To do so, an algorithm based on (42) was used. The constraint 𝑿 ̃ ≥ 0 sets that every 𝒙 𝒋 values is non-negative. This ensures that the solution vector 𝑿 ̃ represents physically meaningful, nonnegative abundances of species. The resulting 𝑿 ̃ vector is still of size 1 × 𝑝 with 𝑥 ̃𝑗 representing the calculated abundance of the j th specie in the sample.