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

*To*: mathgroup at smc.vnet.net*Subject*: [mg115880] Mathematica 20x slower than Java at arithmetic/special functions, is*From*: Leo Alekseyev <dnquark at gmail.com>*Date*: Sun, 23 Jan 2011 17:33:09 -0500 (EST)

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

**Follow-Ups**:**Re: Mathematica 20x slower than Java at arithmetic/special functions, is***From:*Leo Alekseyev <dnquark@gmail.com>