Merge pull request #64626 from Blargian/doc_covarXYZ

Document functions `corr`, `covar`, and their variants
2024-11-22 15:42:02 +00:00 · 2024-06-04 10:27:29 +00:00 · 2024-06-04 10:27:29 +00:00 · a3faaa2129
commit a3faaa2129
parent b4c0a35339 e02cc4c9e0
11 changed files with 652 additions and 121 deletions
--- a/docs/en/sql-reference/aggregate-functions/reference/corr.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/corr.md
@ -5,10 +5,57 @@ sidebar_position: 107

 # corr

-Syntax: `corr(x, y)`
+Calculates the [Pearson correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient):
+
+$$
+\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{\sqrt{\Sigma{(x - \bar{x})^2} * \Sigma{(y - \bar{y})^2}}}
+$$

-Calculates the Pearson correlation coefficient: `Σ((x - x̅)(y - y̅)) / sqrt(Σ((x - x̅)^2) * Σ((y - y̅)^2))`.

 :::note
-This function uses a numerically unstable algorithm. If you need [numerical stability](https://en.wikipedia.org/wiki/Numerical_stability) in calculations, use the `corrStable` function. It works slower but provides a lower computational error.
-:::
+This function uses a numerically unstable algorithm. If you need [numerical stability](https://en.wikipedia.org/wiki/Numerical_stability) in calculations, use the [`corrStable`](../reference/corrstable.md) function. It is slower but provides a more accurate result.
+:::
+
+**Syntax**
+
+```sql
+corr(x, y)
+```
+
+**Arguments**
+
+- `x` — first variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+- `y` — second variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- The Pearson correlation coefficient. [Float64](../../data-types/float.md).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS series;
+CREATE TABLE series
+(
+    i UInt32,
+    x_value Float64,
+    y_value Float64
+)
+ENGINE = Memory;
+INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6, -4.4),(2, -9.6, 3),(3, -1.3, -4),(4, 5.3, 9.7),(5, 4.4, 0.037),(6, -8.6, -7.8),(7, 5.1, 9.3),(8, 7.9, -3.6),(9, -8.2, 0.62),(10, -3, 7.3);
+```
+
+```sql
+SELECT corr(x_value, y_value)
+FROM series;
+```
+
+Result:
+
+```response
+┌─corr(x_value, y_value)─┐
+│     0.1730265755453256 │
+└────────────────────────┘
+```
--- a/docs/en/sql-reference/aggregate-functions/reference/corrmatrix.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/corrmatrix.md
@ -0,0 +1,55 @@
+---
+slug: /en/sql-reference/aggregate-functions/reference/corrmatrix
+sidebar_position: 108
+---
+
+# corrMatrix
+
+Computes the correlation matrix over N variables.
+
+**Syntax**
+
+```sql
+corrMatrix(x[, ...])
+```
+
+**Arguments**
+
+- `x` — a variable number of parameters. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned value**
+
