Hybrid Search Implementation

# hybrid-search-implementation — templates and worked examples

## Templates

### Template 1: Reciprocal Rank Fusion

```python
from typing import List, Dict, Tuple
from collections import defaultdict

def reciprocal_rank_fusion(
    result_lists: List[List[Tuple[str, float]]],
    k: int = 60,
    weights: List[float] = None
) -> List[Tuple[str, float]]:
    """
    Combine multiple ranked lists using RRF.

    Args:
        result_lists: List of (doc_id, score) tuples per search method
        k: RRF constant (higher = more weight to lower ranks)
        weights: Optional weights per result list

    Returns:
        Fused ranking as (doc_id, score) tuples
    """
    if weights is None:
        weights = [1.0] * len(result_lists)

    scores = defaultdict(float)

    for result_list, weight in zip(result_lists, weights):
        for rank, (doc_id, _) in enumerate(result_list):
            # RRF formula: 1 / (k + rank)
            scores[doc_id] += weight * (1.0 / (k + rank + 1))

    # Sort by fused score
    return sorted(scores.items(), key=lambda x: x[1], reverse=True)


def linear_combination(
    vector_results: List[Tuple[str, float]],
    keyword_results: List[Tuple[str, float]],
    alpha: float = 0.5
) -> List[Tuple[str, float]]:
    """
    Combine results with linear interpolation.

    Args:
        vector_results: (doc_id, similarity_score) from vector search
        keyword_results: (doc_id, bm25_score) from keyword search
        alpha: Weight for vector search (1-alpha for keyword)
    """
    # Normalize scores to [0, 1]
    def normalize(results):
        if not results:
            return {}
        scores = [s for _, s in results]
        min_s, max_s = min(scores), max(scores)
        range_s = max_s - min_s if max_s != min_s else 1
        return {doc_id: (score - min_s) / range_s for doc_id, score in results}

    vector_scores = normalize(vector_results)
    keyword_scores = normalize(keyword_results)

    # Combine
    all_docs = set(vector_scores.keys()) | set(keyword_scores.keys())
    combined = {}

    for doc_id in all_docs:
        v_score = vector_scores.get(doc_id, 0)
        k_score = keyword_scores.get(doc_id, 0)
        combined[doc_id] = alpha * v_score + (1 - alpha) * k_score

    return sorted(combined.items(), key=lambda x: x[1], reverse=True)
```

### Template 2: PostgreSQL Hybrid Search

```python
import asyncpg
from typing import List, Dict, Optional
import numpy as np

class PostgresHybridSearch:
    """Hybrid search with pgvector and full-text search."""

    def __init__(self, pool: asyncpg.Pool):
        self.pool = pool

    async def setup_schema(self):
        """Create tables and indexes."""
        async with self.pool.acquire() as conn:
            await conn.execute("""
                CREATE EXTENSION IF NOT EXISTS vector;

                CREATE TABLE IF NOT EXISTS documents (
                    id TEXT PRIMARY KEY,
                    content TEXT NOT NULL,
                    embedding vector(1536),
                    metadata JSONB DEFAULT '{}',
                    ts_content tsvector GENERATED ALWAYS AS (
                        to_tsvector('english', content)
                    ) STORED
                );

                -- Vector index (HNSW)
                CREATE INDEX IF NOT EXISTS documents_embedding_idx
                ON documents USING hnsw (embedding vector_cosine_ops);

                -- Full-text index (GIN)
                CREATE INDEX IF NOT EXISTS documents_fts_idx
                ON documents USING gin (ts_content);
            """)

    async def hybrid_search(
        self,
        query: str,
        query_embedding: List[float],
        limit: int = 10,
        vector_weight: float = 0.5,
        filter_metadata: Optional[Dict] = None
    ) -> List[Dict]:
        """
        Perform hybrid search combining vector and full-text.

        Uses RRF fusion for combining results.
        """
        async with self.pool.acquire() as conn: