feat: add Vector Index API (#894)

* chore: Update gapic-generator-python to v1.16.1

PiperOrigin-RevId: 618243632

Source-Link: googleapis/googleapis@078a38b

Source-Link: googleapis/googleapis-gen@7af768c
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* 🦉 Updates from OwlBot post-processor

See https://github.com/googleapis/repo-automation-bots/blob/main/packages/owl-bot/README.md

* feat: add Vector Index API

PiperOrigin-RevId: 618867415

Source-Link: googleapis/googleapis@277145d

Source-Link: googleapis/googleapis-gen@adcd307
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---------

Co-authored-by: Owl Bot <gcf-owl-bot[bot]@users.noreply.github.com>

google/cloud/firestore_admin_v1/types/index.py

@@ -177,6 +177,11 @@ class IndexField(proto.Message):
                 Indicates that this field supports operations on
                 ``array_value``\ s.
 
+                This field is a member of `oneof`_ ``value_mode``.
+            vector_config (google.cloud.firestore_admin_v1.types.Index.IndexField.VectorConfig):
+                Indicates that this field supports nearest
+                neighbors and distance operations on vector.
+
                 This field is a member of `oneof`_ ``value_mode``.
         """
 
@@ -211,6 +216,41 @@ class ArrayConfig(proto.Enum):
             ARRAY_CONFIG_UNSPECIFIED = 0
             CONTAINS = 1
 
+        class VectorConfig(proto.Message):
+            r"""The index configuration to support vector search operations
+
+            .. _oneof: https://proto-plus-python.readthedocs.io/en/stable/fields.html#oneofs-mutually-exclusive-fields
+
+            Attributes:
+                dimension (int):
+                    Required. The vector dimension this
+                    configuration applies to.
+                    The resulting index will only include vectors of
+                    this dimension, and can be used for vector
+                    search with the same dimension.
+                flat (google.cloud.firestore_admin_v1.types.Index.IndexField.VectorConfig.FlatIndex):
+                    Indicates the vector index is a flat index.
+
+                    This field is a member of `oneof`_ ``type``.
+            """
+
+            class FlatIndex(proto.Message):
+                r"""An index that stores vectors in a flat data structure, and
+                supports exhaustive search.
+
+                """
+
+            dimension: int = proto.Field(
+                proto.INT32,
+                number=1,
+            )
+            flat: "Index.IndexField.VectorConfig.FlatIndex" = proto.Field(
+                proto.MESSAGE,
+                number=2,
+                oneof="type",
+                message="Index.IndexField.VectorConfig.FlatIndex",
+            )
+
         field_path: str = proto.Field(
             proto.STRING,
             number=1,
@@ -227,6 +267,12 @@ class ArrayConfig(proto.Enum):
             oneof="value_mode",
             enum="Index.IndexField.ArrayConfig",
         )
+        vector_config: "Index.IndexField.VectorConfig" = proto.Field(
+            proto.MESSAGE,
+            number=4,
+            oneof="value_mode",
+            message="Index.IndexField.VectorConfig",
+        )
 
     name: str = proto.Field(
         proto.STRING,