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MapThread works fine and dandy with rectangular list structures:

MapThread[f, {{{a, b}, {c, d}}, {{1, 2}, {3, 4}}}, 2]

{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4]}}

But with a ragged structure, it starts complaining:

MapThread[f, {{{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}}, 2]

MapThread::mptd: "Object {{a,b},{c,d,e}} at position {2, 1} in MapThread[f,{{{a,b},{c,d,e}},{{1,2},{3,4,5}}},2] has only 1 of required 2 dimensions."

whereas I'd like:

{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4], f[e, 5]}}

I can't see any obvious way to achieve a pairing of the corresponding elements, but maybe you can?

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9 Answers 9

16
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Perhaps something like this, as a more general alternative? However, without tweaking it forget about level specification

Function[Null, f[##], Listable] @@ A
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3
  • $\begingroup$ The magic of Listable! I knew there must have been some nice way to do it. $\endgroup$
    – wxffles
    May 28, 2012 at 4:27
  • $\begingroup$ @wxffles I like it. If you actually want to give the arguments as separate lists like in your solution, you don't even need the Apply $\endgroup$
    – Rojo
    May 28, 2012 at 4:37
  • $\begingroup$ This is crazy amazing! MMA is effin' nuts in its state space a.e.! $\endgroup$
    – Gravifer
    Nov 1, 2022 at 14:09
13
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Here's a way to do it by mapping MapThread:

MapThread[f, #] & /@ Transpose[{{{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}}]
(* {{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4], f[e, 5]}} *)
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2
  • 1
    $\begingroup$ This works great if you are working at level 2. I was hoping for something more general. Next time I'll try asking! $\endgroup$
    – wxffles
    May 28, 2012 at 3:42
  • 4
    $\begingroup$ @wxffles please provide more examples if you want a more general solution. $\endgroup$
    – Mr.Wizard
    May 28, 2012 at 3:47
12
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It's probably bad form to answer your own question, but I did manage to get something to work while I was waiting:

myMapThread[f_, list1_, list2_, level_] := 
  Module[{s}, Function[s, 
     Reap[MapIndexed[Sow[f[#1, s[[Sequence @@ #2]]]] &, list1, {level}]][[1]]]
     [list2]];

Usage:

myMapThread[f, {{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}, 2]

{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4], f[e, 5]}}

It's quite ugly though.

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1
7
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ClearAll[raggedThread]
raggedThread = Inner[Thread @* #, ##2, List] &;

Example:

raggedThread[f, {{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}]
{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4], f[e, 5]}}
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2
  • $\begingroup$ Necromancer badge :-) $\endgroup$
    – Mr.Wizard
    Jun 13, 2020 at 13:38
  • $\begingroup$ Thank you @Mr.Wizard. $\endgroup$
    – kglr
    Jun 13, 2020 at 16:03
6
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MapThread[f, lst[[1 ;; 2, #]]] & /@ {1, 2}

gives

(*{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4], f[e, 5]}}*)

If

lst2 = {{{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}, {{aa, bb}, {cc, dd, ee}}};
MapThread[f, lst2[[1 ;; 3, #]]] & /@ {1, 2}

gives

(*{{f[a, 1, aa], f[b, 2, bb]}, {f[c, 3, cc], f[d, 4, dd], f[e, 5, ee]}}*)
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2
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x = {{a, b}, {c, d, e}};
y = {{1, 2}, {3, 4, 5}};

MapApply[f] /@ Transpose /@ Transpose[{x, y}]

{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4], f[e, 5]}}

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1
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Using the third argument of GroupBy to cover the ragged array case:

myMapThread[f_, list_] := 
If[TensorQ[list], f @@@ # &@*Thread /@ Transpose@list, 
Values[GroupBy[Catenate[list], Length, f @@@ # &@*Thread]]]

Testing myMapThread:

list1 = {{{a, b}, {c, d}}, {{1, 2}, {3, 4}}};
list2 = {{{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}};

myMapThread[f, list1]

(*{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4]}}*)

myMapThread[f, list2]

(*{{f[a, 1], f[b, 2]}, {f[c, 3], f[d, 4], f[e, 5]}}*)
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0
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threadRagged = Apply[#, Flatten[{##2}, {{2}, {3}}], {2}] &;

Examples:

{x, y} = {{{a, b}, {c, d, e}}, y = {{1, 2}, {3, 4, 5}}};

threadRagged[f, x, y]
{{f[a, 1], f[b, 2]},   
 {f[c, 3], f[d, 4], f[e, 5]}}
lst2 = {{{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}, {{aa, bb}, {cc, dd, ee}}};

threadRagged[F, ## & @@ lst2]
 {{F[a, 1, aa], F[b, 2, bb]},   
  {F[c, 3, cc], F[d, 4, dd], F[e, 5, ee]}}
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0
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threadTwice = Map[Thread]@Thread[#@##2, List, Length @ {##2}] &;

Examples:

{x, y} = {{{a, b}, {c, d, e}}, y = {{1, 2}, {3, 4, 5}}};

threadTwice[f, x, y]
 {{f[a, 1], f[b, 2]},   
  {f[c, 3], f[d, 4], f[e, 5]}}
lst2 = {{{a, b}, {c, d, e}}, {{1, 2}, {3, 4, 5}}, {{aa, bb}, {cc, dd, ee}}};

threadTwice[f, ## & @@ lst2]
{{f[a, 1, aa], f[b, 2, bb]},   
 {f[c, 3, cc], f[d, 4, dd], f[e, 5, ee]}}
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