+- Correlation matrix. [Array](../../data-types/array.md)([Array](../../data-types/array.md)([Float64](../../data-types/float.md))).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS test;
+CREATE TABLE test
+(
+    a UInt32,
+    b Float64,
+    c Float64,
+    d Float64
+)
+ENGINE = Memory;
+INSERT INTO test(a, b, c, d) VALUES (1, 5.6, -4.4, 2.6), (2, -9.6, 3, 3.3), (3, -1.3, -4, 1.2), (4, 5.3, 9.7, 2.3), (5, 4.4, 0.037, 1.222), (6, -8.6, -7.8, 2.1233), (7, 5.1, 9.3, 8.1222), (8, 7.9, -3.6, 9.837), (9, -8.2, 0.62, 8.43555), (10, -3, 7.3, 6.762);
+```
+
+```sql
+SELECT arrayMap(x -> round(x, 3), arrayJoin(corrMatrix(a, b, c, d))) AS corrMatrix
+FROM test;
+```
+
+Result:
+
+```response
+   ┌─corrMatrix─────────────┐
+1. │ [1,-0.096,0.243,0.746] │
+2. │ [-0.096,1,0.173,0.106] │
+3. │ [0.243,0.173,1,0.258]  │
+4. │ [0.746,0.106,0.258,1]  │
+   └────────────────────────┘
+```
--- a/docs/en/sql-reference/aggregate-functions/reference/corrstable.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/corrstable.md
@ -0,0 +1,58 @@
+---
+slug: /en/sql-reference/aggregate-functions/reference/corrstable
+sidebar_position: 107
+---
+
+# corrStable
+
+Calculates the [Pearson correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient): 
+
+$$
+\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{\sqrt{\Sigma{(x - \bar{x})^2} * \Sigma{(y - \bar{y})^2}}}
+$$
+
+Similar to the [`corr`](../reference/corr.md) function, but uses a numerically stable algorithm. As a result, `corrStable` is slower than `corr` but produces a more accurate result.
+
+**Syntax**
+
+```sql
+corrStable(x, y)
+```
+
+**Arguments**
+
+- `x` — first variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+- `y` — second variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- The Pearson correlation coefficient. [Float64](../../data-types/float.md).
+
+***Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS series;
+CREATE TABLE series
+(
+    i UInt32,
+    x_value Float64,
+    y_value Float64
+)
+ENGINE = Memory;
+INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6, -4.4),(2, -9.6, 3),(3, -1.3, -4),(4, 5.3, 9.7),(5, 4.4, 0.037),(6, -8.6, -7.8),(7, 5.1, 9.3),(8, 7.9, -3.6),(9, -8.2, 0.62),(10, -3, 7.3);
+```
+
+```sql
+SELECT corrStable(x_value, y_value)
+FROM series;
+```
+
+Result:
+
+```response
+┌─corrStable(x_value, y_value)─┐
+│          0.17302657554532558 │
+└──────────────────────────────┘
+```
--- a/docs/en/sql-reference/aggregate-functions/reference/covarpop.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/covarpop.md
@ -1,14 +1,54 @@
 ---
 slug: /en/sql-reference/aggregate-functions/reference/covarpop
-sidebar_position: 36
+sidebar_position: 37
 ---

