## Regression of a vector in a optimization problem

### Ronny Rives (view profile)

on 31 Jul 2019
Latest activity Commented on by Matt J

on 13 Aug 2019

### Matt J (view profile)

Hello everyone,
I need to fit experimental data to an analytical solution. The analytical solution has the form:
• C(z,t) = C_eq*f(z,t,D)
where f(z,t,D) is a known function of time (t) and position (z), and D and C_eq are parameters to regress.
I have already determined D and C_eq using the routine fminsearch. However, I would like to consider that C_eq does not necessarily have to be constant and can change over time.
My question is whether it is possible to regress C_eq as a vector instead of a constant? In this case, which routine is the most appropriate?
P.D: parameter D could also be considered as a vector if necessary.

Torsten

### Torsten (view profile)

on 31 Jul 2019
You shouldn't work with too many degrees of freedom for C_eq.
E.g. if you consider it as a function of time and position, you could choose it as
C_eq = C_experimental/f(z,t,D)
which gives a 100% fit between experimental and theoretical values.
If you consider it as a function of time and you have experimental data at times
t1 < t2 < ... < tn,
you can choose C_eq between 0 and t1 such that it fits best your data at t1, you can choose C_eq between t1 and t2 such that it fits best your data at t2 and so on.
But I think this only gives you more degrees of freedom in the fitting process, but doesn't make much sense from the physics point of view.
Ronny Rives

### Ronny Rives (view profile)

on 31 Jul 2019
Torsten,
In my calculations it is possible to determine an average C_eq at different times, i.e.,
C_eq1-->(0<t<t1);
C_eq2-->(t1<t<t2);
...
C_eqn-->(tn-1<t<tn).
Then,
C_eq = average(C_eq1;C_eq2;...C_eqn)
My question is whether it is possible to regress C_eq as a column vector without the need to manually divide my experimental data into time intervals?
Is there a routine in matlab, that allows to obtain a vector as a result of the regression instead of constant fitting parameter(s) (as in the case of fminsearch, lsqnonlin, etc.)?
Torsten

### Torsten (view profile)

on 1 Aug 2019
Use "lsqcurvefit" with the parameter vector x = (C_eq(1),C_eq(2),...,C_eq(n)).

### Matt J (view profile)

on 13 Aug 2019

As the others have said, all regression routines in the Optimization Toolbox allow you to represent the unknown variable in vector form. However, fminspleas might work especially well for your problem
since you only have one parameter that is intrinsically non-linear.

### Sai Bhargav Avula (view profile)

on 13 Aug 2019

As mentioned by Torsten, lsqcurvefit can be used to obtain a vector as a result of the regression. But those values use the entire data for getting the output values . For you particular case you should segment the data based on time stamps and perform lsqcurvefit in a for loop.

Matt J

### Matt J (view profile)

on 13 Aug 2019
I don't think a loop would be appropriate here, actually, because as I understand it, the parameter D is shared by all time blocks.