langchain/utils/math.py

"""Math utils."""
import logging
from typing import List, Optional, Tuple, Union

import numpy as np

logger = logging.getLogger(__name__)

Matrix = Union[List[List[float]], List[np.ndarray], np.ndarray]


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}."
        )
    try:
        import simsimd as simd

        X = np.array(X, dtype=np.float32)
        Y = np.array(Y, dtype=np.float32)
        Z = 1 - simd.cdist(X, Y, metric="cosine")
        if isinstance(Z, float):
            return np.array([Z])
        return Z
    except ImportError:
        logger.info(
            "Unable to import simsimd, defaulting to NumPy implementation. If you want "
            "to use simsimd please install with `pip install simsimd`."
        )
        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


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.

    Returns:
        Tuple of two lists. First contains two-tuples of indices (X_idx, Y_idx),
            second contains corresponding cosine similarities.
    """
    if len(X) == 0 or len(Y) == 0:
        return [], []
    score_array = cosine_similarity(X, Y)
    score_threshold = score_threshold or -1.0
    score_array[score_array < score_threshold] = 0
    top_k = min(top_k or len(score_array), np.count_nonzero(score_array))
    top_k_idxs = np.argpartition(score_array, -top_k, axis=None)[-top_k:]
    top_k_idxs = top_k_idxs[np.argsort(score_array.ravel()[top_k_idxs])][::-1]
    ret_idxs = np.unravel_index(top_k_idxs, score_array.shape)
    scores = score_array.ravel()[top_k_idxs].tolist()
    return list(zip(*ret_idxs)), scores  # type: ignore