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"""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 - np.array(simd.cdist(X, Y, metric="cosine"))
return 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 = 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
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