Re: Faster Random Walk Simulation ?!?
- To: mathgroup at smc.vnet.net
- Subject: [mg66232] Re: Faster Random Walk Simulation ?!?
- From: Roland Franzius <roland.franzius at uos.de>
- Date: Fri, 5 May 2006 05:02:05 -0400 (EDT)
- Organization: Universitaet Hannover
- References: <e39k1n$cmn$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
mfific at gmail.com schrieb: > Dear All, > I am running a simulation with Mathematica 5 that includes random walk > described below. The argument boundaryA is upper and lower boundary for > a random walk. Parameter "value" is just a constant arbitrarily set to > 0.5. The output of the table function is the 10000 random walks, and > their path to either +5 or -5 boundary value. > While everything works as expected, it takes considerable duration of > time. For example it takes 2.6 seconds to generate the table output, on > a relatively fast computer. > > I would very appreciate if any significantly faster solution could be > suggested. > > > value = .5 > > > RandomWalk[boundaryA_] := Block[{l = {{0, 0}}, x = 0, > i = 0 }, While[boundaryA > x > -boundaryA, > x += If[Random[] > value, 1, -1]; > l = Append[l, {++i, x}]]; > l] > > Timing[Table[RandomWalk[5], {i, 1, 10000}];] > > Out[420]= > {2.672 Second, Null} Does not save much time but a bit Step=(2*Random[Integer, {0, 1}] + # - 1) & cd[bound_] := (Transpose[{Range[1, Length[#]], #}] &)[ NestWhileList[Step,0, Abs[ #] < bound &] ] Timing[Table[cd[5], {10000}];] {1.472 Second, Null} Mathematica 5.2 Windows XP Centrino 1.5 MHz running at 500 MHz {1.332 Second, Null} running full speed at 1.5 MHz -- Roland Franzius