Re: Swiftest code to turn list of ordered pairs into Markov matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg29710] Re: Swiftest code to turn list of ordered pairs into Markov matrix*From*: tgayley at wolfram.com (Todd Gayley)*Date*: Wed, 4 Jul 2001 03:08:34 -0400 (EDT)*Organization*: Wolfram Research, Inc.*References*: <9hs1a0$bs9$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Tue, 3 Jul 2001 08:55:28 +0000 (UTC), "Seth Chandler" <SChandler at Central.UH.Edu> wrote: >Suppose one has a list of ordered pairs oplist such as >{{1,5},{1,6},{2,3},{2,3} ... }. All the values in the list are positive >integers. The highest value in oplist is known to be some value z. > >Now one wishes to form a matrix such that the value at element i,j is equal >to >Count[oplist,{i,j}]. One terribly slow way to do this is > >Table[Count[oplist,{i,j}],{i,1,z},{j,1,z}] > >A faster way to do this is as follows: >Fold[ReplacePart[#,Extract[#,#2]+1,{#2}]&,Table[0,{z},{z}],oplist] > >Does anyone have a considerably faster way? A speed up of 100% or more would >be very helpful. > >For what it's worth Count[oplist,{something_,_}] is the same for all values >of something. > >P.S. The problem arises in converting a representation of a directed graph >into a Markov transition matrix. Seth, This is much faster for most z and lengths of oplist. The idea is to build and apply a set of replacement rules that associate an {i,j} pair with its count. Note the use of Dispatch, which makes an enormous difference. Array[List, {z,z}] /. Dispatch[First[#]->Length[#]& /@ Split[Sort[oplist]]] /. {_, _} -> 0 --Todd Gayley Wolfram Research