From the previous entry, but I wanted to dedicate an entry just that implementation, Bamdev Mishra also mentions the release of Manopt. Please note the tutorial page and a forum:
Manopt is a Matlab toolbox for optimization on manifolds. Optimization on manifolds is a powerful paradigm to address nonlinear optimization problems. With Manopt, it is easy to deal with various types of constraints that arise naturally in applications, such as orthonormality or low rank. It comes with a large library of manifolds and ready-to-use Riemannian optimization algorithms. It is well documented and includes diagnostics tools to help you get started quickly and make sure you make no mistakes along the way. It is designed to provide great flexibility in describing your cost function and incorporates an optional caching system for more efficiency.
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