Our tests for the subspace embedding properties of Gaussian and uniform operators rely on a probabilistic analysis of the power method. That analysis assumes the initial vector is drawn uniformly from the unit sphere. It isn't appropriate to use our internal functions for sampling from the Gaussian distribution to draw this vector. Instead, we can use the normal distribution in the C++ STL with the Mersenne Twister as the underlying engine.
Interesting fact: C++26 will ship with Philox in the STL!
Our tests for the subspace embedding properties of Gaussian and uniform operators rely on a probabilistic analysis of the power method. That analysis assumes the initial vector is drawn uniformly from the unit sphere. It isn't appropriate to use our internal functions for sampling from the Gaussian distribution to draw this vector. Instead, we can use the normal distribution in the C++ STL with the Mersenne Twister as the underlying engine.
Interesting fact: C++26 will ship with Philox in the STL!