Re: Functional programming puzzle

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1822] Re: Functional programming puzzle*From*: drc at gate.net (David Cabana)*Date*: Thu, 3 Aug 1995 23:51:55 -0400

In article <DCGM0w.5GH at wri.com>, "Wm. Martin McClain" <wmm at chem.wayne.edu> wrote: >Dear functional programers: > >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] > >But Mathematica returns a mess, because Outer seems >to Flatten the ptList before running the outer >product loops. ... >I am so frustrated that I am TEMPTED to do it with >explicit indices. > >Please, somebody help me before this happens. Martin, One way to clean things up is to introduce a datatype, the point. Then things will work the way you want: In[54]:= ptList = {point[1,1,2], point[2,1,3], point[1,3,2]}; distance[x_point,y_point]:= Module[{a,b}, a=Apply[List,x]; b=Apply[List,y]; Sqrt[(a-b).(a-b)] ]; Outer[distance,ptList,ptList] Out[56]= {{0, Sqrt[2], 2}, {Sqrt[2], 0, Sqrt[6]}, {2, Sqrt[6], 0}} Regards, -- David Cabana drc at gate.net