Collaborative filtering prediction

Implement a single user-based collaborative-filtering prediction. You are given ratings, a dict mapping user id (string) to a dict of {item id (string): rating (number)}; a target user u; and an item i. Predict u's rating for i as the cosine-weighted average of the ratings other users gave to i, weighted by their cosine similarity to u (cosine over the items both users have rated; 0 if they share no items). Only include neighbors who have rated i and whose similarity to u is strictly positive. If the sum of used similarities is 0 (no positive-similarity neighbor rated i), return 0.0. Return the predicted rating rounded to 6 decimals.