---
toc_priority: 66
toc_title: Tuples
---

# Functions for Working with Tuples {#tuple-functions}

## tuple {#tuple}

A function that allows grouping multiple columns.
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.
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.

The function implements the operator `(x, y, …)`.

**Syntax**

``` sql
tuple(x, y, …)
```

## tupleElement {#tupleelement}

A function that allows getting a column from a tuple.
‘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.
There is no cost to execute the function.

The function implements the operator `x.N`.

**Syntax**

``` sql
tupleElement(tuple, n)
```

## untuple {#untuple}

Performs syntactic substitution of [tuple](../../sql-reference/data-types/tuple.md#tuplet1-t2) elements in the call location.

**Syntax**

``` sql
untuple(x)
```

You can use the `EXCEPT` expression to skip columns as a result of the query.

**Arguments**

-   `x` — A `tuple` function, column, or tuple of elements. [Tuple](../../sql-reference/data-types/tuple.md).

**Returned value**

-   None.

**Examples**

Input table:

``` text
┌─key─┬─v1─┬─v2─┬─v3─┬─v4─┬─v5─┬─v6────────┐
│   1 │ 10 │ 20 │ 40 │ 30 │ 15 │ (33,'ab') │
│   2 │ 25 │ 65 │ 70 │ 40 │  6 │ (44,'cd') │
│   3 │ 57 │ 30 │ 20 │ 10 │  5 │ (55,'ef') │
│   4 │ 55 │ 12 │  7 │ 80 │ 90 │ (66,'gh') │
│   5 │ 30 │ 50 │ 70 │ 25 │ 55 │ (77,'kl') │
└─────┴────┴────┴────┴────┴────┴───────────┘
```

Example of using a `Tuple`-type column as the `untuple` function parameter:

Query:

``` sql
SELECT untuple(v6) FROM kv;
```

Result:

``` text
┌─_ut_1─┬─_ut_2─┐
│    33 │ ab    │
│    44 │ cd    │
│    55 │ ef    │
│    66 │ gh    │
│    77 │ kl    │
└───────┴───────┘
```

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`.

Example of using an `EXCEPT` expression:

Query:

``` sql
SELECT untuple((* EXCEPT (v2, v3),)) FROM kv;
```

Result:

``` text
┌─key─┬─v1─┬─v4─┬─v5─┬─v6────────┐
│   1 │ 10 │ 30 │ 15 │ (33,'ab') │
│   2 │ 25 │ 40 │  6 │ (44,'cd') │
│   3 │ 57 │ 10 │  5 │ (55,'ef') │
│   4 │ 55 │ 80 │ 90 │ (66,'gh') │
│   5 │ 30 │ 25 │ 55 │ (77,'kl') │
└─────┴────┴────┴────┴───────────┘
```

**See Also**

-   [Tuple](../../sql-reference/data-types/tuple.md)

## tupleHammingDistance {#tuplehammingdistance}

Returns the [Hamming Distance](https://en.wikipedia.org/wiki/Hamming_distance) between two tuples of the same size.

**Syntax**

``` sql
tupleHammingDistance(tuple1, tuple2)
```

**Arguments**

-   `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
-   `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).

Tuples should have the same type of the elements.

**Returned value**

-   The Hamming distance.

Type: [UInt8](../../sql-reference/data-types/int-uint.md).

**Examples**

Query:

``` sql
SELECT tupleHammingDistance((1, 2, 3), (3, 2, 1)) AS HammingDistance;
```

Result:

``` text
┌─HammingDistance─┐
│               2 │
└─────────────────┘
```

Can be used with [MinHash](../../sql-reference/functions/hash-functions.md#ngramminhash) functions for detection of semi-duplicate strings:

``` sql
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);
```

Result:

``` text
┌─HammingDistance─┐
│               2 │
└─────────────────┘
```

## tuplePlus {#tupleplus}

Calculates the sum of corresponding values of two tuples of the same size.

**Syntax**

```sql
tuplePlus(tuple1, tuple2)
```

Alias: `vectorSum`.

**Arguments**

-   `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
-   `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).

**Returned value**

-   Tuple with the sum.

Type: [Tuple](../../sql-reference/data-types/tuple.md).

**Example**

Query:

```sql
SELECT tuplePlus((1, 2), (2, 3));
```

Result:

```text
┌─tuplePlus((1, 2), (2, 3))─┐
│ (3,5)                     │
└───────────────────────────┘
```

## tupleMinus {#tupleminus}

Calculates the subtraction of corresponding values of two tuples of the same size.

**Syntax**

```sql
tupleMinus(tuple1, tuple2)
```

Alias: `vectorDifference`.

**Arguments**

-   `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
-   `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).

**Returned value**

-   Tuple with the result of subtraction.

Type: [Tuple](../../sql-reference/data-types/tuple.md).

