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Re: Re: Threading objects of unequal length

  • To: mathgroup at
  • Subject: [mg8251] Re: [mg8163] Re: [mg8112] Threading objects of unequal length
  • From: "w.meeussen" <meeussen.vdmcc at>
  • Date: Sat, 23 Aug 1997 01:58:49 -0400
  • Sender: owner-wri-mathgroup at


the Null element in lists are a kind of dummy that can be used as
placeholders to keep the structure of a list intact. They can be removed by:

{{a, Null, c}, {d, Null, {Null, e, {f, Null}}}, g}
{{a, c}, {d, {e, {f}}}, g}

it would indeed be usefull to have a function to convert a list into a
tensor by padding Null elements where nescessary.


At 11:51 16-08-97 -0400, Olivier Gerard wrote:
>C. Woll wrote
>> Hi group,
>> I'm interested in adding variable length List. For example, I would like
>> to do something like
>> {a,b}+{c,d,e}+{f}
>> to return
>> {a+c+f,b+d,e}
>> Of course, Plus doesn't work, since you can't thread objects of unequal
>> length.
>>  [ more follows...]
>For the specific task of Plus, which is very easy to
>handle because there is a neutral element (namely 0),
>you can do something like that:
>PaddedPlus[ jk__List ] :=
>Module[{mlotl}, mlotl=Max[Map[Length, List[jk]]];
>Plus@@Map[Join[#1,Array[0&,mlotl-Length[#1]]]&, List[jk]] ]
>PaddedPlus[ {a,b}, {c,d,e,f},{g,h,i}]
>{a + c + g, b + d + h, e + i, f}
>This is only a rough interpretation, mostly valable for
>sets of lists irregular only at the first level. For more
>nested cases, one should be a bit more cautious and imaginative.
>Also, the reason why Thread does not do something like this
>is that many behaviors are possible in this situation.
>(By the way, my code is easy modifiable to the case were
>you want the lists to be justified to the right instead of the
>left or even to a few differents kind of centering).
>> So what is a good way of defining a function to do this? To be specific, I
>> would like a function g which accepts multiple arguments, and when given
>> an input like
>> g[{a,b}, {c,d,e}, {f}]
>> returns
>> {h[a,c,f],h[b,d],h[e]}
>> where in my particular application, I want h to be Plus. However, it would
>> be nice to have the function work for arbitrary heads.
>> I could do something like padding each of the arguments with some dummy
>> variable so that everything has the same length, then threading, then
>> removing the dummy variable, but that seems very cumbersome. Can anyone
>> think of a better way?
>> Thanks for any comments.
>> Carl Woll
>> Physics Dept
>> U of Washington
>A good way in my opinion would be to have a very powerful syntax
>for a generalization of Transpose and a neutral element for being
>in a list or for list ap/pre-pending.
>I have been proposing that many times to WRI. Anyone listening ?
>Here is an easy implementation of the idea you mention, restricted
>to your original purpose and you can see it is not so cumbersome:
>(* Code *)
>TestEltQ[NotAnElt] = False;
>TestEltQ[__] = True;
>SetAttributes[PaddedThread, HoldAll]
>PaddedThread[ hd_Symbol[jk__List] ] :=
>Module[{mlotl=Max[Map[Length, List[jk]]]},
>Map[ hd@@Select[#1,TestEltQ]&,
>Transpose[Map[Join[#1,Array[NotAnElt&,mlotl-Length[#1]]]&, List[jk]]] ]
>(* Example *)
>PaddedThread[ FTGT[{a,b}, {c,d,e,f},{g,h,i}] ]
>{FTGT[a, c, g], FTGT[b, d, h], FTGT[e, i], FTGT[f]}
>This 'version' of Thread has not all the features of the original
>but it would not be difficult to make it so. We can imagine an
>option with values Left, Right for the kind of padding and a few other things.
>Another way of doing what you want to do is to play with indices
>of elements in the lists. It is often inefficient in Mathematica
>compared to List programming. I would be very interested if someone
>has another idea.
>Of course, the ideas I alluded to have broader uses and could
>be a significant addition to Mathematica programming language
>but to be implemented both generally and efficiently they require
>more code and intermediate functions to help users master their power.
>Hope this helps,
>Olivier Gerard
>Mathematica Developper

Dr. Wouter L. J. MEEUSSEN
eu000949 at
w.meeussen.vdmcc at

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