feat: Add VEC_PRODUCT, VEC_ELEM_PRODUCT, VEC_NORM. (#5303)

* feat: Add `vec_product(col)` function.

* feat: Add `vec_elem_product` function

* feat: Add `vec_norm` function.

src/query/src/tests.rs

@@ -33,6 +33,7 @@ mod time_range_filter_test;
 
 mod function;
 mod pow;
+mod vec_product_test;
 mod vec_sum_test;
 
 async fn exec_selection(engine: QueryEngineRef, sql: &str) -> Vec<RecordBatch> {

src/query/src/tests/vec_product_test.rs

@@ -0,0 +1,67 @@
+// Copyright 2023 Greptime Team
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+use std::borrow::Cow;
+
+use common_function::scalars::vector::impl_conv::{
+    as_veclit, as_veclit_if_const, veclit_to_binlit,
+};
+use datatypes::prelude::Value;
+use nalgebra::{Const, DVectorView, Dyn, OVector};
+
+use crate::tests::{exec_selection, function};
+
+#[tokio::test]
+async fn test_vec_product_aggregator() -> Result<(), common_query::error::Error> {
+    common_telemetry::init_default_ut_logging();
+    let engine = function::create_query_engine_for_vector10x3();
+    let sql = "select VEC_PRODUCT(vector) as vec_product from vectors";
+    let result = exec_selection(engine.clone(), sql).await;
+    let value = function::get_value_from_batches("vec_product", result);
+
+    let mut expected_value = None;
+
+    let sql = "SELECT vector FROM vectors";
+    let vectors = exec_selection(engine, sql).await;
+
+    let column = vectors[0].column(0);
+    let vector_const = as_veclit_if_const(column)?;
+
+    for i in 0..column.len() {
+        let vector = match vector_const.as_ref() {
+            Some(vector) => Some(Cow::Borrowed(vector.as_ref())),
+            None => as_veclit(column.get_ref(i))?,
+        };
+        let Some(vector) = vector else {
+            expected_value = None;
+            break;
+        };
+        expected_value
+            .get_or_insert_with(|| {
+                OVector::from_iterator_generic(
+                    Dyn(vector.len()),
+                    Const::<1>,
+                    (0..vector.len()).map(|_| 1.0),
+                )
+            })
+            .component_mul_assign(&DVectorView::from_slice(&vector, vector.len()));
+    }
+    let expected_value = match expected_value.map(|v| veclit_to_binlit(v.as_slice())) {
+        None => Value::Null,
+        Some(bytes) => Value::from(bytes),
+    };
+    assert_eq!(value, expected_value);
+
+    Ok(())
+}