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MathGroup Archive 1999

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Re: NonlinearRegress and numerical functions...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20186] Re: [mg20132] NonlinearRegress and numerical functions...
  • From: Larske Ragnarsson <loke at ic.chalmers.se>
  • Date: Tue, 5 Oct 1999 04:04:17 -0400
  • Organization: Chalmers University of Technology
  • References: <7t8d2v$gei@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Thanks for the feedback!!!
The simple problem I provided was only to illustrate the problem. I
DO need
to use NDSolve... and the solution is integrated over energy. I want
to fit
the parameters which are involved both in NDSolve and the integration
which
means that I DO have to solver it each time (at least to my knowledge...)
Here is what I'm trying to solve:
k0[T_,Ef0_]:=1.43 10^-12 E^-(Ef0/keV/T)
k1[T_,Ef1_]:=1.43 10^-12 E^-(Ef1/keV/T)
Pb0H2[t_, T_, Ef0_, Ef1_, H20_, Pb00_,
 Pb10_] := (Pb0[t] /. (NDSolve[{Pb0'[t] == -k0[T,
Ef0] H2[t]Pb0[t],
 Pb1'[t] == -k1[T, Ef1] H2[t]Pb1[t],
 H2'[t] == -k0[T, Ef0]/tox H2[t] Pb0[t]
- k1[T, Ef1]/tox H2[t] Pb1[t],
 Pb0[0] == Pb00, Pb1[0] == Pb10, H2[0] == H20},
{Pb0[t], Pb1[t], H2[t]},
 {t,0,10000}, MaxSteps -> 100000])[[1]])/Pb00
Pb0H2p[t_, T_, Ef0_, Ef1_, H20_, Pb00_, Pb10_] := Pb0H2[t0, T, Ef0,
Ef1,
H20, Pb00, Pb10] /. {t0 -> t}
Pb0H2DistDouble[t_, T_, Ef0_, sigma0_, Ef1_, sigma1_, H20_, Pb00_, Pb10_]
:=
 NIntegrate[(Pb0H2p[t, T, Eff0, Eff1, H20, Pb00, Pb10]*
 PDF[NormalDistribution[Ef0,
sigma0], Eff0]*
 PDF[NormalDistribution[Ef1,
sigma1], Eff1]), {Eff0, Ef0 - 5sigma0,
 Ef0 + 5sigma0}, {Eff1, Ef1 - 5sigma1,
Ef1 + 5sigma1},
 Method -> Trapezoidal, AccuracyGoal -> 2, PrecisionGoal
-> 2]
Then I try to use Pb0H2DistDouble in NonlinearRegress (with one or more
variables...) In this case I chose only one to see if it worked, but
I
ultimately want to fit on at least three of the variables (Ef0,Ef1,H20):
NonlinearRegress[fittingdata, Pb0H2DistSingle[t, T, 1.51, 0.14, 1.57,
0.15,
H20, 1.4 10^16, 1.1 10^16], {t, T}, {H20,{10^23,10^24},10^21,10^25}]

Thank you for any help

Regards
Larske



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