Thread Subject:

Two curves fitting with two equations

Dear all,

I want to fit two curves with two equations which share several parameters. For example,
y1(x) = a1*f1(x)+b1*f2(x);
y2(x) = a1*f1(x)+b2*f2(x).

Does anyone know how to do this kind of fitting?

Thanks in advance.

"Chong " <wingser719@gmail.com> wrote in message <k6jibg$hd1$1@newscl01ah.mathworks.com>...
> Dear all,
>
> I want to fit two curves with two equations which share several parameters. For example,
> y1(x) = a1*f1(x)+b1*f2(x);
> y2(x) = a1*f1(x)+b2*f2(x).
>
> Does anyone know how to do this kind of fitting?
>
> Thanks in advance.

This is a non linear least squares problem. lscurvefit, lsqnonlin or nlinfit in the optimization and stats toolboxes will do the job.

I assume you have data for 'x' and are measuring y1 and y2 as responses. For most of these functions setting up y (and x for that matter) as vectors will be the way to go.
 
Check out the documentation for the optimization tool box or curve fitting toolbox.

Thank you for your reply. Maybe I didn't describe my question clearly.
Here y1 and y2 are equations I used for fitting two curves, which need to be input by myself. Since they share the parameter a1, I need to fit the two curves simultaneously.
My question is: In cftool, how to input two equations at the same time? Or any other methods to do this kind of fitting?
Thanks a lot.

"Marc" wrote in message <k6jun4$rd3$1@newscl01ah.mathworks.com>...
> "Chong " <wingser719@gmail.com> wrote in message <k6jibg$hd1$1@newscl01ah.mathworks.com>...
> > Dear all,
> >
> > I want to fit two curves with two equations which share several parameters. For example,
> > y1(x) = a1*f1(x)+b1*f2(x);
> > y2(x) = a1*f1(x)+b2*f2(x).
> >
> > Does anyone know how to do this kind of fitting?
> >
> > Thanks in advance.
>
> This is a non linear least squares problem. lscurvefit, lsqnonlin or nlinfit in the optimization and stats toolboxes will do the job.
>
> I assume you have data for 'x' and are measuring y1 and y2 as responses. For most of these functions setting up y (and x for that matter) as vectors will be the way to go.
>
> Check out the documentation for the optimization tool box or curve fitting toolbox.

"Chong " <wingser719@gmail.com> wrote in message <k6l554$3ej$1@newscl01ah.mathworks.com>...
> Thank you for your reply. Maybe I didn't describe my question clearly.
> Here y1 and y2 are equations I used for fitting two curves, which need to be input by myself. Since they share the parameter a1, I need to fit the two curves simultaneously.
> My question is: In cftool, how to input two equations at the same time? Or any other methods to do this kind of fitting?
> Thanks a lot.

For tool such as lsqnonlin, it does'nt matter if you have one, two or more curves. Just concatenate two function resultants in a long vector.

Bruno

"Chong " <wingser719@gmail.com> wrote in message <k6jibg$hd1$1@newscl01ah.mathworks.com>...
> Dear all,
>
> I want to fit two curves with two equations which share several parameters. For example,
> y1(x) = a1*f1(x)+b1*f2(x);
> y2(x) = a1*f1(x)+b2*f2(x).
=============

I don't know why the others have concluded that this is a non-linear problem. Looks pretty linear to me, assuming a1,b1,b2 are the unknowns. If there are no errors in x, you can just use backslash, or otherwise, total least squares.

"Matt J" wrote in message <k6m1vk$bqm$1@newscl01ah.mathworks.com>...
> "Chong " <wingser719@gmail.com> wrote in message <k6jibg$hd1$1@newscl01ah.mathworks.com>...
> > Dear all,
> >
> > I want to fit two curves with two equations which share several parameters. For example,
> > y1(x) = a1*f1(x)+b1*f2(x);
> > y2(x) = a1*f1(x)+b2*f2(x).
> =============
>
> I don't know why the others have concluded that this is a non-linear problem. Looks pretty linear to me, assuming a1,b1,b2 are the unknowns. If there are no errors in x, you can just use backslash, or otherwise, total least squares.

