Re: fastest way to do pair-sum / make pair-list

*To*: mathgroup at smc.vnet.net*Subject*: [mg23185] Re: [mg23170] fastest way to do pair-sum / make pair-list*From*: "Ralf D. Pluch" <aon.912308612 at aon.at>*Date*: Mon, 24 Apr 2000 01:11:56 -0400 (EDT)*References*: <200004210348.XAA19772@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

ladies & gentlemen, please use following adress for your comments. duke_of_snowboard at gmx.at thank's a lot in advance. Philipp Pluch Wijnand Schepens schrieb: > 1. > > What is the most efficient way to calculate the sum > > Sum f [ (x[[i]]-x[[j]])^2 ] > i<j > > ?? > > Example: > > I have a vector of real numbers: > lst = N[Range[100]]; > and a function operating on a number: > f[r2_]:=(r2-1.0)^2 > > Is > > Sum[ Sum[ f [ (lst[[i]]-lst[[j]])^2 ] , {j,i+1,Length[lst]}], > {i,1,Length[lst-1]}] > > the fastest way?? > > This kind of sum is very common in Molecular Modelling, where the total > energy of a system is often a sum of pair-energies, which only depend on > the distance between atoms. > I was surprised that I didn't find anything on sums over pairs in > Mathematica... > > 2. > > What is the most efficient way to generate a list of pairs starting from > a list?? > Is there a standard Mathematica routine which does this? > > e.g. {a,b,c,d} ----> {{a,b},{a,c},{a,d},{b,c},{b,d},{c,d}} > > or {x1,x2,...} -----> { {xi,xj} ...} > with i<j > > Best solution I found was > topairs[lst_] := > Module[{l=Length[lst]}, > Map[(Sequence @@ #1) &, > Table[ lst [[{i, j}]], {i, 1, l - 1}, {j, i + 1, l}] > ] > ] > > Another possibility would be > topairs2[lst_] := > Module[{l = Length[lst]}, > Partition[ > Flatten[ > Table[ lst[[{i, j}]], {i, 1, l - 1}, {j, i + 1, l}] > ], 2 > ] > ] > > but this doesn't have the same effect if operating on a list of lists > topairs[{{a1, a2}, {b1, b2}, {c1, c2}}] > gives what we want, > topairs2[{{a1, a2}, {b1, b2}, {c1, c2}}] > not

**References**:**fastest way to do pair-sum / make pair-list***From:*Wijnand Schepens <Wijnand.Schepens@rug.ac.be>