Re: Re: distance function

*To*: mathgroup at smc.vnet.net*Subject*: [mg68805] Re: [mg68772] Re: distance function*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 19 Aug 2006 00:41:08 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200608160736.DAA06170@smc.vnet.net> <ec1aub$ou9$1@smc.vnet.net> <200608180712.DAA02070@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

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. >>> >>> > > -- 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

**References**:**distance function***From:*dimmechan@yahoo.com

**Re: distance function***From:*Jens-Peer Kuska <kuska@informatik.uni-leipzig.de>