  Coherence vectors and correlation matrices are important functions frequently
used in physics. The numerical calculation of these functions directly from
their definitions, which involves Kronecker products and matrix
multiplications, may seem to be a reasonable option. Notwithstanding, as we
demonstrate in this article, some algebraic manipulations before programming
can reduce considerably their computational complexity. Besides, we provide
Fortran code to generate generalized Gell Mann matrices and to compute the
optimized and unoptimized versions of the associated Bloch's vectors and
correlation matrix, in the case of bipartite quantum systems. As a code test
and application example, we consider the calculation of Hilbert-Schmidt quantum
discords.
