embeddings.py

"""Explicit 2D vector embeddings and cosine similarity calculations."""

import math

VECTORS = {
    "query": [0.10, 0.90],
    "calculator": [0.95, 0.05],
    "graph_lookup": [0.15, 0.85]
}


def dot_product(vector_a: list[float], vector_b: list[float]) -> float:
    return vector_a[0] * vector_b[0] + vector_a[1] * vector_b[1]


def magnitude(vector: list[float]) -> float:
    return math.sqrt(vector[0] ** 2 + vector[1] ** 2)


def calculate_cosine_similarity(vector_a: list[float], vector_b: list[float]) -> float:
    """Compute cosine similarity from first principles.

    Similarity = (A ⋅ B) / (||A|| ||B||)
    """
    denom = magnitude(vector_a) * magnitude(vector_b)
    if denom == 0:
        return 0.0
    return dot_product(vector_a, vector_b) / denom