Writing a function with variable arguments

Question

I want to write a function which takes multiple arguments varying from 1 to n, where each argument is a triplet.

sublistProduct[{$a_1,b_1,c_1$},{$a_2,b_2,c_2$},...] = { $\Pi_{i=1}^{i=n}a_i ,\Pi_{i=1}^{i=n} b_i,\forall i \;\;max(c_i) $}

Any suggestions to write this function without multiple declaration and overloading.

For example sublistProduct[{1,2,3},{2,3,3},{3,4,5}] = {6,24,5} There can be any number of inputs(triplets) to the functions

@Mr.Wizard definitely related. BTW, how do you keep track of all your answers? :) — rcollyer, Apr 08 '15 at 15:17
@rcollyer For a while I was keeping a list, not only of my posts but any that were frequent duplicates, but recently I've just been using search which I seem to be getting better with. However since I remember my own wording or style better than I recall others I seem to find more of my own answers. I encourage you to link any I miss as you are able. By the way I just added two more links; I think at least one of these is a duplicate. Please vote if you agree. — Mr.Wizard, Apr 08 '15 at 15:20
@rcollyer Oops, one of those links was not a duplicate; I remembered it wrong. See, I don't keep track very well. ;-p — Mr.Wizard, Apr 08 '15 at 15:23
@rcollyer So I see. By the way I did vote for your answer below; it is specifically useful. — Mr.Wizard, Apr 08 '15 at 16:05
@Mr.Wizard thanks. I need to stay ahead of the whippersnappers who are trying to push me off the first page. — rcollyer, Apr 08 '15 at 16:10
15749 , is not related to this. Also 26686 this shows how to operate inside the tuple. It is possible to take transpose and operate over the elements, but I am not giving a list as input. So I have to convert it to a list. — drdebmath, Apr 10 '15 at 07:28
@drdebmath 15749 is somewhat related though not an answer to this. However this answer of mine shows exactly the same Transpose method and Repeated pattern that the Accepted answer below does, therefore I believe this does already have an answer as marked. The only possible difference that I can see is the "convert it to a list" part which is exactly what 15749 is about. — Mr.Wizard, Apr 10 '15 at 18:02
@Mr.Wizard the references sure did help. Thanks for your other answers.. :) — drdebmath, Apr 11 '15 at 06:09

rcollyer · Accepted Answer · 2015-04-10T17:41:51.663

1

The key is in defining the pattern correctly. I would use something like this:

Clear[f]
f[terms : {_, _, _} ..] := terms

which when used does this

f[{1,2,3}]
(* {1,2,3} *)
f[{1,2,3}, {2,3,4}]
(* Sequence[{1,2,3}, {2,3,4}] *)

So, to make effective use of that pattern, I would then put it into a list, e.g.

Clear[f]
f[terms : {_, _, _} ..] := {terms}

so that I can manipulate it at will. For instance,

Clear[f]
sublistProduct[terms : {_, _, _} ..] := 
  {Times@@#1, Times@@#2, Max@#3}& @@ Transpose[{terms}]

edited Apr 10 '15 at 17:41

answered Apr 08 '15 at 14:51

rcollyer

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This just creates clubbed list of terms in the first and second position of the triplet. Like sublistProduct[{1,2,2},{2,3,4}] = {{1,2},{2,3},4} – drdebmath Apr 10 '15 at 07:16
TImes function doesn't work on lists. Is there a method to remove the brackets from a list, when passing it to a function? – drdebmath Apr 10 '15 at 07:33
It worked, Just had to add another function Times2[{a__}]:= Times[a].. Thanks for the answer. I would have accepted it, had you included this also. – drdebmath Apr 10 '15 at 08:55
2

Better yet, just replace Times@ with Times@@ – LLlAMnYP Apr 10 '15 at 09:56
@LLlAMnYP yes, that's a mistake in my answer. Fixing now. – rcollyer Apr 10 '15 at 17:41

score 0 · Answer 2 · answered Apr 08 '15 at 14:51

Use BlankSequence in function definition, e.g. to get a list of all the first elements:

f[triplets__] := {triplets}[[All, 1]]

so you can use it as

f[{a1, b1, c1}, {a2, b2, c2}]
(* {a1, a2} *)

Note that this doesn't actually restrict you to using triplets as arguments for f, just that you have to give it one or more arguments.

Writing a function with variable arguments

2 Answers2