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| 1 | +# How to calculate common vectors distances in T-SQL |
| 2 | + |
| 3 | +The sample data used to show how to calculate the common vector distances in T-SQL the following |
| 4 | + |
| 5 | +```sql |
| 6 | +declare @v1 nvarchar(max) = '[1,3,-5]'; |
| 7 | +declare @v2 nvarchar(max) = '[4,-2,-1]'; |
| 8 | + |
| 9 | +drop table if exists #v1; |
| 10 | +select |
| 11 | + cast([key] as int) as [vector_value_id], |
| 12 | + cast([value] as float) as [vector_value] |
| 13 | +into |
| 14 | + #v1 |
| 15 | +from |
| 16 | + openjson(@v1); |
| 17 | + |
| 18 | +drop table if exists #v2; |
| 19 | +select |
| 20 | + cast([key] as int) as [vector_value_id], |
| 21 | + cast([value] as float) as [vector_value] |
| 22 | +into |
| 23 | + #v2 |
| 24 | +from |
| 25 | + openjson(@v2); |
| 26 | +``` |
| 27 | + |
| 28 | +## Cosine Distance |
| 29 | + |
| 30 | +The cosine distance can be calculated as follows: |
| 31 | + |
| 32 | +```sql |
| 33 | +select |
| 34 | + 1-SUM(v1.[vector_value] * v2.[vector_value]) / |
| 35 | + ( |
| 36 | + SQRT(SUM(v1.[vector_value] * v1.[vector_value])) |
| 37 | + * |
| 38 | + SQRT(SUM(v2.[vector_value] * v2.[vector_value])) |
| 39 | + ) as cosine_distance |
| 40 | +from |
| 41 | + #v1 as v1 |
| 42 | +inner join |
| 43 | + #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id] |
| 44 | +``` |
| 45 | + |
| 46 | +## Dot Product |
| 47 | + |
| 48 | +The dot produce can be calculated as follows: |
| 49 | + |
| 50 | +```sql |
| 51 | +select |
| 52 | + SUM(v1.[vector_value] * v2.[vector_value]) as dot_product |
| 53 | +from |
| 54 | + #v1 as v1 |
| 55 | +inner join |
| 56 | + #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id] |
| 57 | +``` |
| 58 | + |
| 59 | +## Euclidean Distance |
| 60 | + |
| 61 | +The euclidean distance can be calculated as follows: |
| 62 | + |
| 63 | +```sql |
| 64 | +select |
| 65 | + SQRT(SUM(POWER(v1.[vector_value] - v2.[vector_value], 2))) as euclidean_distance |
| 66 | +from |
| 67 | + #v1 as v1 |
| 68 | +inner join |
| 69 | + #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id] |
| 70 | +``` |
| 71 | + |
| 72 | +## Manhattan Distance |
| 73 | + |
| 74 | +The manhattan distance can be calculated as follows: |
| 75 | + |
| 76 | +```sql |
| 77 | +select |
| 78 | + SUM(ABS(v1.[vector_value] - v2.[vector_value])) as manhattan_distance |
| 79 | +from |
| 80 | + #v1 as v1 |
| 81 | +inner join |
| 82 | + #v2 as v2 on v1.[vector_value_id] = v2.[vector_value_id] |
| 83 | +``` |
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