Construction of completely positive matrices

If a symmetric matrix A can be factorized of the form A = BB^T where B is an entry wise nonnegative matrix, then A is called a Completely Matrix (CP). Completely positive matrices have arisen in some situations in economic modelling and appear to have some applications in statistics, and they are also appear in quadratic optimization. If we pick a random matrix, most probably it is not CP. In this paper we give an algorithm to construct a CP matrix from two given nonnegative spectrum.