       RE: Re: Re: distance function

• To: mathgroup at smc.vnet.net
• Subject: [mg70014] RE: [mg68805] Re: [mg68772] Re: distance function
• From: "Coleman, Mark" <Mark.Coleman at LibertyMutual.com>
• Date: Sat, 30 Sep 2006 05:12:45 -0400 (EDT)

```
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: [mg70014] [mg68805] Re: [mg68772] 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
>>>
>>> "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

>>>
>>> Thanks in advance for any help.
>>>
>>>
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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