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1044 lines
23 KiB
Markdown
1044 lines
23 KiB
Markdown
---
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toc_priority: 66
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toc_title: Tuples
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---
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# Functions for Working with Tuples {#tuple-functions}
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## tuple {#tuple}
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A function that allows grouping multiple columns.
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For columns with the types T1, T2, …, it returns a Tuple(T1, T2, …) type tuple containing these columns. There is no cost to execute the function.
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Tuples are normally used as intermediate values for an argument of IN operators, or for creating a list of formal parameters of lambda functions. Tuples can’t be written to a table.
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The function implements the operator `(x, y, …)`.
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**Syntax**
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``` sql
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tuple(x, y, …)
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```
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## tupleElement {#tupleelement}
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A function that allows getting a column from a tuple.
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‘N’ is the column index, starting from 1. N must be a constant. ‘N’ must be a constant. ‘N’ must be a strict postive integer no greater than the size of the tuple.
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There is no cost to execute the function.
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The function implements the operator `x.N`.
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**Syntax**
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``` sql
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tupleElement(tuple, n)
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```
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## untuple {#untuple}
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Performs syntactic substitution of [tuple](../../sql-reference/data-types/tuple.md#tuplet1-t2) elements in the call location.
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**Syntax**
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``` sql
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untuple(x)
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```
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You can use the `EXCEPT` expression to skip columns as a result of the query.
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**Arguments**
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- `x` — A `tuple` function, column, or tuple of elements. [Tuple](../../sql-reference/data-types/tuple.md).
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**Returned value**
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- None.
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**Examples**
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Input table:
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``` text
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┌─key─┬─v1─┬─v2─┬─v3─┬─v4─┬─v5─┬─v6────────┐
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│ 1 │ 10 │ 20 │ 40 │ 30 │ 15 │ (33,'ab') │
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│ 2 │ 25 │ 65 │ 70 │ 40 │ 6 │ (44,'cd') │
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│ 3 │ 57 │ 30 │ 20 │ 10 │ 5 │ (55,'ef') │
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│ 4 │ 55 │ 12 │ 7 │ 80 │ 90 │ (66,'gh') │
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│ 5 │ 30 │ 50 │ 70 │ 25 │ 55 │ (77,'kl') │
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└─────┴────┴────┴────┴────┴────┴───────────┘
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```
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Example of using a `Tuple`-type column as the `untuple` function parameter:
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Query:
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``` sql
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SELECT untuple(v6) FROM kv;
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```
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Result:
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``` text
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┌─_ut_1─┬─_ut_2─┐
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│ 33 │ ab │
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│ 44 │ cd │
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│ 55 │ ef │
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│ 66 │ gh │
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│ 77 │ kl │
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└───────┴───────┘
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```
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Note: the names are implementation specific and are subject to change. You should not assume specific names of the columns after application of the `untuple`.
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Example of using an `EXCEPT` expression:
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Query:
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``` sql
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SELECT untuple((* EXCEPT (v2, v3),)) FROM kv;
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```
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Result:
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``` text
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┌─key─┬─v1─┬─v4─┬─v5─┬─v6────────┐
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│ 1 │ 10 │ 30 │ 15 │ (33,'ab') │
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│ 2 │ 25 │ 40 │ 6 │ (44,'cd') │
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│ 3 │ 57 │ 10 │ 5 │ (55,'ef') │
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│ 4 │ 55 │ 80 │ 90 │ (66,'gh') │
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│ 5 │ 30 │ 25 │ 55 │ (77,'kl') │
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└─────┴────┴────┴────┴───────────┘
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```
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**See Also**
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- [Tuple](../../sql-reference/data-types/tuple.md)
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## tupleHammingDistance {#tuplehammingdistance}
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Returns the [Hamming Distance](https://en.wikipedia.org/wiki/Hamming_distance) between two tuples of the same size.
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**Syntax**
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``` sql
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tupleHammingDistance(tuple1, tuple2)
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```
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**Arguments**
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- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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- `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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Tuples should have the same type of the elements.
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**Returned value**
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- The Hamming distance.
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Type: [UInt8](../../sql-reference/data-types/int-uint.md).