I simply assumed that f1(x) and f2(x) was "highly" complex and non-linear. Hence pointing to the various non linear solvers.

I hope, albeit, maybe me being a bit optimistic, that if it was a simple linear problem, why would the OP bother with the f1(x) and f2(x)....

ie....

y(1) = a1*x+b1*x;
y(2) = a1*x+b2*x;

"Marc" wrote in message <k9up6k$l5g$1@newscl01ah.mathworks.com>...
>
> > I don't know why the others have concluded that this is a non-linear problem. Looks pretty linear to me, assuming a1,b1,b2 are the unknowns. If there are no errors in x, you can just use backslash, or otherwise, total least squares.
>
> I simply assumed that f1(x) and f2(x) was "highly" complex and non-linear. Hence pointing to the various non linear solvers.
>
> I hope, albeit, maybe me being a bit optimistic, that if it was a simple linear problem, why would the OP bother with the f1(x) and f2(x)....
================

It is still a linear problem regardless of the form of f1(x) and f2(x). It is not the form of the dependence on x that matters as far as linearity is concerned. It is the dependence of y on the unknown parameters a1,b1,b2 and that dependence is linear. A linear equation solver can be used to find the unknowns here.

"Matt J" wrote in message <k9v886$8pa$1@newscl01ah.mathworks.com>...
> "Marc" wrote in message <k9up6k$l5g$1@newscl01ah.mathworks.com>...
> >
> > > I don't know why the others have concluded that this is a non-linear problem. Looks pretty linear to me, assuming a1,b1,b2 are the unknowns. If there are no errors in x, you can just use backslash, or otherwise, total least squares.
> >
> > I simply assumed that f1(x) and f2(x) was "highly" complex and non-linear. Hence pointing to the various non linear solvers.
> >
> > I hope, albeit, maybe me being a bit optimistic, that if it was a simple linear problem, why would the OP bother with the f1(x) and f2(x)....
> ================
>
> It is still a linear problem regardless of the form of f1(x) and f2(x). It is not the form of the dependence on x that matters as far as linearity is concerned. It is the dependence of y on the unknown parameters a1,b1,b2 and that dependence is linear. A linear equation solver can be used to find the unknowns here.

Since I have no idea what f1(x) and f2(x) look like and they are being used in both equations, I think we should both be able to agree that I can come up with forms of f1(x) and f2(x) which would make this a non linear problem.

Assuming all of the coefficients of f1(x) and f2(x) are known and not being solved for, I agree with you that this could be a very simple backslash problem.

"Marc" wrote in message <k6jun4$rd3$1@newscl01ah.mathworks.com>...
> "Chong " <wingser719@gmail.com> wrote in message <k6jibg$hd1$1@newscl01ah.mathworks.com>...
> > Dear all,
> >
> > I want to fit two curves with two equations which share several parameters. For example,
> > y1(x) = a1*f1(x)+b1*f2(x);
> > y2(x) = a1*f1(x)+b2*f2(x).
> >
> > Does anyone know how to do this kind of fitting?
> >
> > Thanks in advance.
>
> This is a non linear least squares problem. lscurvefit, lsqnonlin or nlinfit in the optimization and stats toolboxes will do the job.
>
> I assume you have data for 'x' and are measuring y1 and y2 as responses. For most of these functions setting up y (and x for that matter) as vectors will be the way to go.
>
> Check out the documentation for the optimization tool box or curve fitting toolbox.


Hey there
Sounds you can help me, I have got very similar and simpler case here
(y1-f1(x,t))^2+(y2-f2(x,t))^2=0 were x, y1 and y2 are known arrays(same size), and I just want to fit x and t.

unfortunately cftool cant help me, I cant import a second independent variable there (y1 and y2), I tried optimtool but its damn complicated! but if it is the last option can you give me some hints?

Thanks and advance!