something like

In[1]:= list = Table[{p, q}, {p, 1, 9, 2}, {q, -p, p, 2}];

In[2]:= Fun[x_, y_] := Total[Sqrt[x^2 + y^2]]

In[3]:= Map[Fun @@ # &, list, {2}]

Out[3]= {{5/2, 5/2}, {3 + Sqrt[2], 21/2, 21/2, 
  3 + Sqrt[2]}, {5 + Sqrt[2], 69/2, 53/2, 53/2, 69/2, 
  5 + Sqrt[2]}, {7 + Sqrt[2], 149/2, 117/2, 5 + Sqrt[2], 5 + Sqrt[2], 
  117/2, 149/2, 7 + Sqrt[2]}, {9 + Sqrt[2], 261/2, 213/2, 
  3 + Sqrt[10], 165/2, 165/2, 3 + Sqrt[10], 213/2, 261/2, 
  9 + Sqrt[2]}}