Compiled functions in NDSolve.
Daniel Lisak
I have some compiled functions (they all depend on 3 real
variables: t, ro, v):
potencjalX = Compile[{t, ro, v}, -176.276/(ro^2 + v^2 t^2)^3];
potencjalA = Compile[{t, ro, v}, -248.279/(ro^2 + v^2 t^2)^3];
potencjalB = Compile[{t, ro, v}, -319.691/(ro^2 + v^2 t^2)^3];
funfi = Compile[{t, ro, v}, ArcSin[ro/Sqrt[ro^2 + v^2t^2]]];
funF = Compile[{t, ro, v}, (potencjalB[t, ro, v] - potencjalA[t, ro, v])/2];
funv1 = Compile[{t, ro, v}, (potencjalA[t, ro, v] + potencjalB[t, ro,
v])/2];
and I want to solve ordinary differential equations:
rozw[apocz_, ro_, v_, tend_, nieskoncz_] := NDSolve[{
a1'[t] == a1[t] potencjalX[t, ro, v]/I,
a2'[t] == a2[t] potencjalB[t, ro, v]/I,
a3'[t] == a3[t] funv1[t, ro, v]/I +
a4[t] funF[t, ro, v] Exp[2I funfi[t, ro, v]]/I,
a4'[t] == a3[t] funF[t, ro, v] Exp[-2I funfi[t, ro, v]]/I +
a4[t] funv1[t, ro, v]/I,
a1[-nieskoncz] == apocz[[1]],
a2[-nieskoncz] == apocz[[2]],
a3[-nieskoncz] == apocz[[3]],
a4[-nieskoncz] == apocz[[4]]},
{a1, a2, a3, a4}, {t, -tend, tend}, MaxSteps -> 100000]
when I evaluate this function:
rozw[{0, 0, 1, 0}, 3, 0.0003, 75000., 75000.]
I see the following error:
CompiledFunction::cfsa: Argument t at position 1 should be a machine-size
real number.
Does anybody know how can I use these compiled functions in NDSolve ?
Daniel
Jens-Peer Kuska
a) it is useless to compile parts of the equations because
NDSolve[] compile the explicit rhs sides again. The function
call in a compiled function may slow down the computation speed.
b) you need a wrapper function that call the compiled funtion only for
numeric arguments
(* the compiled stuff *)
potx = Compile[{{x, _Real}, {y, _Real}}, x + y]
poty = Compile[{{x, _Real}, {y, _Real}}, x*y]
(* the wrapper patterns that prevent the evaluation with
symbolic arguments *)
PotX[x_?NumericQ, y_?NumericQ] := potx[x, y]
PotY[x_?NumericQ, y_?NumericQ] := poty[x, y]
NDSolve[{x'[t] == PotX[x[t], y[t]],
y'[t] == PotY[x[t], y[t]], x[0] == 1, y[0] == 1}, {x[t],
y[t]}, {t, 0, 1}]
Hope that helps
Jens