Re: Newbie question: pairswise function application

*To*: mathgroup at smc.vnet.net*Subject*: [mg23869] Re: [mg23857] Newbie question: pairswise function application*From*: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>*Date*: Thu, 15 Jun 2000 00:51:07 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

on 6/12/00 2:17 PM, Sidney Cadot at sidney at janis.pds.tudelft.nl wrote: > Hi, > > Wandering through the 1500-odd pages of the Mathematica book, I can't > find the solution to the following rather silly problem: > > I have a list L consisting of (a lot of) integers, and I want to apply a > function f to all pairs of numbers; furthermore, I don't want to > calculate both f[a,b] and f[b,a]: > > L = {1,5,19,100}; > > ... and I want: > > { f[1,5], f[1,19], f[1,100], f[5,19], f[5,100], f[19,100] } > > Can anyone please tell me how to do this? I'd prefer a smart solution > (i.e., not just generating all pairs, then throwing away a lot of them) > since my lists tend to get rather large. > > Thanks in advance, > > Sidney Cadot > sidney at janis.pds.twi.tudelft.nl > There is already such a faunction in the package DiscreteMath`Combinatorica`. It is called KSubsets: << DiscreteMath`Combinatorica` In[2]:= f @@@ KSubsets[{1, 5, 19, 100}, 2] Out[2]= {f[1, 5], f[1, 19], f[1, 100], f[5, 19], f[5, 100], f[19, 100]} I do not know how fast this is (functions in this package tend to be not teribly fast since it has not been significantly updated for a long time) but it uses backtracking so it should do better than making a list of all pairs and throwing away some. There is actually a vast number of ways to program something like this. I shall not try to consider efficiency (there are regular contributors to this list who know a lot more about this aspect than me and I expect some of them will contribute their versions) but instead give an example of the kind of Mathematica programming style which is the reason why I think Mathematica is such a fantastic programming language for a mathematician: In[1]:= L = {1, 5, 19, 100}; In[2]:= Clear[myfunction] In[3]:= myfunction[i_, j_] /; i >= j := Sequence[]; myfunction[i_, j_] /; i < j := f[i, j] In[5]:= Distribute[myfunction[L, L], List] Out[5]= {f[1, 5], f[1, 19], f[1, 100], f[5, 19], f[5, 100], f[19, 100]} -- Andrzej Kozlowski Toyama International University, JAPAN For Mathematica related links and resources try: <http://www.sstreams.com/Mathematica/>