Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2001
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2001

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: Re: Equations
  • Next by Date: newsgroup use
  • Previous by thread: Re: Swiftest code to turn list of ordered pairs into Markov matrix
  • Next by thread: Re: Swiftest code to turn list of ordered pairs into Markov matrix