Using lsqcurvefit without knowning the function

This is what I understand from the matlab help

 x = lsqcurvefit(@myfun,x0,xdata,ydata)
 function F = myfun(x,xdata)
   F = ...     % Compute function values at x, xdata

The least square non-linear fit will match the ydata and the F-output by changing the x value.

My question is that " is xdata the input to calculate F?" Does xdata have to have the same size as ydata?

It is hard for me to apply lsqcurvefit to my problem. I have Xdata_e, Ydata_e from the experiments ( XYdata_e combines Xdata_e and Ydata_e) and I want to match with Xdata_s, Ydata_s from the simulation by changing the parameter x.

I have

       function F = myfun(x,XYdata_s) % where XYdata_s contains Xdata_s and Ydata_s
       giving the initial position X0 contains both x,y. Also giving time step, so on  
       The code will calculate Xdata_s, Ydata_s
       F= the code that solves for Xdata_s and Ydata_s from simulation. Xdata_s is NOT using to    calculate Ydata.
       I set F=XYdata_s;

This is my lsqcurvefit

        x = lsqcurvefit(@myfun,x0,XYdata_s,XYdata_e) % x0 is initial guess of x

I feel like there is something wrong in my code because XYdata_s is NOT the input to calculate F. Because XYdata_s is the matrix of my output that I want to match with XYdata_e. Basing on my code, the input is the initial position of x and y which does not have the same dimension as XYdata_e. The initial position X0 contains both x and y having the dimension of 6 x1. However, the dimension of XYdata_e has the dimension of 100 x 6. I dont know how to set it correctly. Please helps.

Any thoughts will be appreciated. Thank you.

[Matt J]

Laura,

Please don't delete your Comments/Questions from the thread (assuming it was you!) once people have responded to them. It makes the thread hard to interpret for others who read it later.

Answer 1

[Matt J]

However, the dimension of XYdata_e has the dimension of 100 x 6. I dont know how to set it correctly.

If the given target data XYdata_e has dimension 100 x 6, then F(x,XYdata_s) must always return an output array of dimension 100x6. That is the only restriction.

[Matt J]

x = lsqcurvefit(@myfun,x0,X0,XYdata_e)

does look correct. The dimension of X0 has no importance. Only that F(x,X0) produce an output the same size as your measured output data XYdata_e.

The input X0 can even be empty [] as the following example shows

>> f=@(x,X0)(1:6)*x; X0=[]; XYdata_e=(1:6)*2;

>> x_estimate= lsqcurvefit(f,0,X0,XYdata_e)

x_estimate =

       2