Levenberg–Marquardt algorithm - Gaussian amplitude function

I post here Levenberg–Marquardt algorithm to fit the Gaussian function with amplitude.

The Gaussian functions are widely used in optical spectroscopy like Raman spectroscopy, X-ray diffraction and optics in general. Therefore, it is necessary to know non-linear least square fitting algorithms. Here, I post Levenberg–Marquardt algorithm to fit Gaussian function with amplitude. The Gaussian function is fully decribed by amplitude, center, width and offset. The FWHM of Gaussian function is given as 2.35482*width. The Levenberg–Marquardt algorithm was taken from document "METHODS FOR NON-LINEAR LEAST SQUARES PROBLEMS" written by K. Madsen, H.B. Nielsen, O. Tingleff (Technical University of Denmark). This pdf document can be found on the web-page <http://www2.imm.dtu.dk/pubdb/edoc/imm3215.pdf>. You can also use the Eigen C++ library for linear algebra to rewrite Matlab code for C++ if necessary. Enjoy the algorithm.