Re: Mathematica 20x slower than Java at arithmetic/special functions, is

*To*: mathgroup at smc.vnet.net*Subject*: [mg115888] Re: Mathematica 20x slower than Java at arithmetic/special functions, is*From*: "Vivek J. Joshi" <vivekj at wolfram.com>*Date*: Mon, 24 Jan 2011 05:23:25 -0500 (EST)

Without going into too much detail, a simple compilation of the function gives approx 6x to 25x speed up, ClearAll[grid1dc]; grid1dc[x_,y_]=(With[{d=0.1,NN=50}, Sum[Re[N[d BesselJ[1,2 Pi d Sqrt[m^2+n^2]]/Sqrt[m^2+n^2+10^-7]] Exp[I 2.0 Pi (m x+n y)]],{m,-NN,NN,1},{n,-NN,NN,1}]])//N; gridres1da=With[{delta=0.5,xlim=2.5,ylim=2.5}, Table[{x,y,grid1dc[x,y]},{x,-xlim,xlim,delta},{y,-ylim,ylim,delta}]];//AbsoluteTiming {7.371354,Null} Clear[cfunc]; cfunc = Compile[{{x,_Real},{y,_Real}},Evaluate[grid1dc[x,y]]]; gridres1da2=With[{delta=0.5,xlim=2.5,ylim=2.5}, Table[{x,y,cfunc[x,y]},{x,-xlim,xlim,delta},{y,-ylim,ylim,delta}]];//AbsoluteTiming {1.237029,Null} Norm[gridres1da[[All,All,3]]-gridres1da2[[All,All,3]]]//Chop 0 Following gives about 25x speedup, Clear[cfunc2]; cfunc2= Compile[{{xlim,_Real},{ylim,_Real},{delta,_Real}}, Block[{x,y}, Table[{x,y,cfunc[x,y]},{x,-xlim,xlim,delta},{y,-ylim,ylim,delta}]]]; gridres1da3=cfunc2[2.5,2.5,0.5];//AbsoluteTiming {0.292562,Null} Norm[gridres1da[[All,All,3]]-gridres1da3[[All,All,3]]]//Chop 0 Vivek J. Joshi Kernel Developer Wolfram Research Inc. On Jan 24, 2011, at 4:03 AM, Leo Alekseyev wrote: > I was playing around with JLink the other day, and noticed that Java > seems to outperform Mathematica by ~20x in an area where I'd expect > Mathematica to be rather well optimized -- arithmetic involving special > functions. In my particular example, I am simply evaluating a sum of > Bessel functions. I understand that much depends on the underlying > implementation, but I just want to run this by Mathgroup to see if > this is to be expected, or maybe if I'm doing something suboptimal in > Mathematica. Here's the code that I'm running: > > grid1dc[x_, > y_] = (With[{d = 0.1, NN = 50}, > Sum[Re[N[ > d BesselJ[1, 2 Pi d Sqrt[m^2 + n^2]]/ > Sqrt[m^2 + n^2 + 10^-7]] Exp[ > I 2.0 Pi (m x + n y)]], {m, -NN, NN, 1}, {n, -NN, NN, 1}]]) // > N > > and > > gridres1da = > With[{delta = 0.5, xlim = 2.5, ylim = 2.5}, > Table[{x, y, grid1dc[x, y]}, {x, -xlim, xlim, delta}, {y, -ylim, > ylim, delta}]] > > > Java implementation uses Colt and Apache common math libraries for the > Bessels and complex numbers, uses a double for loop, and consistently > runs 15-20 times faster. > > --Leo >