python - Converting nested loop for faster computation of adjusted cosine similarity for sparse matrices -

i have following function calculating adjusted cosine similarity. takes in 2 numpy matrices. mean centered ratings matrix of size 22000 users x 503 items , similarity matrix empty matrix of size 22000 x 22000 since user user similarity. takes hours calculate similarity. how can make run faster?

def adjusted_cosine_similarity(ratings_centered_matrix, similarity_matrix):      x in range(0, ratings_centered_matrix.shape[0]):  # index of array         y in range(0, ratings_centered_matrix.shape[0]):             s = np.sum(ratings_centered_matrix[x, :] * ratings_centered_matrix[y, :]             si = np.sqrt(np.sum(ratings_centered_matrix[x, :] ** 2))             sj = np.sqrt(np.sum(ratings_centered_matrix[y, :] ** 2))             sim = s / (si * sj)             similarity_matrix[x, y] = round(sim, 2)             similarity_matrix[x, y] = sim