docs: show stateful class Functions

The Functions page only showed a plain function, so it never said where a class's `__init__` runs. Users loading a large model need to know it is not the client: registration reads the signature and ships the source.

This adds a section on class Functions: `__init__` runs once per instance on the worker, then `__call__` per row or batch and `close()` on retirement, state is per instance, and `__init__` parameters are initialization fields set per binding. The example's test asserts that registering the class does not construct it.

docs/web-tests/py/test_function.py

@@ -50,6 +50,25 @@ def describe(value: float):
     return {"half": value / 2, "note": None}
 
 
+# --8<-- [start:function_class_define]
+@udf(pip=["sentence-transformers"])
+class embed:
+    def __init__(self, model: str = "all-MiniLM-L6-v2"):
+        # Runs on the worker, once per instance: only the worker needs the package.
+        from sentence_transformers import SentenceTransformer
+
+        self.model = SentenceTransformer(model)
+
+    def __call__(self, text: str) -> list[float]:
+        return self.model.encode(text).tolist()
+
+    def close(self):
+        del self.model
+
+
+# --8<-- [end:function_class_define]
+
+
 # A Function version as the service returns it after registration: the SDK's
 # shared golden reply, with the name and signature of the definition above.
 SERVICE_REPLY = (
@@ -166,6 +185,31 @@ def test_function_version_binds_a_column(tmp_path):
         table.add_columns({"doubled": application})
 
 
+def test_class_function_is_constructed_only_where_it_runs():
+    # Registration reads __init__'s signature; it never constructs the class,
+    # so the model's package need not be installed here.
+    assert "sentence_transformers" not in sys.modules
+    signature = embed.registration_request.signature
+    assert [
+        (field.name, field.arrow_type, field.nullable)
+        for field in signature.initialization
+    ] == [("model", "utf8", True)]
+    assert [(p.name, p.arrow_type) for p in signature.inputs] == [("text", "utf8")]
+    assert "sentence_transformers" not in sys.modules
+
+    embedder = registered_version(embed)
+    # --8<-- [start:function_class_apply]
+    from lancedb import col
+
+    application = embedder(text=col("text"), model="all-mpnet-base-v2")
+    # --8<-- [end:function_class_apply]
+    assert application.initialization == {"model": "all-mpnet-base-v2"}
+    # The default applies to an omitted field.
+    assert embedder(text=col("text")).initialization == {}
+    with pytest.raises(TypeError, match="unknown arguments"):
+        embedder(text=col("text"), device="cuda")
+
+
 def test_function_enterprise(monkeypatch):
     require_deployment()