Suggestions for improving speed

*To*: mathgroup at smc.vnet.net*Subject*: [mg113304] Suggestions for improving speed*From*: Joe Hays <hays.joe at gmail.com>*Date*: Sat, 23 Oct 2010 07:04:10 -0400 (EDT)

Hello all, Today I've been studying B-Splines. I know that Mathematica has a built-in function to build the basis of a B-Spline but I wanted to better understand it so I coded up my own following the "Cox-de Boor recursion formula" found at: http://en.wikipedia.org/wiki/B-spline#Cubic_B-Spline I tested it against Mathematica's version to make sure things were working OK. After I got the right answer I timed the two implementations. Mathematica's took ~ 0.12 seconds. My version took ~15.53 seconds. I expected my implementation to be slower but not 125X slower! I realize that I still approach things from the procedural point of view. So, I thought I'd ask the Mathematica gurus if they see obvious coding choices that cause the drastic slow down... My tests were: Given, m=15; n=3; knots=Range[0,m-1] j=3; time=3.5; Mathematica's version: <snip> tmpT=AbsoluteTime[]; Plot[Table[BSplineBasis[{n,knots},j,time],{j,0,m-n-2}],{time,0,m-1}, PlotRange->All] AbsoluteTime[] - tmpT </snip> this took ~0.12 seconds my version, <snip> tmpT=AbsoluteTime[]; Plot[Table[NthBasisRecursive[{n,knots},j,time],{j,0,m-n-2}],{time,0,m-1}, PlotRange->All] AbsoluteTime[] - tmpT </snip> this took ~15.53 seconds Now, for my code defining "NthBasisRecursive" %%%%%%%%%%%%%%%%%%%%%%%%%%%% NthBasisRecursive[{n_, knots_}, j_, time_] := Module[{jj, nn, myBasis, jIdx}, myBasis = ConstantArray[0, {n + 1, n + 1}]; For[nn = 1, nn <= n + 1, nn++, For[jj = 1, jj <= n + 1, jj++, jIdx = j + jj; (* Need to offset the knot indexing by the jth basis I'm solving for *) If[nn == 1, If[knots[[jIdx]] <= time < knots[[jIdx + 1]], myBasis[[jj, nn]] = 1; ]; , If[(jj - 1) <= n - (nn - 1), myBasis[[jj, nn]] = (time - knots[[jIdx]])/(knots[[jIdx + nn - 1]] - knots[[jIdx]])*myBasis[[jj, (nn - 1)]] + (knots[[jIdx + nn]] - time)/(knots[[jIdx + nn]] - knots[[jIdx + 1]])*myBasis[[(jj + 1), (nn - 1)]]; , ];(* end of inner IF *) ];(* end of outer IF *) ];(* end of JJ loop *) ];(* end of nn loop *) myBasis[[1, n + 1]] ] %%%%%%%%%%%%%%%%%%%%%%%%%%%% Any insight to help me learn how to make things faster would be greatly appreciated! Joe