Construction of completely positive matrices

If a symmetric matrix A can be factorized of the form A = BBT where B is an entrywise nonnegative matrix, then A is called a Completely Matrix (CP). Completelypositive matrices have arisen in some situations in economic modelling and appear tohave 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 givean algorithm to construct a CP matrix from two given nonnegative spectrum.