Source code for langchain.utils.math
"""Math utils."""
from typing import List, Optional, Tuple, Union
import numpy as np
Matrix = Union[List[List[float]], List[np.ndarray], np.ndarray]
[docs]def cosine_similarity(X: Matrix, Y: Matrix) -> np.ndarray:
    """Row-wise cosine similarity between two equal-width matrices."""
    if len(X) == 0 or len(Y) == 0:
        return np.array([])
    X = np.array(X)
    Y = np.array(Y)
    if X.shape[1] != Y.shape[1]:
        raise ValueError(
            f"Number of columns in X and Y must be the same. X has shape {X.shape} "
            f"and Y has shape {Y.shape}."
        )
    X_norm = np.linalg.norm(X, axis=1)
    Y_norm = np.linalg.norm(Y, axis=1)
    # Ignore divide by zero errors run time warnings as those are handled below.
    with np.errstate(divide="ignore", invalid="ignore"):
        similarity = np.dot(X, Y.T) / np.outer(X_norm, Y_norm)
    similarity[np.isnan(similarity) | np.isinf(similarity)] = 0.0
    return similarity
[docs]def cosine_similarity_top_k(
    X: Matrix,
    Y: Matrix,
    top_k: Optional[int] = 5,
    score_threshold: Optional[float] = None,
) -> Tuple[List[Tuple[int, int]], List[float]]:
    """Row-wise cosine similarity with optional top-k and score threshold filtering.
    Args:
        X: Matrix.
        Y: Matrix, same width as X.
        top_k: Max number of results to return.
        score_threshold: Minimum cosine similarity of results.