       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

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
>

```

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