 # covarPop

-Syntax: `covarPop(x, y)`
+Calculates the population covariance:

-Calculates the value of `Σ((x - x̅)(y - y̅)) / n`.
+$$
+\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{n}
+$$

 :::note
-This function uses a numerically unstable algorithm. If you need [numerical stability](https://en.wikipedia.org/wiki/Numerical_stability) in calculations, use the `covarPopStable` function. It works slower but provides a lower computational error.
-:::
+This function uses a numerically unstable algorithm. If you need [numerical stability](https://en.wikipedia.org/wiki/Numerical_stability) in calculations, use the [`covarPopStable`](../reference/covarpopstable.md) function. It works slower but provides a lower computational error.
+:::
+
+**Syntax**
+
+```sql
+covarPop(x, y)
+```
+
+**Arguments**
+
+- `x` — first variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+- `y` — second variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- The population covariance between `x` and `y`. [Float64](../../data-types/float.md).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS series;
+CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
+INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6, -4.4),(2, -9.6, 3),(3, -1.3, -4),(4, 5.3, 9.7),(5, 4.4, 0.037),(6, -8.6, -7.8),(7, 5.1, 9.3),(8, 7.9, -3.6),(9, -8.2, 0.62),(10, -3, 7.3);
+```
+
+```sql
+SELECT covarPop(x_value, y_value)
+FROM series;
+```
+
+Result:
+
+```reference
+┌─covarPop(x_value, y_value)─┐
+│                   6.485648 │
+└────────────────────────────┘
+```
--- a/docs/en/sql-reference/aggregate-functions/reference/covarpopmatrix.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/covarpopmatrix.md
@ -0,0 +1,55 @@
+---
+slug: /en/sql-reference/aggregate-functions/reference/covarpopmatrix
+sidebar_position: 36
+---
+
+# covarPopMatrix
+
+Returns the population covariance matrix over N variables.
+
+**Syntax**
+
+```sql
+covarPopMatrix(x[, ...])
+```
+
+**Arguments**
+
+- `x` — a variable number of parameters. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- Population covariance matrix. [Array](../../data-types/array.md)([Array](../../data-types/array.md)([Float64](../../data-types/float.md))).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS test;
+CREATE TABLE test
+(
+    a UInt32,
+    b Float64,
+    c Float64,
+    d Float64
+)
+ENGINE = Memory;
+INSERT INTO test(a, b, c, d) VALUES (1, 5.6, -4.4, 2.6), (2, -9.6, 3, 3.3), (3, -1.3, -4, 1.2), (4, 5.3, 9.7, 2.3), (5, 4.4, 0.037, 1.222), (6, -8.6, -7.8, 2.1233), (7, 5.1, 9.3, 8.1222), (8, 7.9, -3.6, 9.837), (9, -8.2, 0.62, 8.43555), (10, -3, 7.3, 6.762);
+```
+
+```sql
+SELECT arrayMap(x -> round(x, 3), arrayJoin(covarPopMatrix(a, b, c, d))) AS covarPopMatrix
+FROM test;
+```
+
+Result:
+
+```reference
+   ┌─covarPopMatrix────────────┐
+1. │ [8.25,-1.76,4.08,6.748]   │
+2. │ [-1.76,41.07,6.486,2.132] │
+3. │ [4.08,6.486,34.21,4.755]  │
+4. │ [6.748,2.132,4.755,9.93]  │
+   └───────────────────────────┘
+```
--- a/docs/en/sql-reference/aggregate-functions/reference/covarpopstable.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/covarpopstable.md
@ -0,0 +1,60 @@
+---
+slug: /en/sql-reference/aggregate-functions/reference/covarpopstable
+sidebar_position: 36
+---
+
+# covarPopStable
+
+Calculates the value of the population covariance:
+
+$$
+\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{n}
+$$
+
+It is similar to the [covarPop](../reference/covarpop.md) function, but uses a numerically stable algorithm. As a result, `covarPopStable` is slower than `covarPop` but produces a more accurate result.
+
+
+**Syntax**
+
+```sql
+covarPop(x, y)
+```
+
+**Arguments**
+
+- `x` — first variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+- `y` — second variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- The population covariance between `x` and `y`. [Float64](../../data-types/float.md).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS series;
+CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
+INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);
+```
+
+```sql
+SELECT covarPopStable(x_value, y_value)
+FROM
+(
+    SELECT
+        x_value,
+        y_value
+    FROM series
+);
+```
+
+Result:
+
+```reference
+┌─covarPopStable(x_value, y_value)─┐
+│                         6.485648 │
+└──────────────────────────────────┘
+```
+
--- a/docs/en/sql-reference/aggregate-functions/reference/covarsamp.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/covarsamp.md
@ -7,8 +7,74 @@ sidebar_position: 37

 Calculates the value of `Σ((x - x̅)(y - y̅)) / (n - 1)`.

