MATLAB: Lsqcurvefit: what is behind

levenberg marquardtlsqcurvefitOptimization Toolbox

How lsqcurvefit works?

Lsqcurvefit fits a multi-parameter non-linear function through a single data point using Levenberg-Marquardt algorithm. But for e.g. three parameters I need at least three data points to fit the curve? What is the theory behing this function?

Thank you.

Best Answer

This link describes the algorithms used by lsqcurvefit and the other least squares optimizers

http://www.mathworks.com/help/optim/ug/least-squares-model-fitting-algorithms.html#brnoycf

BTW, I believe the trust-region method is the default for LSQCURVEFIT, not Levenberg-Marquardt.

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MATLAB: Lsqcurvefit: not enough input arguments

You need to pass function handle

fit=lsqcurvefit(@fLCST,[1 1 36 1],xdata,ydata,[],[],options)
               %^ put @ here

MATLAB: Lsqcurvefit

Since the distance between two complex numbers a+i*b and c+i*d is (a-c)^2 + (b-d)^2, you could treat each complex number as a pair of independent real numbers. Wrap fun in a function rfun that returns the real and complex parts of the output. For example, assuming rfun returns a column vector,

function y = rfun(x)
  y = rfun(x);
  y = [real(y); imag(y)];
end

Similarly, you could replace ydata by

rdata = [real(ydata); imag(ydata)].

Then you have the first two inputs for lsqcurvefit.

Best Answer

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MATLAB: Lsqcurvefit: not enough input arguments

MATLAB: Lsqcurvefit

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