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Code Optimization for For Loops in Task Parameterized Gaussian Mixture Models

I’m currently developing TPGMM from Salinon’s work (https://calinon.ch/papers/Calinon-JIST2015.pdf). I’m dealing with large matrix operations using CuPy as shown in the code below. However, I’m having trouble vectorizing the nested for loops in the EM function to make it more efficient. Are there any libraries or algorithms for this sort of vectorization?