-Returns Float64. When `n <= 1`, returns `nan`.
-
 :::note
-This function uses a numerically unstable algorithm. If you need [numerical stability](https://en.wikipedia.org/wiki/Numerical_stability) in calculations, use the `covarSampStable` function. It works slower but provides a lower computational error.
+This function uses a numerically unstable algorithm. If you need [numerical stability](https://en.wikipedia.org/wiki/Numerical_stability) in calculations, use the [`covarSampStable`](../reference/covarsamp.md) function. It works slower but provides a lower computational error.
 :::
+
+**Syntax**
+
+```sql
+covarSamp(x, y)
+```
+
+**Arguments**
+
+- `x` — first variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+- `y` — second variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- The sample covariance between `x` and `y`. For `n <= 1`, `nan` is returned. [Float64](../../data-types/float.md).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS series;
+CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
+INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);
+```
+
+```sql
+SELECT covarSamp(x_value, y_value)
+FROM
+(
+    SELECT
+        x_value,
+        y_value
+    FROM series
+);
+```
+
+Result:
+
+```reference
+┌─covarSamp(x_value, y_value)─┐
+│           7.206275555555556 │
+└─────────────────────────────┘
+```
+
+Query:
+
+```sql
+SELECT covarSamp(x_value, y_value)
+FROM
+(
+    SELECT
+        x_value,
+        y_value
+    FROM series LIMIT 1
+);
+
+```
+
+Result:
+
+```reference
+┌─covarSamp(x_value, y_value)─┐
+│                         nan │
+└─────────────────────────────┘
+```
+
+
--- a/docs/en/sql-reference/aggregate-functions/reference/covarsampmatrix.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/covarsampmatrix.md
@ -0,0 +1,57 @@
+---
+slug: /en/sql-reference/aggregate-functions/reference/covarsampmatrix
+sidebar_position: 38
+---
+
+# covarSampMatrix
+
+Returns the sample covariance matrix over N variables.
+
+**Syntax**
+
+```sql
+covarSampMatrix(x[, ...])
+```
+
+**Arguments**
+
+- `x` — a variable number of parameters. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- Sample covariance matrix. [Array](../../data-types/array.md)([Array](../../data-types/array.md)([Float64](../../data-types/float.md))).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS test;
+CREATE TABLE test
+(
+    a UInt32,
+    b Float64,
+    c Float64,
+    d Float64
+)
+ENGINE = Memory;
+INSERT INTO test(a, b, c, d) VALUES (1, 5.6, -4.4, 2.6), (2, -9.6, 3, 3.3), (3, -1.3, -4, 1.2), (4, 5.3, 9.7, 2.3), (5, 4.4, 0.037, 1.222), (6, -8.6, -7.8, 2.1233), (7, 5.1, 9.3, 8.1222), (8, 7.9, -3.6, 9.837), (9, -8.2, 0.62, 8.43555), (10, -3, 7.3, 6.762);
+```
+
+```sql
+SELECT arrayMap(x -> round(x, 3), arrayJoin(covarSampMatrix(a, b, c, d))) AS covarSampMatrix
+FROM test;
+```
+
+Result:
+
+```reference
+   ┌─covarSampMatrix─────────────┐
+1. │ [9.167,-1.956,4.534,7.498]  │
+2. │ [-1.956,45.634,7.206,2.369] │
+3. │ [4.534,7.206,38.011,5.283]  │
+4. │ [7.498,2.369,5.283,11.034]  │
+   └─────────────────────────────┘
+```
+
+
--- a/docs/en/sql-reference/aggregate-functions/reference/covarsampstable.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/covarsampstable.md
@ -0,0 +1,73 @@
+---
+slug: /en/sql-reference/aggregate-functions/reference/covarsampstable
+sidebar_position: 37
+---
+
+# covarSampStable
+
+Calculates the value of `Σ((x - x̅)(y - y̅)) / (n - 1)`. Similar to [covarSamp](../reference/covarsamp.md) but works slower while providing a lower computational error.
+
+**Syntax**
+
+```sql
+covarSampStable(x, y)
+```
+
+**Arguments**
+
+- `x` — first variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+- `y` — second variable. [(U)Int*](../../data-types/int-uint.md), [Float*](../../data-types/float.md), [Decimal](../../data-types/decimal.md).
+
+**Returned Value**
+
+- The sample covariance between `x` and `y`. For `n <= 1`, `inf` is returned. [Float64](../../data-types/float.md).
+
+**Example**
+
+Query:
+
+```sql
+DROP TABLE IF EXISTS series;
+CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
+INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);
+```
+
+```sql
+SELECT covarSampStable(x_value, y_value)
+FROM
+(
+    SELECT
+        x_value,
+        y_value
+    FROM series
+);
+```
+
+Result:
+
+```reference
+┌─covarSampStable(x_value, y_value)─┐
+│                 7.206275555555556 │
+└───────────────────────────────────┘
+```
+
+Query:
+
+```sql
+SELECT covarSampStable(x_value, y_value)
+FROM
+(
+    SELECT
+        x_value,
+        y_value
+    FROM series LIMIT 1
+);
+```
+
+Result:
+
+```reference
+┌─covarSampStable(x_value, y_value)─┐
+│                               inf │
+└───────────────────────────────────┘
+```
--- a/docs/en/sql-reference/aggregate-functions/reference/index.md
+++ b/docs/en/sql-reference/aggregate-functions/reference/index.md
@ -9,110 +9,116 @@ toc_hidden: true

 Standard aggregate functions:

- [count](/docs/en/sql-reference/aggregate-functions/reference/count.md)
- [min](/docs/en/sql-reference/aggregate-functions/reference/min.md)
- [max](/docs/en/sql-reference/aggregate-functions/reference/max.md)
- [sum](/docs/en/sql-reference/aggregate-functions/reference/sum.md)
- [avg](/docs/en/sql-reference/aggregate-functions/reference/avg.md)
- [any](/docs/en/sql-reference/aggregate-functions/reference/any.md)
- [stddevPop](/docs/en/sql-reference/aggregate-functions/reference/stddevpop.md)
- [stddevPopStable](/docs/en/sql-reference/aggregate-functions/reference/stddevpopstable.md)
- [stddevSamp](/docs/en/sql-reference/aggregate-functions/reference/stddevsamp.md)
- [stddevSampStable](/docs/en/sql-reference/aggregate-functions/reference/stddevsampstable.md)
- [varPop](/docs/en/sql-reference/aggregate-functions/reference/varpop.md)
- [varSamp](/docs/en/sql-reference/aggregate-functions/reference/varsamp.md)
- [corr](./corr.md)
- [covarPop](/docs/en/sql-reference/aggregate-functions/reference/covarpop.md)
- [covarSamp](/docs/en/sql-reference/aggregate-functions/reference/covarsamp.md)
- [entropy](./entropy.md)
- [exponentialMovingAverage](./exponentialmovingaverage.md)
- [intervalLengthSum](./intervalLengthSum.md)
- [kolmogorovSmirnovTest](./kolmogorovsmirnovtest.md)
- [mannwhitneyutest](./mannwhitneyutest.md)
- [median](./median.md)
- [rankCorr](./rankCorr.md)
- [sumKahan](./sumkahan.md)
- [studentTTest](./studentttest.md)
- [welchTTest](./welchttest.md)
+- [count](../reference/count.md)
+- [min](../reference/min.md)
+- [max](../reference/max.md)
+- [sum](../reference/sum.md)
+- [avg](../reference/avg.md)
+- [any](../reference/any.md)
+- [stddevPop](../reference/stddevpop.md)
+- [stddevPopStable](../reference/stddevpopstable.md)
+- [stddevSamp](../reference/stddevsamp.md)
+- [stddevSampStable](../reference/stddevsampstable.md)
+- [varPop](../reference/varpop.md)
+- [varSamp](../reference/varsamp.md)
+- [corr](../reference/corr.md)
+- [corr](../reference/corrstable.md)
+- [corrMatrix](../reference/corrmatrix.md)
+- [covarPop](../reference/covarpop.md)
+- [covarStable](../reference/covarpopstable.md)
+- [covarPopMatrix](../reference/covarpopmatrix.md)
+- [covarSamp](../reference/covarsamp.md)
+- [covarSampStable](../reference/covarsampstable.md)
+- [covarSampMatrix](../reference/covarsampmatrix.md)
+- [entropy](../reference/entropy.md)
+- [exponentialMovingAverage](../reference/exponentialmovingaverage.md)
+- [intervalLengthSum](../reference/intervalLengthSum.md)
+- [kolmogorovSmirnovTest](../reference/kolmogorovsmirnovtest.md)
+- [mannwhitneyutest](../reference/mannwhitneyutest.md)
+- [median](../reference/median.md)
+- [rankCorr](../reference/rankCorr.md)
+- [sumKahan](../reference/sumkahan.md)
+- [studentTTest](../reference/studentttest.md)
+- [welchTTest](../reference/welchttest.md)

 ClickHouse-specific aggregate functions:

