custom fitting / additional boudary conditions on parameters

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Onufry Torbus
Onufry Torbus 2015-2-5
评论： Onufry Torbus 2015-2-7
Hi there,
I am working on a custom curve fitting. It is a set of exponential functions, see below. My problem is that I have to apply constraints on paramateres g1, g2 and g3, in a way that: g1 + g2 + g3 = 1.
Can you help me out? /OT
ft = fittype(['E0*((1-g1-g2-g3)*t+g1*tau1*(1-exp(-t/tau1))+g2*tau2*(1-exp(-t/tau2))+g3*tau3*(1-exp(-t/tau3)))'],'independent', 't', 'dependent', 'y' );
opts = fitoptions( ft );
opts.Display = 'Off';
opts.Lower = [0 0 0 0 0 0 0];
opts.StartPoint = [0 0 0 0 1 10 100];
opts.Upper = [Inf 1 1 1 Inf Inf Inf];
  2 个评论
Torsten
Torsten 2015-2-6
I just looked at the type of fit you defined in your question.
If you want f1+f2+f3=1 in the above fittype, the factor in front of t, namely 1-f1-f2-f3, becomes zero. Is this really what you intend ?
Best wishes
Torsten.
Onufry Torbus
Onufry Torbus 2015-2-7
I made a mistake before, I edited this and now should look more clear

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采纳的回答

Torsten
Torsten 2015-2-5
Use fmincon to be able to account for your constraints.
Best wishes
Torsten.
  3 个评论
显示 1更早的评论
Torsten
Torsten 2015-2-5
As objective function, you provide
sum_{i=1}^{n} (y_i-f(t_i))^2
with
f(t)=A*((1-f1-f2-f3)*t+g1*t1*(1-exp(-t/t1))+g2*tau2*(1-exp(-t/t2))+g3*t3*(1-exp(-t/t3)))
and as constraints your lower and upper bounds for the parameters to be fitted together with the additional constraints from above.
Read the documentation of fmincon on how to set up the call:
http://de.mathworks.com/help/optim/ug/fmincon.html
Best wishes
Torsten.
Onufry Torbus
Onufry Torbus 2015-2-6
编辑：Onufry Torbus 2015-2-6
Dear Torstane,
I am beginner with Matlab and the environment is not always clear for me. I read the documentation of fmincon. As far as I understood I have to prepare mfunction file first (in a separate m file) and then make a call in my m script (curve fitting).
1. I created a file "objfun.m" as:
function f = objfun(x)
f = sum((y(i)-f(t(i))^2, i=1..n) % I am not sure if this is correct...
2.Now the call in my script:
ft = fittype(['A*((1-f1-f2-f3)*t+g1*t1*(1-exp(-t/t1))+g2*tau2*(1-exp(-t/t2))+g3*t3*(1-exp(-t/t3)))'],'independent', 't', 'dependent', 'y' );
opts = fitoptions( ft );
opts.Display = 'Off';
A = [1 1 1] % constraints
B = [0] % constraints
g0 = [0.1;0.3;0.6]; % Starting guess
[g,fval] = fmincon(@objfun,x0,A,B);
opts.Lower = [_Inf g(1) g(2) g(3) 0 0 0];
opts.StartPoint = [0 g0(1) g0(2) g0(3) 1 10 100];
opts.Upper = [Inf g(1) g(2) g(3) Inf Inf Inf];
Am I heading in good direction?

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