Re: Slow iteration in a functional program

*To*: mathgroup at smc.vnet.net*Subject*: [mg35650] Re: [mg35630] Slow iteration in a functional program*From*: Sseziwa Mukasa <mukasa at jeol.com>*Date*: Wed, 24 Jul 2002 02:06:21 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On Tuesday, July 23, 2002, at 01:51 AM, Matthew Rosen wrote: > Everyone, > I've been trying to recast an iterative calculation I do as a > procedural program in C as an elegant functional program in > Mathematica 4.1. The Mathematica code is much more transparent, but > the resultant execution time is more than two orders of magnitude > longer. Any suggestions would be greatly appreciated.The following is > a schematic of the problem. > > > There are three equations in the iteration variable, n: > > G[n_] := ListIntegrate[xsec Phi[n]] Both xsec and Phi[n] are > 400 points long. > > P[n_] := G[n]/(G[n]+(a constant)+D[n]) D[n] is a simple algebraic > function of n. > > Phi[1] = Flux; Flux is 400 points long. > Phi{n_] := Phi[n-1] Exp[-(1-P[n-1])*xsec > > > The goal is to evaluate P[n_] for an n around 1000. After running, I > need to know all the values of P[n] and Phi[n] at each n from 1 to > nmax. Note, P[n] is a number and Phi[n] is 400 points long. > > Currently, > > Timing[P[1]] = 0.1 s > Timing[P[2]] = 0.2 s > Timing[P[5]] = 8.4 s. > > I dont dare try to evaluate P[1000] as I need to do. Every time I > evaluate these functions they recalculate from scratch. I think I > need to somehow tell Mathematica to save the intermediate values. > Curious is that the calculation time is going up like n^2, not like n > as I would have thought. The equivalent procedural c-code runs in > less than 1 second to evaluate P[1000]. > > Thanks in advance for any guidance! > > You may want to cache your values, especially since none of the lists are very long. Try defining P as P[n_]:=P[n]=G[n]/(G[n]+...) and Phi[n_] as Phi[n_]:=Phi[n]=Phi[n-1] Exp[-(1-P[n-1])*xsec]. For that matter you may want to do the same thing with G. Doing this for a simplified version of your system (constant = 1, D[n_]:=n^2 etc.) I get the following timings (Dialog) In[153]:= Timing[P[1];] Timing[P[2];] Timing[P[5];] (Dialog) Out[153]= {0.02 Second,Null} (Dialog) Out[154]= {0.03 Second,Null} (Dialog) Out[155]= {0.07 Second,Null} Regards, Ssezi