MATLAB: Non linear data fit (weighted least square)

non linear data fitweighted least square

Hello, I would like to fit a data set (X,Y) with a non linear function y=f(x,a,b) where a and b are the paramters to be fitted.

In my case both X and Y have an uncertainty.

Is there a way to carry out a weighted least square with MATLAB?

Can the uncertainty on X be taken into account?

I spent nearly one hour looking around for a way to do that but I had no success.

Thank you,

Best Answer

check:

-lsqcurvefit

-lsqnonlin (both are in optimization toolbox though)

im not sure how you want to take account of the uncertainty in x, but you can also program any optimization yourself. basically you just have to write an objective function and plug that into:

-fminsearch

or if you have optimization toolbox:

-fminunc (unconstrained optimization)

-fmincon (constrained opt.)

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MATLAB: Matrix solving via least-squares: Y = A*B where Y, A and B are all matrices

Since your model is linear and you have linear constraints on B (its row sums), then LSQLIN is the better tool to use

   b=lsqlin(C,d,[],[],Aeq,beq);
   B=reshape(b,m,n);

where

    C=kron(speye(n),A);
    d=Y(:);
    Aeq=kron(ones(1,n),speye(m));
    beq=rowsums;

MATLAB: Can the multiobjective optimization solver GAMULTIOBJ work with least squares

Thanks for the clarification. Perhaps you can simply use lsqcurvefit or lsqnonlin with a modification to your model functions. The following is not really code, but should give you enough information to write the code you need.

Augment your data matrix x with a row containing a 1 wherever you want to use f1 as your model function, and a 0 wherever you want to use f2. Then write your total model function F = x(newrow)*f1(x,a,b,c) + (1-x(newrow))*f2(x,b,c,d). Your responses Y1 and Y2 are similarly combined into one output data matrix or vector.

Now lsqcurvefit will attempt to find a,b,c,d to minimize the total sum of squares.

I hope this works for you.

Alan Weiss

MATLAB mathematical toolbox documentation

Best Answer

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MATLAB: Matrix solving via least-squares: Y = A*B where Y, A and B are all matrices

MATLAB: Can the multiobjective optimization solver GAMULTIOBJ work with least squares

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