Code Optimization

where: and are square square matrices of N x N size , respectively, are transposed , respectively transposed is the multiplication operation is the assembly operation the application results in a matrix of the same dimensions as the matrix A and for which the elements above and the main diagonal are those in the matrix A on the corresponding positions, the other elements being 0 is raised to square It is desirable to implement the above operation in C / C ++ in 4 ways:  blas - a variant that uses one or more functions in BLAS Atlas 1)  neopt - a "hand" version without improvements  opt_m - an improved version of the above version. Improving is only about modifying the code to get better performance  opt_f - another improved version obtained by compiling code from neopt with other compilation flags that bring a performance bonus