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**Examples**
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Query:
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``` sql
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SELECT tupleHammingDistance((1, 2, 3), (3, 2, 1)) AS HammingDistance;
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```
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Result:
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``` text
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┌─HammingDistance─┐
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│ 2 │
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└─────────────────┘
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```
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Can be used with [MinHash](../../sql-reference/functions/hash-functions.md#ngramminhash) functions for detection of semi-duplicate strings:
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``` sql
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SELECT tupleHammingDistance(wordShingleMinHash(string), wordShingleMinHashCaseInsensitive(string)) as HammingDistance FROM (SELECT 'ClickHouse is a column-oriented database management system for online analytical processing of queries.' AS string);
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```
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Result:
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``` text
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┌─HammingDistance─┐
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│ 2 │
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└─────────────────┘
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```
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## tupleToNameValuePairs {#tupletonamevaluepairs}
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Turns a named tuple into an array of (name, value) pairs. For a `Tuple(a T, b T, ..., c T)` returns `Array(Tuple(String, T), ...)`
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in which the `Strings` represents the named fields of the tuple and `T` are the values associated with those names. All values in the tuple should be of the same type.
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**Syntax**
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``` sql
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tupleToNameValuePairs(tuple)
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```
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**Arguments**
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- `tuple` — Named tuple. [Tuple](../../sql-reference/data-types/tuple.md) with any types of values.
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**Returned value**
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- An array with (name, value) pairs.
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Type: [Array](../../sql-reference/data-types/array.md)([Tuple](../../sql-reference/data-types/tuple.md)([String](../../sql-reference/data-types/string.md), ...)).
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**Example**
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Query:
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``` sql
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CREATE TABLE tupletest (`col` Tuple(user_ID UInt64, session_ID UInt64) ENGINE = Memory;
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INSERT INTO tupletest VALUES (tuple( 100, 2502)), (tuple(1,100));
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SELECT tupleToNameValuePairs(col) FROM tupletest;
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```
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Result:
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``` text
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┌─tupleToNameValuePairs(col)────────────┐
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│ [('user_ID',100),('session_ID',2502)] │
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│ [('user_ID',1),('session_ID',100)] │
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└───────────────────────────────────────┘
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```
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It is possible to transform colums to rows using this function:
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``` sql
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CREATE TABLE tupletest (`col` Tuple(CPU Float64, Memory Float64, Disk Float64)) ENGINE = Memory;
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INSERT INTO tupletest VALUES(tuple(3.3, 5.5, 6.6));
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SELECT arrayJoin(tupleToNameValuePairs(col))FROM tupletest;
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```
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Result:
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``` text
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┌─arrayJoin(tupleToNameValuePairs(col))─┐
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│ ('CPU',3.3) │
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│ ('Memory',5.5) │
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│ ('Disk',6.6) │
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└───────────────────────────────────────┘
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```
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If you pass a simple tuple to the function, ClickHouse uses the indexes of the values as their names:
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``` sql
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SELECT tupleToNameValuePairs(tuple(3, 2, 1));
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```
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Result:
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``` text
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┌─tupleToNameValuePairs(tuple(3, 2, 1))─┐
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│ [('1',3),('2',2),('3',1)] │
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└───────────────────────────────────────┘
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## tuplePlus {#tupleplus}
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Calculates the sum of corresponding values of two tuples of the same size.
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**Syntax**
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```sql
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tuplePlus(tuple1, tuple2)
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```
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Alias: `vectorSum`.
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**Arguments**
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- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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- `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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**Returned value**
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- Tuple with the sum.
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Type: [Tuple](../../sql-reference/data-types/tuple.md).
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**Example**
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Query:
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```sql
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SELECT tuplePlus((1, 2), (2, 3));
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```
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Result:
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```text
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┌─tuplePlus((1, 2), (2, 3))─┐
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│ (3,5) │
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└───────────────────────────┘
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```
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## tupleMinus {#tupleminus}
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Calculates the subtraction of corresponding values of two tuples of the same size.
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**Syntax**
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```sql
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tupleMinus(tuple1, tuple2)
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```
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Alias: `vectorDifference`.
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**Arguments**
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- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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- `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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**Returned value**
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- Tuple with the result of subtraction.
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Type: [Tuple](../../sql-reference/data-types/tuple.md).
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**Example**
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Query:
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```sql
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SELECT tupleMinus((1, 2), (2, 3));
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```
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Result:
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```text
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┌─tupleMinus((1, 2), (2, 3))─┐
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│ (-1,-1) │
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└────────────────────────────┘
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```
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## tupleMultiply {#tuplemultiply}
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Calculates the multiplication of corresponding values of two tuples of the same size.
