Barvinok's naive algorithm in Distance Geometry

In 1997, A. Barvinok gave a probabilistic algorithm to derive a near-feasible solution of a quadratically (equation) constrained problem from its semidefinite relaxation. We generalize this algorithm to handle matrix variables instead of vectors, and to handle two-sided inequalities instead of equations. We derive a heuristic for the distance geometry problem, and showcase its computational performance on a set of instances related to protein conformation.