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Fitting a function - the result of a NDSolve

Posted 11 years ago
Hi Everybody,

I just stumbled upon a problem and cannot move forward, so I'd kindly appreciate your expertise and help. I am trying to perform a simultaneous fit of functions, which are a solution of a set of differential equations. One of the parameters of the fit enters also as a parameter for a starting value in NDSolve ad thus I get an error (initial condition being non-numeric). The fitting is performed by constructing and minimizing a function (a sum of squares). Here's the code below.

The function is defined here:
 ClearAll[Ae, A2e, Ah, A2h, DE, T]; Ts = 10;
 funk[Ae_?NumberQ, A2e_?NumberQ, Ah_?NumberQ, A2h_?NumberQ,
    DE_?NumberQ, Tx_?NumberQ] :=
    {uu, nx, nd, nxp, nxm, n2x},
    uu = NDSolve[{
        nx[T]' == -Ae nx[T] - Ah nx[T] + A2h nxp[T] + A2e nxm[T] + Exp[-(DE/(2 kbev T))] nd[T] - Exp[DE/(2 kbev T)] nx[T],
       nd[T]' == -Ae nd[T] - Ah nd[T] + A2h nxp[T] + A2e nxm[T] - Exp[-(DE/(2 kbev T))] nd[T] + Exp[DE/(2 kbev T)] nx[T],
       nxp[T]' == -Ae nxp[T] - A2h nxp[T] + A2e n2x[T],
       nxm[T]' == -A2e nxm[T] - Ah nxm[T] + A2h n2x[T],
       n2x[T] == -A2e n2x[T] - A2h n2x[T],
       nx[Ts] == Exp[-(DE/(2 kbev Ts))],
       nd[Ts] == Exp[DE/(2 kbev Ts)], nxp[Ts] == nx[Ts],
       nxm[Ts] == nx[Ts], n2x[Ts] == nx[Ts]/2}, {nx[T], nd[T], nxp[T],
        nxm[T], n2x[T]}, {T, 10, 100}][[1]];
   {nx[T], nxp[T], nxm[T], n2x[T]} /. uu /. {T -> Tx}
This is data (for tests only):
osT = {10, 25}; daneX = {1, 0.8}; daneXp = {0.9, 0.3}; daneXm = {1,
  0.8}; dane2X = {0.5, 0.1};

And this is the function to be minimized:
sse[Ae_, A2e_, Ah_, A2h_, DE_] :=
  Apply[Plus, (funk[Ae, A2e, Ah, A2h, DE, osT][[1]] - daneX)^2 +
    (funk[Ae, A2e, Ah, A2h, DE, osT][[2]] - daneXp)^2 +
    (funk[Ae, A2e, Ah, A2h, DE, osT][[3]] - daneXm)^2 +
    (funk[Ae, A2e, Ah, A2h, DE, osT][[4]] - dane2X)^2];

I can evaluate sse, but running FindMinimum results with the error:NDSolve::ndinnt: Initial condition 0.+0.5` 2.71828^(-580.248 DE) is not a number or a rectangular array of numbers.

Any ideas would be much appreciated,


POSTED BY: Elwood Blues
Not obvious.   The ?NumberQ's in the arguments for funk should have prevented that.

Maybe add ?NumberQ to the arguments for sse?

What does the FindMinimum call look like?
POSTED BY: Bruce Miller
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