Powell's dog leg method - fitting sinus function

I present the fitting of the sinus function based on Powell's dog leg method.

Here, I present Powell's dog leg method that is applied to the fitting of sinusoidal function. The general algorithm was taken from document "METHODS FOR NON-LINEAR LEAST SQUARES PROBLEMS" written by authors K. Madsen, H.B. Nielsen, O. Tingleff (Technical University of Denmark). The principles and function of Powell's dog leg method are thoroughly explained in this document. I apply general Powell's dog leg algorithm to sinusoidal function. In order to change the function, you need to rewrite Jacobian matrix, which contains derivatives according to the fitting parameters. The presented algorithm is using mostly Matlab and equation solver Solve from Symbolic Math Toolbox. The solver is used to calculate step in Powell's dog leg method. The fitting parameters are amplitude, phase and offset.