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MathGroup Archive 1996

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Re: array ordered

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3197] Re: array ordered
  • From: Pasquale Nardone <pnardon at ulb.ac.be>
  • Date: Sat, 17 Feb 1996 14:14:36 -0500
  • Organization: Université Libre de Bruxelles
  • Sender: owner-wri-mathgroup at wolfram.com

I propose you to do the following code:
first define a function f with the following defs:
f[x_,f[y__]]:=f[x,y];
f[t___,x_,z___,x_,y___]:=0;
f[t___,x_,z___,y_,u___]:=f[t,y,z,x,u]/;(x>y)
f[0]:=0;
then define the function which will give you all part:

AllCombination[liste_]:=
Module[{tmp,res},
tmp=Select[
Complement[
Flatten[
Outer[f,liste,liste]],{}],(Head[#]==f)&];
res=Join[Map[f,liste],tmp];
Do[
{
tmp=Select[
Complement[
Flatten[Outer[f,liste,tmp]],{}],(Head[#]==f)&];
res=Join[res,tmp]},{Length[liste]-2}];
Return[res]]

that's it:

total=AllCombination[{1,2,3,4,5,6}]

contains all combination: f[1],f[2],...,f[1,2,3,4,5,6].
now you introduce your data

thick={0.48,0.71,1.41,3.45,5.61,13.49};

and an auxillary function:

g[x_]:=thick[[x]];
g[x_,y__]:=thick[[x]]+g[y];

which applyed to total gives:

thethickness=total/.{f->g}
{0.48, 0.71, 1.41, 3.45, 5.61, 13.49, 1.19, 1.89, 3.93, 6.09, 13.97, 
2.12, 4.16, 6.32, 14.2, 4.86, 7.02, 14.9, 9.06, 16.94, 19.1, 2.6, 
4.64, 6.8, 14.68, 5.34, 7.5, 15.38, 9.54, 17.42, 19.58, 5.57, 7.73, 
15.61, 9.77, 17.65, 19.81, 10.47, 18.35, 20.51, 22.55, 6.05, 8.21, 
16.09, 10.25, 18.13, 20.29, 10.95, 18.83, 20.99, 23.03, 11.18,19.06, 
21.22, 23.26, 23.96, 11.66, 19.54, 21.7, 23.74, 24.44, 24.67, 25.15}

now you can even write it in a nicer form:
Thread[List[total,thethickness]]
{
{f[1], 0.48}, 
{f[2], 0.71}, 
{f[3], 1.41},...
{f[1, 3], 1.89}, 
{f[1, 4], 3.93}, 
...
{f[1, 2, 3], 2.6}
...
{f[1, 3, 4, 5, 6], 24.44}, 
{f[2, 3, 4, 5, 6], 24.67}, 
{f[1, 2, 3, 4, 5, 6], 25.15}
}

good luck
--------------------------------------------
 Pasquale Nardone                          *
                                           *
 Universiti Libre de Bruxelles             *
 CP 231, Sciences-Physique                 *
 Bld du Triomphe                           *
 1050 Bruxelles, Belgium                   *
 tel: 650,55,15 fax: 650,57,67 (+32,2)     *
        ,,,
       (o o)
----ooO-(_)-Ooo----

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