added distance calculation samples

Author: yorek

.gitignore

@@ -400,4 +400,5 @@ FodyWeavers.xsd
 # Custom
 *.local.txt
 *.local.sql
-.venv/
+.venv/
+.env

distance-calculations-in-tsql.md

@@ -0,0 +1,83 @@
+# How to calculate common vectors distances in T-SQL
+
+The sample data used to show how to calculate the common vector distances in T-SQL the following
+
+```sql
+declare @v1 nvarchar(max) = '[1,3,-5]';
+declare @v2 nvarchar(max) = '[4,-2,-1]';
+
+drop table if exists #v1;
+select 
+    cast([key] as int) as [vector_value_id], 
+    cast([value] as float) as [vector_value]
+into 
+    #v1 
+from
+    openjson(@v1);
+
+drop table if exists #v2;
+select 
+    cast([key] as int) as [vector_value_id], 
+    cast([value] as float) as [vector_value]
+into 
+    #v2
+from
+    openjson(@v2);
+```
+
+## Cosine Distance
+
+The cosine distance can be calculated as follows:
+
+```sql
+select
+    1-SUM(v1.[vector_value] * v2.[vector_value]) / 
+    (
+        SQRT(SUM(v1.[vector_value] * v1.[vector_value])) 
+        * 
+        SQRT(SUM(v2.[vector_value] * v2.[vector_value]))
+    ) as cosine_distance
+from
+    #v1 as v1
+inner join 
+    #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id]
+```
+
+## Dot Product
+
+The dot produce can be calculated as follows:
+
+```sql
+select
+    SUM(v1.[vector_value] * v2.[vector_value]) as dot_product
+from
+    #v1 as v1
+inner join 
+    #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id]
+```
+
+## Euclidean Distance
+
+The euclidean distance can be calculated as follows:
+
+```sql
+select
+    SQRT(SUM(POWER(v1.[vector_value] - v2.[vector_value], 2))) as euclidean_distance    
+from
+    #v1 as v1  
+inner join
+    #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id]
+```
+
+## Manhattan Distance
+
+The manhattan distance can be calculated as follows:
+
+```sql
+select
+    SUM(ABS(v1.[vector_value] - v2.[vector_value])) as manhattan_distance
+from
+    #v1 as v1  
+inner join
+    #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id]
+```