Powell's dog leg method - fitting Lorentz function with area

Here, I post Powell's dog leg method algorithm for fitting the Lorentz function with the area.

Here, I present Powell's dog leg method that is applied to the fitting of Lorentz function with area. 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 Lorentz function with area. In order to change the fitting 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 area, center, width and offset. To fit data sucessfully, it is good if center position is approximately correct. I wish you a lot of fun with testing of Powell's dog leg algorithm.