Re: Functional programming puzzle

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1827] Re: Functional programming puzzle*From*: Scott.A.Hill at williams.edu (Lancelot)*Date*: Thu, 3 Aug 1995 23:52:49 -0400*Organization*: Williams College, Williamstown MA

In article <DCGM0w.5GH at wri.com>, Wm. Martin McClain <wmm at chem.wayne.edu> wrote: >Let ptList = {{1,1,2},{2,1,3},{1,3,2}}; > >I want a matrix of distances between the points in ptList. >Any human would think you could get it with > >Rij[a_,b_]:=Sqrt[(a-b).(a-b)] > >followed by > >Outer[Rij,ptList,ptList] [snip] >I can do it for a short ptList this way: > >toNbrs = Thread[{p1,p2,p3}->ptList] >{p1->{1,1,2}, p2->{2,1,3}, p3->{1,3,2}} > >RijArray = Outer[Rij,{p1,p2,p3},{p1,p2,p3}]; >(gives output in terms of symbols p1, p2, and p3) > >Then replace the symbolic points by numerical >points, and give it a hand with Dot[0,0]: > >RijNbrs = RijArray /.toNbrs /. Sqrt[0 . 0]->0; > >The answer is, as desired, > >{{ 0, Sqrt[2], 2 }, > {Sqrt[2], 0, Sqrt[6]}, > { 2, Sqrt[6], 0 }} > >But this gets out of hand when ptList is long. Actually, this method will work with an arbitrary number of vectors, with a little bit of tweaking. Try this: Rij[a_,b_]:=Sqrt[(a-b).(a-b)] ptList={{1,1,2},{2,1,3},{1,3,2}} vectors=Table[p[i],{i,Length[ptList]}] toNbrs=Thread[vectors->ptList] RijArray=Outer[Rij,vectors,vectors] RijNbrs=RijArray/.toNbrs/.Sqrt[0 . 0]->0 The trick, of course, is to replace your list {p1,p2,p3} with a list of an aribitrary number of variables. p[1],p[2],p[3],... does the trick. You might want to add a Clear[p] afterwards if you had a large number of vectors and thus used a large number of p's. There _should_ be a more elegant way of doing this, but I don't know how. >Also, with explicit indices I could cut the number of >multiplies more than in half, because I know the >result will be symmetric, with only zeroes on the >diagonal. Is there some way to include this >knowledge in a functionally programmed version? Again, not that I know of. / :@-) Scott \ http://student_97ffa.williams.edu/~shill