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**Syntax**
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```sql
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tupleMultiply(tuple1, tuple2)
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```
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**Arguments**
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- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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- `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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**Returned value**
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- Tuple with the multiplication.
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Type: [Tuple](../../sql-reference/data-types/tuple.md).
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**Example**
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Query:
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```sql
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SELECT tupleMultiply((1, 2), (2, 3));
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```
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Result:
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```text
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┌─tupleMultiply((1, 2), (2, 3))─┐
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│ (2,6) │
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└───────────────────────────────┘
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```
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## tupleDivide {#tupledivide}
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Calculates the division of corresponding values of two tuples of the same size. Note that division by zero will return `inf`.
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**Syntax**
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```sql
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tupleDivide(tuple1, tuple2)
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```
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**Arguments**
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- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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- `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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**Returned value**
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- Tuple with the result of division.
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Type: [Tuple](../../sql-reference/data-types/tuple.md).
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**Example**
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Query:
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```sql
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SELECT tupleDivide((1, 2), (2, 3));
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```
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Result:
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```text
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┌─tupleDivide((1, 2), (2, 3))─┐
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│ (0.5,0.6666666666666666) │
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└─────────────────────────────┘
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```
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## tupleNegate {#tuplenegate}
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Calculates the negation of the tuple values.
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**Syntax**
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```sql
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tupleNegate(tuple)
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```
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**Arguments**
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- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
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**Returned value**
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- Tuple with the result of negation.
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Type: [Tuple](../../sql-reference/data-types/tuple.md).
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**Example**
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Query:
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```sql
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SELECT tupleNegate((1, 2));
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```
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Result:
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```text
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┌─tupleNegate((1, 2))─┐
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│ (-1,-2) │
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└─────────────────────┘
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```
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## tupleMultiplyByNumber {#tuplemultiplybynumber}
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Returns a tuple with all values multiplied by a number.
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**Syntax**
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```sql
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tupleMultiplyByNumber(tuple, number)
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```
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**Arguments**
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- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
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- `number` — Multiplier. [Int/UInt](../../sql-reference/data-types/int-uint.md), [Float](../../sql-reference/data-types/float.md) or [Decimal](../../sql-reference/data-types/decimal.md).
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**Returned value**
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- Tuple with multiplied values.
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Type: [Tuple](../../sql-reference/data-types/tuple.md).
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**Example**
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Query:
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```sql
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SELECT tupleMultiplyByNumber((1, 2), -2.1);
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```
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Result:
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```text
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┌─tupleMultiplyByNumber((1, 2), -2.1)─┐
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│ (-2.1,-4.2) │
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└─────────────────────────────────────┘
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```
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## tupleDivideByNumber {#tupledividebynumber}
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Returns a tuple with all values divided by a number. Note that division by zero will return `inf`.
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**Syntax**
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```sql
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tupleDivideByNumber(tuple, number)
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```
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**Arguments**
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- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
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- `number` — Divider. [Int/UInt](../../sql-reference/data-types/int-uint.md), [Float](../../sql-reference/data-types/float.md) or [Decimal](../../sql-reference/data-types/decimal.md).
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**Returned value**
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- Tuple with divided values.
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Type: [Tuple](../../sql-reference/data-types/tuple.md).
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**Example**
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Query:
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```sql
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SELECT tupleDivideByNumber((1, 2), 0.5);
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```
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Result:
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```text
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┌─tupleDivideByNumber((1, 2), 0.5)─┐
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│ (2,4) │
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└──────────────────────────────────┘
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```
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## dotProduct {#dotproduct}
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Calculates the scalar product of two tuples of the same size.
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**Syntax**
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```sql
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dotProduct(tuple1, tuple2)
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```
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Alias: `scalarProduct`.
|
||
|
||
**Arguments**
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- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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- `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
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**Returned value**
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- Scalar product.
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Type: [Int/UInt](../../sql-reference/data-types/int-uint.md), [Float](../../sql-reference/data-types/float.md) or [Decimal](../../sql-reference/data-types/decimal.md).
