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Re: "misbehaving" Union function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24096] Re: [mg24075] "misbehaving" Union function
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Tue, 27 Jun 2000 00:51:52 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I have to send a correction to this posting. What I wrote was correct, and
the solution given works, but the reason for the problem was not correctly
identified. I looked at your example carefully and now I can see that when
union is applied with the default setting the two elements that look the
same are indeed sorted so as to be adjacent to each other. The problem is,
however, that that are close enough tobe considered Equal but not to be
considered SameQ. (You can see that by applying FullForm to your original
answer). That's why the setting SameTest->Equal will remove the apparent
duplicates while SameTest->Automatic (default) and SameTest->SameQ will not.

Andrzej
on 00.6.23 11:04 PM, Andrzej Kozlowski at andrzej at tuins.ac.jp wrote:

> The explanation is as follows. Union admits one option: SameTest. This comes
> with the default setting of Automatic. With this default setting the
> elements of the list to which Union is being applied are first sorted in
> canonical order and then only the adjacent elements are compared. This has
> the advantage of speed. However, when working with approximate numbers, two
> numbers (or list of numbers in your case) which are close enough to be
> considered equal may not end up as being adjacent after sorting. When that
> happens both may be kept. So the solution is to use an explicit setting for
> SameTest: SameTest->Equal. If you use Union[...,SameTest->Equal] instead of
> Union[...] in your example you will get the output:
> 
> Out[26]=
> {{0, 0.}, {6, 2.}, {14, 6.}, {15, 7.}, {25, 11.}, {26, 12.}}
> 
> Andrzej Kozlowski
> 
> 
> -- 
> Andrzej Kozlowski
> Toyama International University, JAPAN
> 
> For Mathematica related links and resources try:
> <http://www.sstreams.com/Mathematica/>
> 
> 
> 
> on 6/23/00 3:26 PM, Felix Farkas at farkas at ica.epfl.ch wrote:
> 
>> Hi,
>> i am trying to build up a list of points. The input is,
>> a list of events. I use the Union function in order to
>> avoid duplicate points. however i do not have the expected result.
>> i really don't know where the error is coming from.
>> Could somebody, please, tell me where is the fault?
>> I would greatly appreciate any suggestions.
>> 
>> Many thanks in advance.
>> Regards,
>> Felix
>> 
>> Here is the function:
>> 
>> In[1]:= Genpoints[events_] :=
>> Module[
>> {ev = events, rate,
>> duration, time, burst, bytes = 0, points = {}},
>> rate := ee[[3]];
>> duration := ee[[2]];
>> time := ee[[1]];
>> burst := ee[[4]];
>> While[Length[ev] != 0,
>> ee = First[ev];
>> ev = Rest[ev];
>> points = Union[points,
>> If[rate == -1,
>> (*then*)
>> bytes += burst; {{time,
>> bytes - burst}, {time, bytes}},
>> (*else*)
>> bytes += rate*duration;
>> Print[{{time, bytes - rate*duration}, {time + duration,
>> bytes}}];
>> {{time, bytes -
>> rate*duration}, {time + duration, bytes}}]
>> ]
>> ];
>> points
>> ]
>> 
>> The output generated is:
>> 
>> In[2]:= aa = {{0, 6, 0.3333333, 2, 2, 1},
>> {6, 8, 0.5, 4, 2, 1}, {14, 1, 1, 1, 2, 1},
>> {15, 10, 0.4, 4, 2, 1}, {25, 1, 1, 1, 2, 1}};
>> In[3]:=  po2 = Genpoints[aa]
>> Out[3]= {{0, 0.}, {6, 2.}, {6, 2.}, {14, 6.},
>> {15, 7.}, {25, 11.}, {26, 12.}}
>> 
>> 
>> 
>> -----------------------------------------------------------------------------
>> Felix Farkas
>> EPFL-DSC-ICA
>> IN-Ecublens
>> CH-1015 Lausanne
>> Switzerland
>> 
>> tel:       0041 21 693 6601
>> fax:       0041 21 693 6610
>> email:     felix.farkas at epfl.ch
>> 
>> 
>> 
> 

-- 
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/



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