Levenberg Marquardt Curve Fitting Algorithm

I'd like to use the Levenberg Marquardt nonlinear curve fitting algorithm to fit some data. The function is user defined:

y = a*g(x)+b+c*x+d*x^2

g(x) is a constant as a function of x. It is a matrix that I already have defined. So I'm not sure how to load this into the custom equation. The second half of the equation (b+c*x+d*x^2) is just a polynomial.

I can't figure out at all how to do this and I've tried multiple add-ons. Thank you!

Answer 1

[Robert U]

Hi Jonathan Trueblood,

Levenberg-Marquardt-Algorithm is built-in into lsqcurvefit(), Optimization Toolbox. You would have to define its use by setting options accordingly (cf. optimoptions()):

   options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');

Then define your custom function in any way (anonymous, nested or external). Examples, on how to use lsqcurvefit() can be found in documentation.

You may define g(x) as a stand-alone function and plug it into another function:

 g = @(x) x^2+x;
 y = @(x) 5 * g(x) + 1; 

 y(1)
 >> 11

The function handle y can now be used as function to be optimized if parameters have been set accordingly.

y = @(x,xdata) x(1).*g(xdata)+x(2)+x(3).*xdata+x(4)*xdata.^2;

Kind regards,

Robert

Answer 2

[Matt J]

It is overkill to use Levenberg-Marquardt for a problem like this, where the model function is linear in the unknown parameters. Just use a linear solver,

gx=g(x); %the matrix you have

p=[gx(:), x(:).^(0:2)]\y(:);

[a,b,c,d]  = deal(p(1), p(2), p(3), p(4));

[norlaila mustakim]

do you know how to do the code if the model function is nonlinear?

[Matt J]

In that case, youwould indeed use lsqcurvefit or lsqnonlin.