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Compiled function

• To: mathgroup at smc.vnet.net
• Subject: [mg93776] Compiled function
• From: SigmundV <sigmundv at gmail.com>
• Date: Tue, 25 Nov 2008 07:19:23 -0500 (EST)

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