"""Various Utility Functions
- Tools for handling bson.ObjectId
The help IDs live as ObjectId in MongoDB and str in Langchain and JSON.
- Tools for the Maximal Marginal Relevance (MMR) reranking
These are duplicated from langchain_community to avoid cross-dependencies.
Functions "maximal_marginal_relevance" and "cosine_similarity"
are duplicated in this utility respectively from modules:
- "libs/community/langchain_community/vectorstores/utils.py"
- "libs/community/langchain_community/utils/math.py"
"""
from __future__ import annotations
import logging
from datetime import date, datetime
from typing import Any, Dict, List, 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 - 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
[docs]def maximal_marginal_relevance(
query_embedding: np.ndarray,
embedding_list: list,
lambda_mult: float = 0.5,
k: int = 4,
) -> List[int]:
"""Compute Maximal Marginal Relevance (MMR).
MMR is a technique used to select documents that are both relevant to the query
and diverse among themselves. This function returns the indices
of the top-k embeddings that maximize the marginal relevance.
Args:
query_embedding (np.ndarray): The embedding vector of the query.
embedding_list (list of np.ndarray): A list containing the embedding vectors
of the candidate documents.
lambda_mult (float, optional): The trade-off parameter between
relevance and diversity. Defaults to 0.5.
k (int, optional): The number of embeddings to select. Defaults to 4.
Returns:
list of int: The indices of the embeddings that maximize the marginal relevance.
Notes:
The Maximal Marginal Relevance (MMR) is computed using the following formula:
MMR = argmax_{D_i ∈ R \ S} [λ * Sim(D_i, Q) - (1 - λ) * max_{D_j ∈ S} Sim(D_i, D_j)]
where:
- R is the set of candidate documents,
- S is the set of selected documents,
- Q is the query embedding,
- Sim(D_i, Q) is the similarity between document D_i and the query,
- Sim(D_i, D_j) is the similarity between documents D_i and D_j,
- λ is the trade-off parameter.
"""
if min(k, len(embedding_list)) <= 0:
return []
if query_embedding.ndim == 1:
query_embedding = np.expand_dims(query_embedding, axis=0)
similarity_to_query = cosine_similarity(query_embedding, embedding_list)[0]
most_similar = int(np.argmax(similarity_to_query))
idxs = [most_similar]
selected = np.array([embedding_list[most_similar]])
while len(idxs) < min(k, len(embedding_list)):
best_score = -np.inf
idx_to_add = -1
similarity_to_selected = cosine_similarity(embedding_list, selected)
for i, query_score in enumerate(similarity_to_query):
if i in idxs:
continue
redundant_score = max(similarity_to_selected[i])
equation_score = (
lambda_mult * query_score - (1 - lambda_mult) * redundant_score
)
if equation_score > best_score:
best_score = equation_score
idx_to_add = i
idxs.append(idx_to_add)
selected = np.append(selected, [embedding_list[idx_to_add]], axis=0)
return idxs
[docs]def str_to_oid(str_repr: str) -> Any | str:
"""Attempt to cast string representation of id to MongoDB's internal BSON ObjectId.
To be consistent with ObjectId, input must be a 24 character hex string.
If it is not, MongoDB will happily use the string in the main _id index.
Importantly, the str representation that comes out of MongoDB will have this form.
Args:
str_repr: id as string.
Returns:
ObjectID
"""
from bson import ObjectId
from bson.errors import InvalidId
try:
return ObjectId(str_repr)
except InvalidId:
logger.debug(
"ObjectIds must be 12-character byte or 24-character hex strings. "
"Examples: b'heres12bytes', '6f6e6568656c6c6f68656768'"
)
return str_repr
[docs]def oid_to_str(oid: Any) -> str:
"""Convert MongoDB's internal BSON ObjectId into a simple str for compatibility.
Instructive helper to show where data is coming out of MongoDB.
Args:
oid: bson.ObjectId
Returns:
24 character hex string.
"""
return str(oid)
[docs]def make_serializable(
obj: Dict[str, Any],
) -> None:
"""Recursively cast values in a dict to a form able to json.dump"""
from bson import ObjectId
for k, v in obj.items():
if isinstance(v, dict):
make_serializable(v)
elif isinstance(v, list) and v and isinstance(v[0], (ObjectId, date, datetime)):
obj[k] = [oid_to_str(item) for item in v]
elif isinstance(v, ObjectId):
obj[k] = oid_to_str(v)
elif isinstance(v, (datetime, date)):
obj[k] = v.isoformat()