- [analysisOfVariance](/docs/en/sql-reference/aggregate-functions/reference/analysis_of_variance.md)
- [any](/docs/en/sql-reference/aggregate-functions/reference/any_respect_nulls.md)
- [anyHeavy](/docs/en/sql-reference/aggregate-functions/reference/anyheavy.md)
- [anyLast](/docs/en/sql-reference/aggregate-functions/reference/anylast.md)
- [anyLast](/docs/en/sql-reference/aggregate-functions/reference/anylast_respect_nulls.md)
- [boundingRatio](/docs/en/sql-reference/aggregate-functions/reference/boundrat.md)
- [first_value](/docs/en/sql-reference/aggregate-functions/reference/first_value.md)
- [last_value](/docs/en/sql-reference/aggregate-functions/reference/last_value.md)
- [argMin](/docs/en/sql-reference/aggregate-functions/reference/argmin.md)
- [argMax](/docs/en/sql-reference/aggregate-functions/reference/argmax.md)
- [avgWeighted](/docs/en/sql-reference/aggregate-functions/reference/avgweighted.md)
- [topK](/docs/en/sql-reference/aggregate-functions/reference/topk.md)
- [topKWeighted](/docs/en/sql-reference/aggregate-functions/reference/topkweighted.md)
- [deltaSum](./deltasum.md)
- [deltaSumTimestamp](./deltasumtimestamp.md)
- [groupArray](/docs/en/sql-reference/aggregate-functions/reference/grouparray.md)
- [groupArrayLast](/docs/en/sql-reference/aggregate-functions/reference/grouparraylast.md)
- [groupUniqArray](/docs/en/sql-reference/aggregate-functions/reference/groupuniqarray.md)
- [groupArrayInsertAt](/docs/en/sql-reference/aggregate-functions/reference/grouparrayinsertat.md)
- [groupArrayMovingAvg](/docs/en/sql-reference/aggregate-functions/reference/grouparraymovingavg.md)
- [groupArrayMovingSum](/docs/en/sql-reference/aggregate-functions/reference/grouparraymovingsum.md)
- [groupArraySample](./grouparraysample.md)
- [groupArraySorted](/docs/en/sql-reference/aggregate-functions/reference/grouparraysorted.md)
- [groupArrayIntersect](./grouparrayintersect.md)
- [groupBitAnd](/docs/en/sql-reference/aggregate-functions/reference/groupbitand.md)
- [groupBitOr](/docs/en/sql-reference/aggregate-functions/reference/groupbitor.md)
- [groupBitXor](/docs/en/sql-reference/aggregate-functions/reference/groupbitxor.md)
- [groupBitmap](/docs/en/sql-reference/aggregate-functions/reference/groupbitmap.md)
- [groupBitmapAnd](/docs/en/sql-reference/aggregate-functions/reference/groupbitmapand.md)
- [groupBitmapOr](/docs/en/sql-reference/aggregate-functions/reference/groupbitmapor.md)
- [groupBitmapXor](/docs/en/sql-reference/aggregate-functions/reference/groupbitmapxor.md)
- [sumWithOverflow](/docs/en/sql-reference/aggregate-functions/reference/sumwithoverflow.md)
- [sumMap](/docs/en/sql-reference/aggregate-functions/reference/summap.md)
- [sumMapWithOverflow](/docs/en/sql-reference/aggregate-functions/reference/summapwithoverflow.md)
- [sumMapFiltered](/docs/en/sql-reference/aggregate-functions/parametric-functions.md/#summapfiltered)
- [sumMapFilteredWithOverflow](/docs/en/sql-reference/aggregate-functions/parametric-functions.md/#summapfilteredwithoverflow)
- [minMap](/docs/en/sql-reference/aggregate-functions/reference/minmap.md)
- [maxMap](/docs/en/sql-reference/aggregate-functions/reference/maxmap.md)
- [skewSamp](/docs/en/sql-reference/aggregate-functions/reference/skewsamp.md)
- [skewPop](/docs/en/sql-reference/aggregate-functions/reference/skewpop.md)
- [kurtSamp](/docs/en/sql-reference/aggregate-functions/reference/kurtsamp.md)
- [kurtPop](/docs/en/sql-reference/aggregate-functions/reference/kurtpop.md)
- [uniq](/docs/en/sql-reference/aggregate-functions/reference/uniq.md)
- [uniqExact](/docs/en/sql-reference/aggregate-functions/reference/uniqexact.md)
- [uniqCombined](/docs/en/sql-reference/aggregate-functions/reference/uniqcombined.md)
- [uniqCombined64](/docs/en/sql-reference/aggregate-functions/reference/uniqcombined64.md)
- [uniqHLL12](/docs/en/sql-reference/aggregate-functions/reference/uniqhll12.md)
- [uniqTheta](/docs/en/sql-reference/aggregate-functions/reference/uniqthetasketch.md)
- [quantile](/docs/en/sql-reference/aggregate-functions/reference/quantile.md)
- [quantiles](/docs/en/sql-reference/aggregate-functions/reference/quantiles.md)
- [quantileExact](/docs/en/sql-reference/aggregate-functions/reference/quantileexact.md)
- [quantileExactLow](/docs/en/sql-reference/aggregate-functions/reference/quantileexact.md#quantileexactlow)
- [quantileExactHigh](/docs/en/sql-reference/aggregate-functions/reference/quantileexact.md#quantileexacthigh)
- [quantileExactWeighted](/docs/en/sql-reference/aggregate-functions/reference/quantileexactweighted.md)
- [quantileTiming](/docs/en/sql-reference/aggregate-functions/reference/quantiletiming.md)
- [quantileTimingWeighted](/docs/en/sql-reference/aggregate-functions/reference/quantiletimingweighted.md)
- [quantileDeterministic](/docs/en/sql-reference/aggregate-functions/reference/quantiledeterministic.md)
- [quantileTDigest](/docs/en/sql-reference/aggregate-functions/reference/quantiletdigest.md)
- [quantileTDigestWeighted](/docs/en/sql-reference/aggregate-functions/reference/quantiletdigestweighted.md)
- [quantileBFloat16](/docs/en/sql-reference/aggregate-functions/reference/quantilebfloat16.md#quantilebfloat16)
- [quantileBFloat16Weighted](/docs/en/sql-reference/aggregate-functions/reference/quantilebfloat16.md#quantilebfloat16weighted)
- [quantileDD](/docs/en/sql-reference/aggregate-functions/reference/quantileddsketch.md#quantileddsketch)
- [simpleLinearRegression](/docs/en/sql-reference/aggregate-functions/reference/simplelinearregression.md)
- [singleValueOrNull](/docs/en/sql-reference/aggregate-functions/reference/singlevalueornull.md)
- [stochasticLinearRegression](/docs/en/sql-reference/aggregate-functions/reference/stochasticlinearregression.md)
- [stochasticLogisticRegression](/docs/en/sql-reference/aggregate-functions/reference/stochasticlogisticregression.md)
- [categoricalInformationValue](/docs/en/sql-reference/aggregate-functions/reference/categoricalinformationvalue.md)
- [contingency](./contingency.md)
- [cramersV](./cramersv.md)
- [cramersVBiasCorrected](./cramersvbiascorrected.md)
- [theilsU](./theilsu.md)
- [maxIntersections](./maxintersections.md)
- [maxIntersectionsPosition](./maxintersectionsposition.md)
- [meanZTest](./meanztest.md)
- [quantileGK](./quantileGK.md)
- [quantileInterpolatedWeighted](./quantileinterpolatedweighted.md)
- [sparkBar](./sparkbar.md)
- [sumCount](./sumcount.md)
- [largestTriangleThreeBuckets](./largestTriangleThreeBuckets.md)
+- [analysisOfVariance](../reference/analysis_of_variance.md)
+- [any](../reference/any_respect_nulls.md)
+- [anyHeavy](../reference/anyheavy.md)
+- [anyLast](../reference/anylast.md)
+- [anyLast](../reference/anylast_respect_nulls.md)
+- [boundingRatio](../reference/boundrat.md)
+- [first_value](../reference/first_value.md)
+- [last_value](../reference/last_value.md)
+- [argMin](../reference/argmin.md)
+- [argMax](../reference/argmax.md)
+- [avgWeighted](../reference/avgweighted.md)
+- [topK](../reference/topk.md)
+- [topKWeighted](../reference/topkweighted.md)
+- [deltaSum](../reference/deltasum.md)
+- [deltaSumTimestamp](../reference/deltasumtimestamp.md)
+- [groupArray](../reference/grouparray.md)
+- [groupArrayLast](../reference/grouparraylast.md)
+- [groupUniqArray](../reference/groupuniqarray.md)
+- [groupArrayInsertAt](../reference/grouparrayinsertat.md)
+- [groupArrayMovingAvg](../reference/grouparraymovingavg.md)
+- [groupArrayMovingSum](../reference/grouparraymovingsum.md)
+- [groupArraySample](../reference/grouparraysample.md)
+- [groupArraySorted](../reference/grouparraysorted.md)
