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Functional programming puzzle
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg1821] Functional programming puzzle
*From*: "Wm. Martin McClain" <wmm at chem.wayne.edu>
*Date*: Thu, 3 Aug 1995 23:51:45 -0400
*Organization*: Wayne State University, College of Science
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 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.
I am so frustrated that I am TEMPTED to do it with
explicit indices.
Please, somebody help me before this happens.
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?
TIA- Martin McClain, Chemistry, Wayne State, Detroit
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