Rescaling matrix W

[shizukann]

Hi Gregory,

First of all, I'd like to thank you for your great tutorial, especially the valuable appendix, which helps a lot in understanding the Fourier random features and its derivation.

random-fourier-features/rffgpr.py

Line 86 in 7144f02

Z = norm * np.sqrt(2) * np.cos(self.sigma * W @ X.T + B)

However, I don't quite understand why the matrix W is scaled by sigma instead of a lengthscale. I thought lengthscale was in the bracket of exp and sigma was the variance (or standard deviation) of the entire component. Please correct me if I'm misunderstanding the intention here.

Thank you.