import numpy as np

def compute_similarities(ingredients_dict, products_dict):
    """Compute similarities between all products and ingredients using NumPy"""
    # Filter valid ingredients (with non-None embeddings)
    ingredient_names = []
    ingredient_embeddings_list = []
    for ing, emb in ingredients_dict.items():
        if emb is not None:
            ingredient_names.append(ing)
            ingredient_embeddings_list.append(emb)

    # Convert ingredient embeddings to numpy array
    ingredient_embeddings = np.array(ingredient_embeddings_list, dtype=np.float32)

    # Normalize ingredient embeddings for cosine similarity
    ingredient_norms = np.linalg.norm(ingredient_embeddings, axis=1, keepdims=True)
    normalized_ingredients = ingredient_embeddings / ingredient_norms

    # Process all products
    all_similarities = {}
    valid_products = []
    valid_embeddings = []

    for product, embedding in products_dict.items():
        if embedding is not None:
            valid_products.append(product)
            valid_embeddings.append(embedding)

    if not valid_products:
        return {}

    # Convert product embeddings to numpy array
    product_embeddings = np.array(valid_embeddings, dtype=np.float32)

    # Normalize product embeddings
    product_norms = np.linalg.norm(product_embeddings, axis=1, keepdims=True)
    normalized_products = product_embeddings / product_norms

    # Compute all similarities at once using matrix multiplication
    # (dot product of normalized vectors = cosine similarity)
    similarity_matrix = np.dot(normalized_products, normalized_ingredients.T)

    # Process and store results
    for p_idx, product in enumerate(valid_products):
        product_similarities = [(ingredient_names[i_idx], float(similarity_matrix[p_idx, i_idx]))
                              for i_idx in range(len(ingredient_names))]

        # Sort by similarity score (descending)
        product_similarities.sort(key=lambda x: x[1], reverse=True)
        all_similarities[product] = product_similarities

    return all_similarities