**Example**

Query:

```sql
SELECT tupleMinus((1, 2), (2, 3));
```

Result:

```text
┌─tupleMinus((1, 2), (2, 3))─┐
│ (-1,-1)                    │
└────────────────────────────┘
```

## tupleMultiply {#tuplemultiply}

Calculates the multiplication of corresponding values of two tuples of the same size.

**Syntax**

```sql
tupleMultiply(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**

-   Tuple with the multiplication.

Type: [Tuple](../../sql-reference/data-types/tuple.md).

**Example**

Query:

```sql
SELECT tupleMultiply((1, 2), (2, 3));
```

Result:

```text
┌─tupleMultiply((1, 2), (2, 3))─┐
│ (2,6)                         │
└───────────────────────────────┘
```

## tupleDivide {#tupledivide}

Calculates the division of corresponding values of two tuples of the same size. Note that division by zero will return `inf`.

**Syntax**

```sql
tupleDivide(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**

-   Tuple with the result of division.

Type: [Tuple](../../sql-reference/data-types/tuple.md).

**Example**

Query:

```sql
SELECT tupleDivide((1, 2), (2, 3));
```

Result:

```text
┌─tupleDivide((1, 2), (2, 3))─┐
│ (0.5,0.6666666666666666)    │
└─────────────────────────────┘
```

## tupleNegate {#tuplenegate}

Calculates the negation of the tuple values.

**Syntax**

```sql
tupleNegate(tuple)
```

**Arguments**

-   `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).

**Returned value**

-   Tuple with the result of negation.

Type: [Tuple](../../sql-reference/data-types/tuple.md).

**Example**

Query:

```sql
SELECT tupleDivide((1, 2));
```

Result:

```text
┌─tupleNegate((1, 2))─┐
│ (-1,-2)             │
└─────────────────────┘
```

## tupleMultiplyByNumber {#tuplemultiplybynumber}

Returns a tuple with all values multiplied by a number.

**Syntax**

```sql
tupleMultiplyByNumber(tuple, number)
```

**Arguments**

-   `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
-   `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).

**Returned value**

-   Tuple with multiplied values.

Type: [Tuple](../../sql-reference/data-types/tuple.md).

**Example**

Query:

```sql
SELECT tupleMultiplyByNumber((1, 2), -2.1);
```

Result:

```text
┌─tupleMultiplyByNumber((1, 2), -2.1)─┐
│ (-2.1,-4.2)                         │
└─────────────────────────────────────┘
```

## tupleDivideByNumber {#tupledividebynumber}

Returns a tuple with all values divided by a number. Note that division by zero will return `inf`.

**Syntax**

```sql
tupleDivideByNumber(tuple, number)
```

**Arguments**

-   `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).
-   `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).

**Returned value**

-   Tuple with divided values.

Type: [Tuple](../../sql-reference/data-types/tuple.md).

**Example**

Query:

```sql
SELECT tupleDivideByNumber((1, 2), 0.5);
```

Result:

```text
┌─tupleDivideByNumber((1, 2), 0.5)─┐
│ (2,4)                            │
└──────────────────────────────────┘
```

## dotProduct {#dotproduct}

Calculates the scalar product of two tuples of the same size.

**Syntax**

```sql
dotProduct(tuple1, tuple2)
```

Alias: `scalarProduct`.

**Arguments**

-   `tuple1` — First tuple. [Tuple](../../sql-reference/data-types/tuple.md).
-   `tuple2` — Second tuple. [Tuple](../../sql-reference/data-types/tuple.md).

**Returned value**

-   Scalar product.

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).

**Example**

Query:

```sql
SELECT dotProduct((1, 2), (2, 3));
```

Result:

```text
┌─dotProduct((1, 2), (2, 3))─┐
│                          8 │
└────────────────────────────┘
```

## L1Norm {#l1norm}

Calculates the sum of absolute values of a tuple.

**Syntax**

```sql
L1Norm(tuple)
```

Alias: `normL1`.

**Arguments**

-   `tuple` — [Tuple](../../sql-reference/data-types/tuple.md).

**Returned value**

-   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
SELECT L1Norm((1, 2));
```

Result:

```text
┌─L1Norm((1, 2))─┐
│              3 │
└────────────────┘
```

## L2Norm {#l2norm}

Calculates the square root of the sum of the squares of the tuple values.

**Syntax**

```sql
L1Norm(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**

-   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: any number from [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 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 2-norm ([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 [infinity-norm distance](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 [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: any number from [1;inf). [UInt](../../sql-reference/data-types/int-uint.md) or [Float](../../sql-reference/data-types/float.md).

**Returned value**

-   Lp-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 1-norm ([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 2-norm ([Euclidean geometry](https://en.wikipedia.org/wiki/Euclidean_space).

**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 [infinity-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 [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 {#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` — [Tuple](../../sql-reference/data-types/tuple.md).
-   `tuple1` — [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 │
└────────────────────────────────┘
```