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

*To*: mathgroup at smc.vnet.net*Subject*: [mg115890] Re: Mathematica 20x slower than Java at arithmetic/special functions, is*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Mon, 24 Jan 2011 05:56:45 -0500 (EST)*References*: <ihiab8$m3b$1@smc.vnet.net>

Using Mathematica's Compile your function can be speeded up by a factor of about 7. Still a factor of 3 to explain... How did you do the timing BTW? Cheers -- Sjoerd On Jan 23, 11:33 pm, Leo Alekseyev <dnqu... at gmail.com> 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