Re: help in speeding up code involving a recursive function

*To*: mathgroup at smc.vnet.net*Subject*: [mg43926] Re: [mg43907] help in speeding up code involving a recursive function*From*: Dr Bob <drbob at bigfoot.com>*Date*: Sun, 12 Oct 2003 04:03:45 -0400 (EDT)*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

This may help: ClearAll[betacoeff] betacoeff[0, _, _] := 1; betacoeff[k_, 1, _] /; k > 0 := 1/k!; betacoeff[1, r_, _] := r betacoeff[k_, r_, L_] := betacoeff[k, r, L] = Sum[betacoeff[i, r - 1, L]/(k - i)!, {i, Max[0, k - (L - 1)], Min[k, (r - 1)*(L - 1)]}] The key is to avoid recomputing the laborious ones by using "dynamic programmic" (fancy term for saving computed values for later reuse). Double-check that I've duplicated the function properly while I was simplifying it! If you prefer, here's another way to simplify it: ClearAll@betacoeff betacoeff[k_, r_, L_] := Which[ k == 0, 1, r == 1, 1/k!, k == 1, r, True, betacoeff[k, r, L] = Sum[betacoeff[i, r - 1, L]/ (k - i)! , {i, Max[ 0, k - (L - 1)], Min[k, (r - 1) (L - 1)]}] ] Each of those methods took about 11.3 seconds on my machine, and the answer was: {{5.000, 0.027040344}, {10.00, 0.049286903}, {15.00, 0.073548480}} Bobby help in speeding up code involving a recursive function Subject: [mg43926] [mg43907] help in speeding up code involving a recursive function From: "Salman Durrani" <s4001586 at student.uq.edu.au> To: mathgroup at smc.vnet.net Organization: The University of Queensland, Australia Reply-to: "Salman Durrani" <s4001586 at student.uq.edu.au> Hi, In the code below, the input variables are L and a. The code executes correctly and almost instantaneously for L=1 and a=5. However when I run it for L=2 and a=5, the execution is very slow. I ran it on a 2.5 GHz machine for L=2 and a=5 for over 48 hours, without the execution finishing. In the end, I was forced to abort the execution. Can someone please suggest how to speed up the execution. The code can also be downloaded from http://www.itee.uq.edu.au/~dsalman/_downloads/test.nb Thanks in advance. Salman