Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Compiled function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93802] Re: Compiled function
  • From: Michael Weyrauch <michael.weyrauch at gmx.de>
  • Date: Wed, 26 Nov 2008 05:13:17 -0500 (EST)
  • References: <gggqfq$320$1@smc.vnet.net>
  • Reply-to: michael.weyrauch at gmx.de

Hello,

   if you look at the compiled code, you will see, that it does not
fully compile in both cases. It's only somewhat worse in case of
fa with Piecewice[], since expressions with the Head Piecewise cannot be 
compiled anyway, since compiled code only supports real, complex, 
integer and a few other basic data.

I suggest to rewrite the code using IF[] or other Mathematica 
constructs, which can be compiled easily.

(Writing code that compiles properly in Mathematica is more an art than 
a science since Compile[ ] is really poorly documented. I hope this will 
change in the (distant?) future...)

Michael


SigmundV schrieb:
> Dear group,
> 
> Consider the following:
> 
> derData[data_, h_] := (Drop[data, 1] - Drop[data, -1])/h;
> front = With[
>    {fa =
>      Function[{x, y}, Piecewise[{{0, 2 <= x <= 3 && 2 <= y <= 3}}, 1],
> Listable],
>     fc = Function[{x, y}, (x y + 10)^0]},
>    Compile[{{r, _Real, 2}, {dt, _Real}, {\[Theta], _Real}},
>     Module[{x, y, a, b, c, C = Cos[\[Theta]], S = Sin[\[Theta]], da,
>       db, dc, dx, dy, cxy, xy, cxyxy, xnew, ynew,
>       dphi = 2 \[Pi]/1000},
> 
>      x = r[[All, 1]]; y = r[[All, 2]];
>      dx = derData[x, dphi]; dx = Join[dx, {dx[[1]]}];
>      dy = derData[y, dphi]; dy = Join[dy, {dy[[1]]}];
> 
>      a = fa[x, y];
>      b = 2 a; c = fc[x, y];
>      da = derData[a, dphi]; da = Join[da, {da[[1]]}]; db = 2 da;
>      dc = derData[c, dphi]; dc = Join[dc, {dc[[1]]}];
> 
>      cxy = dc dt + S dx + C dy; xy = C dx - S dy;
>      cxyxy = a^2 cxy^2 + b^2 xy^2;
> 
>      xnew =
>       x + dt c S + dt^2 (-a^2 b db (dc dt S + dx))/cxyxy +
>        dt (a^2 C cxy - b^2 S xy) Sqrt[cxyxy - a^2 db^2 dt^2]/cxyxy;
>      ynew =
>       y + dt c C + dt^2 (-a^2 b db (dc dt C + dy))/cxyxy -
>        dt (a^2 S cxy + b^2 C xy) Sqrt[cxyxy - a^2 db^2 dt^2]/cxyxy;
> 
>      Transpose[{xnew, ynew}]
> 
>      ]
>     ]
>    ];
> 
> As you see, fa is a piecewise function, but the module won't compile.
> However, when fa is a continuous function, like Exp[-(x^2 + y^2)], the
> module compiles without problems. Can anyone shed some light on this?
> Why does the compilation work in the latter case, but not in the
> first?
> 
> King regards,
> Sigmund Vestergaard
> 


  • Prev by Date: Re: How to convert a HeavisideTheta to a PieceWise function
  • Next by Date: Re: Primed Symbols in Mathematica
  • Previous by thread: Compiled function
  • Next by thread: Re: Compiled function