Levenberg–Marquardt algorithm - Lorentz function with area

I post here Levenberg–Marquardt algorithm for fitting Lorentz function with the area.

The Lorezntz function is widely used for fitting Raman peaks in Raman spectroscopy. Thus, it is important function in various disciplines of science such as optics and X-ray characterization of materials. Therefore, it is necessary to know and understand non-linear least squares methods for fitting Lorentz functions. Here, I present simple Levenberg–Marquardt algorithm for fitting Lorentz function with area. The fitting parameters are area, center, width and offset. The general Levenberg–Marquardt algorithm was taken from on-line available pdf document "METHODS FOR NON-LINEAR LEAST SQUARES PROBLEMS" written by K. Madsen, H.B. Nielsen, O. Tingleff from Technical University of Denmark.

There are situations in life when optimization toolboxes are too expensive or it is necessary to perform low-level programming in Matlab or C++. Then it is important to understand principles of fitting algorithms. By use of C++ Eigen library, you can transfer algorithm posted here to C++. Enjoy the algorithm.