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57 lines
1.9 KiB
Python
57 lines
1.9 KiB
Python
"""Math utils."""
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from typing import List, Optional, Tuple, Union
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import numpy as np
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Matrix = Union[List[List[float]], List[np.ndarray], np.ndarray]
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def cosine_similarity(X: Matrix, Y: Matrix) -> np.ndarray:
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"""Row-wise cosine similarity between two equal-width matrices."""
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if len(X) == 0 or len(Y) == 0:
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return np.array([])
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X = np.array(X)
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Y = np.array(Y)
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if X.shape[1] != Y.shape[1]:
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raise ValueError(
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f"Number of columns in X and Y must be the same. X has shape {X.shape} "
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f"and Y has shape {Y.shape}."
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)
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X_norm = np.linalg.norm(X, axis=1)
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Y_norm = np.linalg.norm(Y, axis=1)
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similarity = np.dot(X, Y.T) / np.outer(X_norm, Y_norm)
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similarity[np.isnan(similarity) | np.isinf(similarity)] = 0.0
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return similarity
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def cosine_similarity_top_k(
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X: Matrix,
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Y: Matrix,
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top_k: Optional[int] = 5,
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score_threshold: Optional[float] = None,
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) -> Tuple[List[Tuple[int, int]], List[float]]:
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"""Row-wise cosine similarity with optional top-k and score threshold filtering.
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Args:
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X: Matrix.
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Y: Matrix, same width as X.
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top_k: Max number of results to return.
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score_threshold: Minimum cosine similarity of results.
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Returns:
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Tuple of two lists. First contains two-tuples of indices (X_idx, Y_idx),
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second contains corresponding cosine similarities.
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"""
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if len(X) == 0 or len(Y) == 0:
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return [], []
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score_array = cosine_similarity(X, Y)
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sorted_idxs = score_array.flatten().argsort()[::-1]
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top_k = top_k or len(sorted_idxs)
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top_idxs = sorted_idxs[:top_k]
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score_threshold = score_threshold or -1.0
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top_idxs = top_idxs[score_array.flatten()[top_idxs] > score_threshold]
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ret_idxs = [(x // score_array.shape[1], x % score_array.shape[1]) for x in top_idxs]
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scores = score_array.flatten()[top_idxs].tolist()
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return ret_idxs, scores
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