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Re: distance function

• To: mathgroup at smc.vnet.net
• Subject: [mg70037] Re: distance function
• From: Peter Pein <petsie at dordos.net>
• Date: Sun, 1 Oct 2006 04:08:22 -0400 (EDT)
• References: <efldsn$daa$1@smc.vnet.net>

Coleman, Mark schrieb:
>  
> Out of curiosity, I tested these two approaches on a number of data sets
> for which I make frequent use. For some reason Jens code is running
> slower! I've been testing it out some lists of reals of size
> n=500,1000,2500, and 5000. Is it possible that the time for the
> conditional compares is exceeding the computational time of redundant
> calculations? Could someone try this out?
> 
> (note: I'm working on some code for identifying outliers in large data
> sets. The efficient calculation of L-1 and L-2 distance matrices are
> important.)
> 
> Thanks
> 
> Mark
> 
> 
> -----Original Message-----
> From: Murray Eisenberg [mailto:murray at math.umass.edu] 
To: mathgroup at smc.vnet.net
> Subject: [mg70037]  Re: distance function
> 
> Yes, I KNOW that I'm computing the distances twice in my solution: 
> that's why I said it's an "extravagant" solution!
> 
> Jens-Peer Kuska wrote:
>> Hi Murray,
>>
>> at least you should compute the distances not twice because the matrix
> 
>> is symmetric with zero diagonal ...
>>
>> d[{p_,p_}]:=0.0
>> d[{q_,p_}]/; OrderedQ[{q,p}]:=d[{q,p}]= Norm[p - q] 
>> d[{q_,p_}]:=d[{p,q}]
>>
>> Regards
>>    Jens
>>
>>
>> Murray Eisenberg wrote:
>>> If you don't mind an "extravagant" solution -- one that is 
>>> conceptually simple and short but is probably inefficient due to 
>>> redundant calculations -- then this works, I believe:
>>>
>>>    d[{p_, q_}] := Norm[p - q]
>>>    allDistances[pts_] := Union[Flatten[Outer[d, pts, pts]]]
>>>
>>>
>>>
>>> dimmechan at yahoo.com wrote:
>>>> In the book of Gaylord et al. (1996) there is one exercise which 
>>>> asks (see page 113)
>>>>
>>>> "Given a list of points in the plane, write a function that finds 
>>>> the set of all distances between the points."
>>>>
>>>> Although there is one solution, that solution makes use of the Table
> 
>>>> and Length commands.
>>>>
>>>> Is it a way to define the same function using Higher-Order functions
> 
>>>> like Outer, MapThread etc?
>>>>
>>>> Thanks in advance for any help.
>>>>
>>>>
>>
> 

Hi Mark,

  I think the most efficient proposal came from Bob Hanlon. I tested 
some alternatives and the fastest is d @@@S ubsets[pts, {2}] (2.98s for 
1000 points) followed by d @@@ Flatten[MapIndexed[Drop[#1, #2[[1]]-1] &, 
Outer[List, Most@pts, Rest@pts, 1]], 1] with 3.31 s.

Peter