Re: Faster Random Walk Simulation ?!?

*To*: mathgroup at smc.vnet.net*Subject*: [mg66204] Re: Faster Random Walk Simulation ?!?*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 4 May 2006 05:20:06 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <e39k1n$cmn$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

mfific at gmail.com wrote: > 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} > > > Thank you very much, > > Mario Fific > > > Mario Fific > Cognitive Psychology, Cognitive Science > Indiana University > 1101 E. 10th St. > Bloomington, IN 47405-7007 > Hi Mario, Although I have got a speed improvement of about 10% (see RandomWalk2), I doubt we can significantly improve on your code since most of the cpu time must be spent on building the list of lists itself. In[1]:= value = 0.5; 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}]; ][[1]] Out[3]= 2.797*Second In[4]:= RandomWalk2[boundaryA_, value_:0.5] := NestWhileList[{First[#1] + 1, Last[#1] + If[Random[] > value, 1, -1]} & , {0, 0}, -boundaryA < Last[#1] < boundaryA & ]; Timing[Table[RandomWalk2[5], {10000}]; ][[1]] Out[5]= 2.421*Second In[6]:= RandomWalk3 = Compile[{boundaryA, value}, NestWhileList[{First[#1] + 1, Last[#1] + If[Random[] > value, 1, -1]} & , {0, 0}, -boundaryA < Last[#1] < boundaryA & ]; ]; Timing[Table[RandomWalk3[5., 0.5], {10000}]; ][[1]] Out[7]= 2.547*Second Best regards, Jean-Marc