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**Example**
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||
|
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Query:
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||
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```sql
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SELECT dotProduct((1, 2), (2, 3));
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```
|
||
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||
Result:
|
||
|
||
```text
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┌─dotProduct((1, 2), (2, 3))─┐
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│ 8 │
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└────────────────────────────┘
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```
|
||
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## L1Norm {#l1norm}
|
||
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Calculates the sum of absolute values of a tuple.
|
||
|
||
**Syntax**
|
||
|
||
```sql
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L1Norm(tuple)
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```
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||
|
||
Alias: `normL1`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
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- L1-norm or [taxicab geometry](https://en.wikipedia.org/wiki/Taxicab_geometry) distance.
|
||
|
||
Type: [UInt](../../sql-reference/data-types/int-uint.md), [Float](../../sql-reference/data-types/float.md) or [Decimal](../../sql-reference/data-types/decimal.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
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||
SELECT L1Norm((1, 2));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
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||
┌─L1Norm((1, 2))─┐
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||
│ 3 │
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└────────────────┘
|
||
```
|
||
|
||
## L2Norm {#l2norm}
|
||
|
||
Calculates the square root of the sum of the squares of the tuple values.
|
||
|
||
**Syntax**
|
||
|
||
```sql
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||
L2Norm(tuple)
|
||
```
|
||
|
||
Alias: `normL2`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- L2-norm or [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance).
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT L2Norm((1, 2));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌───L2Norm((1, 2))─┐
|
||
│ 2.23606797749979 │
|
||
└──────────────────┘
|
||
```
|
||
|
||
## LinfNorm {#linfnorm}
|
||
|
||
Calculates the maximum of absolute values of a tuple.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
LinfNorm(tuple)
|
||
```
|
||
|
||
Alias: `normLinf`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- Linf-norm or the maximum absolute value.
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT LinfNorm((1, -2));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─LinfNorm((1, -2))─┐
|
||
│ 2 │
|
||
└───────────────────┘
|
||
```
|
||
|
||
## LpNorm {#lpnorm}
|
||
|
||
Calculates the root of `p`-th power of the sum of the absolute values of a tuple in the power of `p`.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
LpNorm(tuple, p)
|
||
```
|
||
|
||
Alias: `normLp`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `p` — The power. Possible values: real number in `[1; inf)`. [UInt](../../sql-reference/data-types/int-uint.md) or [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Returned value**
|
||
|
||
- [Lp-norm](https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm)
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT LpNorm((1, -2), 2);
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─LpNorm((1, -2), 2)─┐
|
||
│ 2.23606797749979 │
|
||
└────────────────────┘
|
||
```
|
||
|
||
## L1Distance {#l1distance}
|
||
|
||
Calculates the distance between two points (the values of the tuples are the coordinates) in `L1` space (1-norm ([taxicab geometry](https://en.wikipedia.org/wiki/Taxicab_geometry) distance)).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
L1Distance(tuple1, tuple2)
|
||
```
|
||
|
||
Alias: `distanceL1`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `tuple1` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- 1-norm distance.
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT L1Distance((1, 2), (2, 3));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─L1Distance((1, 2), (2, 3))─┐
|
||
│ 2 │
|
||
└────────────────────────────┘
|
||
```
|
||
|
||
## L2Distance {#l2distance}
|
||
|
||
Calculates the distance between two points (the values of the tuples are the coordinates) in Euclidean space ([Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance)).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
L2Distance(tuple1, tuple2)
|
||
```
|
||
|
||
Alias: `distanceL2`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `tuple1` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- 2-norm distance.
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT L2Distance((1, 2), (2, 3));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─L2Distance((1, 2), (2, 3))─┐
|
||
│ 1.4142135623730951 │
|
||
└────────────────────────────┘
|
||
```
|
||
|
||
## LinfDistance {#linfdistance}
|
||
|
||
Calculates the distance between two points (the values of the tuples are the coordinates) in `L_{inf}` space ([maximum norm](https://en.wikipedia.org/wiki/Norm_(mathematics)#Maximum_norm_(special_case_of:_infinity_norm,_uniform_norm,_or_supremum_norm))).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
LinfDistance(tuple1, tuple2)
|
||
```
|
||
|
||
Alias: `distanceLinf`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `tuple1` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- Infinity-norm distance.
