Levenberg-Marquardt algorithm - sinus fit - low level 1D

I post the Levenberg-Marquardt algorithm for fitting sinusoidal function using only 1D representation of matrices.

I post here the Levenberg-Marquardt algorithm for fitting sinusoidal function. The sinusiodal function is one of the basic non-linear functions. The sinusoidal function is frequently used in optics in interferometry or electronics. Here, I post Levenberg–Marquardt algorithm for fitting simple sinusoidal function. The study material and detail explanation of algorithm is posted by Technical University of Denmark by Madsen, Nielsen and Tingleff on the web-page <http://www2.imm.dtu.dk/pubdb/edoc/imm3215.pdf>.

The presented algorithm fits amplitude, phase and offset of sinusoidal function. The only difference from my previous posts in file exchange is that in this algorithm I am using matrix multiplication and matrix inversion on the matrices, which all of them are represented as 1D matrices. This was done as preparation to rewrite Matlab code to the C++ code using anly 1D arrays and for cycles. I demonstrate here that sometimes you can use Matlab for prototyping and later you can transfer low level algorithms from Matlab to C++.