custom fitting / additional boudary conditions on parameters

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];

[Torsten]

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]

I made a mistake before, I edited this and now should look more clear

Answer 1

[Torsten]

Use fmincon to be able to account for your constraints.

Best wishes

Torsten.

[Onufry Torbus]

Hej Torsten, Thank you for help. I read manual for fmincon, but cannot get how I can combine fmincon with my custom curve fitting script. Should I put it inside fitting options? Could you provide an example?

[Torsten]

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]

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?