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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
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