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

*To*: mathgroup at smc.vnet.net*Subject*: [mg29714] Re: Swiftest code to turn list of ordered pairs into Markov matrix*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Wed, 4 Jul 2001 03:08:39 -0400 (EDT)*References*: <9hs1a0$bs9$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Seth, z= 50; oplist= Table[Random[Integer,{1,z}],{100000},{2}]; a=Fold[ReplacePart[#,Extract[#,#2]+1,#2]&,Table[0,{z},{z}],oplist];//Timing {44.6 Second,Null} (*I replaced {#2} with #2 -- the former gave trouble that I have not yet tracked down*) (b=Table[0,{z},{z}]; MapThread[(b[[Sequence@@#1]]=#2)&, {First/@#,Length/@# }]&[ Split[Sort[oplist]]]);//Timing {4.84 Second,Null} a===b True -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Seth Chandler" <SChandler at Central.UH.Edu> wrote in message news:9hs1a0$bs9$1 at smc.vnet.net... > 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. > > Thanks, > > Seth J. Chandler > Associate Professor of Law > University of Houston Law Center > > > >