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MathGroup Archive 2000

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Re: Newbie question: pairswise function application

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24015] Re: Newbie question: pairswise function application
  • From: Hartmut Wolf <hwolf at debis.com>
  • Date: Tue, 20 Jun 2000 03:07:31 -0400 (EDT)
  • Organization: debis Systemhaus
  • References: <8i1t6n$jn9@smc.vnet.net> <Pine.GSO.4.21.0006131745370.18990-100000@flip.eecs.umich.edu> <tXg25.30$x6.4664@ralph.vnet.net> <8ihv93$lfd@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Allan, 

a little remark to be made, see below:

Allan Hayes schrieb:
> 
> I have been concerned that the solution in my earlier posting did not give
> the requested order.
> The following slighty slower version does give the requested order and, on
> my tests,  is about three times as fast as fastest other solution posted.
> 
> pairs[data_, f_] :=
>   MapThread[f,
>     {Join @@ (NestList[Rest, Table[1, {# - 1}],
>                   # - 2]Drop[data, -1]),
>           Join @@ (NestList[Drop[#, 1] &, Drop[data, 1], # - 2])
>           } &[Length[data]]
> 
>     ]
> 
> If only the pairs are needed then the following seems to be particularly
> fast
> 
> pairs[data_] := Transpose[
>     {Join @@ (NestList[Rest, Table[1, {# - 1}],
>                   # - 2]Drop[data, -1]),
>           Join @@ (NestList[Drop[#, 1] &, Drop[data, 1], # - 2])
>           } &[Length[data]]
> 
>     ]
> 


your function indeed is fast 

In[20]:= 
Print[Timing[pairs[#, Times]][[1]]] & /@ (Range[100 #] & /@ Range[8]);
>From In[20]:= 0.191 Second
>From In[20]:= 0.55 Second
>From In[20]:= 1.181 Second
>From In[20]:= 2.143 Second
>From In[20]:= 3.365 Second
>From In[20]:= 5.277 Second
>From In[20]:= 7.401 Second
>From In[20]:= 9.764 Second

however has a less fortunate time complexity than what I had proposed earlier:

In[15]:=
Print[Timing[MapThread[Function[y, Times[#1, y]] /@ #2 &, 
                Through[{First, Rest}[NestList[Rest, #, Length[#]]]]] // 
              Flatten][[1]]] & /@ (Range[100 #] & /@ Range[8]);
>From In[15]:= 0.371 Second
>From In[15]:= 0.591 Second
>From In[15]:= 0.901 Second
>From In[15]:= 1.302 Second
>From In[15]:= 1.843 Second
>From In[15]:= 2.413 Second
>From In[15]:= 3.224 Second
>From In[15]:= 4.056 Second

Kind regards, 
	Hartmut



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