Source code for langchain_community.utils.math

"""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]

[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}." ) 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 np.array(Z) except ImportError: logger.debug( "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 =, 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. 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