Re: programming problem about elements taken (CORRECTION)

• To: mathgroup at smc.vnet.net
• Subject: [mg72479] Re: [mg72470] programming problem about elements taken (CORRECTION)
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 31 Dec 2006 05:27:05 -0500 (EST)
• Reply-to: hanlonr at cox.net

The second function should have been written as

choose2[a_?VectorQ, epsilon_?NumericQ] := Module[
{sa = Sort[a], sel},
sel = Fold[If[#2 - Last[#1] > epsilon,
Append[#1, #2], #1] &, {First[sa]}, Rest[sa]];
Select[a, MemberQ[sel, #] &]];

Still much slower than choose1 but much better than the original choose2.

Bob Hanlon

---- Bob Hanlon <hanlonr at cox.net> wrote:
> For a sorted output:
>
> choose1[a_?VectorQ, epsilon_?NumericQ]:=Module[
>       {sa=Sort[a]},
>       Fold[If[#2-Last[#1]>epsilon,
>             Append[#1,#2],#1]&,{First[sa]},Rest[sa]]];
>
> To retain the original element order:
>
> choose2[a_?VectorQ, epsilon_?NumericQ]:=Module[
>       {sa=Sort[a]},
>       Select[a,MemberQ[Fold[If[#2-Last[#1]>epsilon,
>                   Append[#1,#2],#1]&,{First[sa]},Rest[sa]], #]&]];
>
> a=Table[Random[],{20}]
>
> {0.67319,0.378445,0.981498,0.579474,0.798173,0.537112,0.884835,0.534093,0.\
> 0471484,0.0516117,0.988746,0.570592,0.261828,0.632062,0.754747,0.436792,0.\
> 669037,0.149373,0.802271,0.484141}
>
> choose1[a,0.1]
>
> {0.0471484,0.149373,0.261828,0.378445,0.484141,0.632062,0.754747,0.884835,0.\
> 988746}
>
> choose2[a,0.1]
>
> {0.378445,0.884835,0.0471484,0.988746,0.261828,0.632062,0.754747,0.149373,0.\
> 484141}
>
> %%==Sort[%]
>
> True
>
> However, the second method (original order) is much slower for a large list.
>
> a=Table[Random[],{1000}];
>
> Timing[choose1[a,0.1];]
>
> {0.008364 Second,Null}
>
> Timing[choose2[a,0.1];]
>
> {1.23431 Second,Null}
>
>
> Bob Hanlon
>
> ---- Barrow <GRseminar at gmail.com> wrote:
> > Dear all,
> >   I have a list of numbers (A),in fact, they are numbers distributed
> > over [0,1].  Given parameter \epsilon, I have to choose elements from A
> > such that their distances are larger than \epsilon, so the elements are
> > "distringuishable". My goal is to find the maximum number of elements
> > from A to meet the above "distinct criterion".
> >   How to do it with the functions build-in in mathematica ??
> >   Thanks in advence.           Sincerely           Barrow
> >



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