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT LinfDistance((1, 2), (2, 3));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─LinfDistance((1, 2), (2, 3))─┐
|
||
│ 1 │
|
||
└──────────────────────────────┘
|
||
```
|
||
|
||
## LpDistance {#lpdistance}
|
||
|
||
Calculates the distance between two points (the values of the tuples are the coordinates) in `Lp` space ([p-norm distance](https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm)).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
LpDistance(tuple1, tuple2, p)
|
||
```
|
||
|
||
Alias: `distanceLp`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `tuple1` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `p` — The power. Possible values: real number from `[1; inf)`. [UInt](../../sql-reference/data-types/int-uint.md) or [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Returned value**
|
||
|
||
- p-norm distance.
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT LpDistance((1, 2), (2, 3), 3);
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─LpDistance((1, 2), (2, 3), 3)─┐
|
||
│ 1.2599210498948732 │
|
||
└───────────────────────────────┘
|
||
```
|
||
|
||
## L1Normalize {#l1normalize}
|
||
|
||
Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in `L1` space ([taxicab geometry](https://en.wikipedia.org/wiki/Taxicab_geometry)).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
L1Normalize(tuple)
|
||
```
|
||
|
||
Alias: `normalizeL1`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- Unit vector.
|
||
|
||
Type: [Tuple](../../sql-reference/data-types/tuple.md) of [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT L1Normalize((1, 2));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─L1Normalize((1, 2))─────────────────────┐
|
||
│ (0.3333333333333333,0.6666666666666666) │
|
||
└─────────────────────────────────────────┘
|
||
```
|
||
|
||
## L2Normalize {#l2normalize}
|
||
|
||
Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in Euclidean space (using [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance)).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
L2Normalize(tuple)
|
||
```
|
||
|
||
Alias: `normalizeL1`.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- Unit vector.
|
||
|
||
Type: [Tuple](../../sql-reference/data-types/tuple.md) of [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT L2Normalize((3, 4));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─L2Normalize((3, 4))─┐
|
||
│ (0.6,0.8) │
|
||
└─────────────────────┘
|
||
```
|
||
|
||
## LinfNormalize {#linfnormalize}
|
||
|
||
Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in `L_{inf}` space (using [maximum norm](https://en.wikipedia.org/wiki/Norm_(mathematics)#Maximum_norm_(special_case_of:_infinity_norm,_uniform_norm,_or_supremum_norm))).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
LinfNormalize(tuple)
|
||
```
|
||
|
||
Alias: `normalizeLinf `.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- Unit vector.
|
||
|
||
Type: [Tuple](../../sql-reference/data-types/tuple.md) of [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT LinfNormalize((3, 4));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─LinfNormalize((3, 4))─┐
|
||
│ (0.75,1) │
|
||
└───────────────────────┘
|
||
```
|
||
|
||
## LpNormalize {#lpnormalize}
|
||
|
||
Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in `Lp` space (using [p-norm](https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm)).
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
LpNormalize(tuple, p)
|
||
```
|
||
|
||
Alias: `normalizeLp `.
|
||
|
||
**Arguments**
|
||
|
||
- `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `p` — The power. Possible values: any number from [1;inf). [UInt](../../sql-reference/data-types/int-uint.md) or [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Returned value**
|
||
|
||
- Unit vector.
|
||
|
||
Type: [Tuple](../../sql-reference/data-types/tuple.md) of [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT LpNormalize((3, 4),5);
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─LpNormalize((3, 4), 5)──────────────────┐
|
||
│ (0.7187302630182624,0.9583070173576831) │
|
||
└─────────────────────────────────────────┘
|
||
```
|
||
|
||
## cosineDistance {#cosinedistance}
|
||
|
||
Calculates the cosine distance between two vectors (the values of the tuples are the coordinates). The less the returned value is, the more similar are the vectors.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
cosineDistance(tuple1, tuple2)
|
||
```
|
||
|
||
**Arguments**
|
||
|
||
- `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
- `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).
|
||
|
||
**Returned value**
|
||
|
||
- Cosine of the angle between two vectors substracted from one.
|
||
|
||
Type: [Float](../../sql-reference/data-types/float.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT cosineDistance((1, 2), (2, 3));
|
||
```
|
||
|
||
Result:
|
||
|
||
```text
|
||
┌─cosineDistance((1, 2), (2, 3))─┐
|
||
│ 0.007722123286332261 │
|
||
└────────────────────────────────┘
|
||
```
|