feat: support multivector type (#2005)

Signed-off-by: BubbleCal <bubble-cal@outlook.com>

docs/src/search.md

@@ -138,6 +138,36 @@ LanceDB supports binary vectors as a data type, and has the ability to search bi
         --8<-- "python/python/tests/docs/test_binary_vector.py:async_binary_vector"
         ```
 
+## Multivector type
+
+LanceDB supports multivector type, this is useful when you have multiple vectors for a single item (e.g. with ColBert and ColPali).
+
+You can index on a column with multivector type and search on it, the query can be single vector or multiple vectors. If the query is multiple vectors `mq`, the similarity (distance) from it to any multivector `mv` in the dataset, is defined as:
+
+![maxsim](assets/maxsim.png)
+
+where `sim` is the similarity function (e.g. cosine).
+
+For now, only `cosine` metric is supported for multivector search.
+
+=== "Python"
+
+    === "sync API"
+
+        ```python
+        --8<-- "python/python/tests/docs/test_multivector.py:imports"
+
+        --8<-- "python/python/tests/docs/test_multivector.py:sync_multivector"
+        ```
+
+    === "async API"
+
+        ```python
+        --8<-- "python/python/tests/docs/test_multivector.py:imports"
+
+        --8<-- "python/python/tests/docs/test_multivector.py:async_multivector"
+        ```
+
 ## Search with distance range
 
 You can also search for vectors within a specific distance range from the query vector. This is useful when you want to find vectors that are not just the nearest neighbors, but also those that are within a certain distance. This can be done by using the `distance_range` method.

docs/src/sql.md

@@ -18,7 +18,7 @@ import numpy as np
 
 uri = "data/sample-lancedb"
 data = [{"vector": row, "item": f"item {i}", "id": i}
-    for i, row in enumerate(np.random.random((10_000, 2)).astype('int'))]
+    for i, row in enumerate(np.random.random((10_000, 2)))]
 
 # Synchronous client
 db = lancedb.connect(uri)