# Input Problems with LMF(Levenberg-Marquard-Formula)

Hello Matlab-Programmer!
I'm working on a Programm that gets a cooling curve of an Diode or IGBT and calculate the thermal impedance. Therefore i use an Algorithmus (Levenberg-Marquard-Algorithmus). It is called with:

[x,ssq,cnt] = LMFnlsq(res,x0);

Here is a Little Example:
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a = 10;
b = -8;
c = -.2; % Model parameters
t = (0:.1:1)'; % should be a column vector

f = a + b*(1-exp(t/c)) + .2*randn(size(t));

% Column vector of residuals (function)
res = @(x) x(1) + x(2)*(1-exp(t/x(3)))- f;
% solve it with rather bad estimate of parameters (start values)
x0 = [0,0];
[x,ssq,cnt] = LMFnlsq(res,x0);
plot(t,f, t,res(x)+f,'r'), grid;

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In my Programm the function f(in the example) is a fitted function of the type cfit:
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myfit(t) = r1*(1-exp(-t/tau1))+r2*(1-exp(-t/tau2))+r3*(1-exp(-t/tau3))
Coefficients (with 95% confidence bounds):
r1 = 82.06 (72.67, 91.45)
r2 = 12.85 (10.52, 15.17)
r3 = 82.41 (72.3, 92.52)
tau1 = 14.38 (12.25, 16.51)
tau2 = 0.06762 (0.0008762, 0.1344)
tau3 = 3.31 (2.883, 3.737)
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As you can see the function f in the example is from type double and my function (myfit) from type cfit. But i convert it to string with "formula":
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funktion_fit=formula(myfit);
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I get the coefficients (of the fitted function myfit) with that calling:
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coeff_val=coeffvalues(myfit);
coeff_fit=coeffnames(myfit);
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But i can't convert it in a form to put it in like in the example.
The next Problem is the "function handle":
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res=@(x) x(1) + x(2)*(1-exp(t/x(3)))-f;
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The fucntion: x(1) + x(2)*(1-exp(t/x(3))) is in my Programm a string (dynamic). Here an example:
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funktion_string =

'x(1)*exp(-t/(x(2)))+x(3)*exp(-t/(x(4)))+x(5)*exp(-t/(x(6)))'
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Here is the same Problem. I can't get the string in the form like the example.

Can you help me?

Thank you