Building covariance matrices with the desired structure

• We propose a heuristic method to build a covariance matrix with a fixed structure.
• We generalize previous methods from the literature.
• The matlab code for the algorithm is provided.

The problem of building a covariance matrix by fixing their diagonal values (variances) and all or a subset of its eigenvalues has been solved in different ways in the literature. In this paper we propose an iterative heuristic method to build such covariance matrix when a subset of its covariances is also chosen from the user. This provides a more flexible approach than those available in the literature for designing covariance matrices with the desired structure. As in other related approaches, the proposal can be useful for testing the performance of chemometric methods with data sets matching the theoretical conditions for their applicability or checking their robustness when the hypothesized properties fail.