Avoiding For loops to perform an assignment to a variable with indices of user-choice

Question

I am looking for an efficient way to perform the following operation without For loops

For[a = 1, a <= 2, a++,
 For[b = 1, b <= 2, b++,
  For[c = 1, c <= 2, c++,
   Subscript[
     EV, Aindex[[a]], Bindex[[b]], Cindex[[c]]] = 
     EVec[[a, b, c]];
   ]
  ]
 ]

where Aindex (similarly B,C) is a vector of indices relevant to my problem. In other words all I am doing is changing the label of the index. EVec carries all the information that I need, but using array index a,b,c >=1 is not an intuitive way of indexing in my case. Suggestions?

Have you seen `Do[]? Also see https://mathematica.stackexchange.com/questions/134609/why-should-i-avoid-the-for-loop-in-mathematica — Michael E2, Jul 26 '21 at 18:27
FYI, re Subscript: https://mathematica.stackexchange.com/a/18395/4999, point 3. "Really the best way to use subscripts is to not use them." — Michael E2, Jul 27 '21 at 15:36
I would have thought converting to a Do loop was easy, efficient, and morever, clear: Do[ Subscript[EV, Aindex[[a]], Bindex[[b]], Cindex[[c]]] = EVec[[a, b, c]], {a, 2}, {b, 2}, {c, 2}] — Michael E2, Jul 27 '21 at 22:36

Alan · Answer 1 · 2021-07-27T21:55:38.050

0

Can we assume the index vectors have no duplicates? If so, then using a helper function:

ClearAll[EV, Subscript]
Evec = RandomInteger[{0, 10}, {3, 3, 3}]  (* arbitrary *)
{Aindex, Bindex, Cindex} = Permutations[Range[3]][[;; 3]] - 2(* for example *)
fpos[i_, j_, k_] := Flatten@MapThread[Position, {{Aindex, Bindex, Cindex}, {i, j, k}}]
Subscript[EV, i_, j_, k_] := Extract[Evec, fpos[i, j, k]]

edited Jul 27 '21 at 21:55

answered Jul 26 '21 at 19:28

Alan

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Hi Alan, this wouldn't work. Because i,j,k in your suggestion will have to be integers as they index an array. I want to have the subscript to be read from a different list Aindex[[i]], Bindex[[i]] etc. In other words, its like a hash-lookup table that I am creating. – Saurabh Maiti Jul 27 '21 at 04:30
See edit for a new possibility. – Alan Jul 27 '21 at 15:13
It still looks like i,j,k need to be positive integers. Sorry for not being clear earlier. Let me explain the expected output. EVec[[a,b,c]] is NxNxN where a,b,c\in{1,2,...N} each. But the indices 1,2,3 etc are abstract. It helps, in my case to map {a,b,c} to a different scheme {Aindex,Bindex,Cindex} such that Aindex\in{-1,0.5,...}. Similarly something for B,C. The labels in the Aindex make it intuitive to write a larger code. In other words, for a triplet {a,b,c} there is a unique triplet (Aindex,Bindex,Cindex) such that Evec[a,b,c] = EV[Aindex,Bindex,Cindex]. That's what my 3 for loops did. – Saurabh Maiti Jul 27 '21 at 19:11
@SaurabhMaiti Oh right, sorry. I think I understand now. (New edit.) – Alan Jul 27 '21 at 21:56

Avoiding For loops to perform an assignment to a variable with indices of user-choice

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