Forgive me for being slow, but this line checks whether at least one of ['xbar_', 'scalings_'] is fitted, but lower down, in X_new = np.dot(X - self.xbar_, self.scalings_) both of them are needed. Shouldn't any --> all?

And further down X_new = np.dot(X, self.scalings_) makes me conclude that at least scalings_ is indispensable?

I didn't write these lines, but I guess if the solver is eigen you only have scalings and if solver="svd" you have both. I could remove xbar_ from it, but I don't feel that would make it better or worse. I could branch the check on the solver parameter but I'm not sure how helpful that would be.

Well my concern was that check_is_fitted is fine with only xbar_ fitted which is useful nowhere. So I would remove xbar_ at least from that check for logical consistency.

For completeness a check_is_fitted(self, 'xbar_') could then go in the appropriate decision branch. But I don't insist on that one because from what I see check_is_fitted is about throwing graceful errors if the variable concerned hasn't been fitted. For x_bar_ not to be fitted if solver == 'svd', the user must have called fit with a different solver and then changed the solver by hand, which I consider advanced (and weird), so that the user can then also deal with the ensuing error message.

This basically also invalidates what I said above. I will post this message to be able to remember the reasoning, but I agree with you that nothing needs to be changed.