+- [groupArrayIntersect](../reference/grouparrayintersect.md)
+- [groupBitAnd](../reference/groupbitand.md)
+- [groupBitOr](../reference/groupbitor.md)
+- [groupBitXor](../reference/groupbitxor.md)
+- [groupBitmap](../reference/groupbitmap.md)
+- [groupBitmapAnd](../reference/groupbitmapand.md)
+- [groupBitmapOr](../reference/groupbitmapor.md)
+- [groupBitmapXor](../reference/groupbitmapxor.md)
+- [sumWithOverflow](../reference/sumwithoverflow.md)
+- [sumMap](../reference/summap.md)
+- [sumMapWithOverflow](../reference/summapwithoverflow.md)
+- [sumMapFiltered](../parametric-functions.md/#summapfiltered)
+- [sumMapFilteredWithOverflow](../parametric-functions.md/#summapfilteredwithoverflow)
+- [minMap](../reference/minmap.md)
+- [maxMap](../reference/maxmap.md)
+- [skewSamp](../reference/skewsamp.md)
+- [skewPop](../reference/skewpop.md)
+- [kurtSamp](../reference/kurtsamp.md)
+- [kurtPop](../reference/kurtpop.md)
+- [uniq](../reference/uniq.md)
+- [uniqExact](../reference/uniqexact.md)
+- [uniqCombined](../reference/uniqcombined.md)
+- [uniqCombined64](../reference/uniqcombined64.md)
+- [uniqHLL12](../reference/uniqhll12.md)
+- [uniqTheta](../reference/uniqthetasketch.md)
+- [quantile](../reference/quantile.md)
+- [quantiles](../reference/quantiles.md)
+- [quantileExact](../reference/quantileexact.md)
+- [quantileExactLow](../reference/quantileexact.md#quantileexactlow)
+- [quantileExactHigh](../reference/quantileexact.md#quantileexacthigh)
+- [quantileExactWeighted](../reference/quantileexactweighted.md)
+- [quantileTiming](../reference/quantiletiming.md)
+- [quantileTimingWeighted](../reference/quantiletimingweighted.md)
+- [quantileDeterministic](../reference/quantiledeterministic.md)
+- [quantileTDigest](../reference/quantiletdigest.md)
+- [quantileTDigestWeighted](../reference/quantiletdigestweighted.md)
+- [quantileBFloat16](../reference/quantilebfloat16.md#quantilebfloat16)
+- [quantileBFloat16Weighted](../reference/quantilebfloat16.md#quantilebfloat16weighted)
+- [quantileDD](../reference/quantileddsketch.md#quantileddsketch)
+- [simpleLinearRegression](../reference/simplelinearregression.md)
+- [singleValueOrNull](../reference/singlevalueornull.md)
+- [stochasticLinearRegression](../reference/stochasticlinearregression.md)
+- [stochasticLogisticRegression](../reference/stochasticlogisticregression.md)
+- [categoricalInformationValue](../reference/categoricalinformationvalue.md)
+- [contingency](../reference/contingency.md)
+- [cramersV](../reference/cramersv.md)
+- [cramersVBiasCorrected](../reference/cramersvbiascorrected.md)
+- [theilsU](../reference/theilsu.md)
+- [maxIntersections](../reference/maxintersections.md)
+- [maxIntersectionsPosition](../reference/maxintersectionsposition.md)
+- [meanZTest](../reference/meanztest.md)
+- [quantileGK](../reference/quantileGK.md)
+- [quantileInterpolatedWeighted](../reference/quantileinterpolatedweighted.md)
+- [sparkBar](../reference/sparkbar.md)
+- [sumCount](../reference/sumcount.md)
+- [largestTriangleThreeBuckets](../reference/largestTriangleThreeBuckets.md)
--- a/utils/check-style/aspell-ignore/en/aspell-dict.txt
+++ b/utils/check-style/aspell-ignore/en/aspell-dict.txt
@ -989,6 +989,7 @@ URLHash
 URLHierarchy
 URLPathHierarchy
 USearch
+UTCTimestamp
 UUIDNumToString
 UUIDStringToNum
 UUIDToNum
@ -1366,6 +1367,10 @@ const
 contrib
 convertCharset
 coroutines
+corrMatrix
+corrStable
+corrmatrix
+corrstable
 cosineDistance
 countDigits
 countEqual
@ -1375,10 +1380,19 @@ countSubstrings
 countSubstringsCaseInsensitive
 countSubstringsCaseInsensitiveUTF
 covarPop
+covarPopMatrix
+covarPopStable
 covarSamp
+covarSampMatrix
+covarSampStable
+covarStable
 covariates
 covarpop
+covarpopmatrix
+covarpopstable
 covarsamp
+covarsampmatrix
+covarsampstable
 covid
 cpp
 cppkafka
@ -1609,6 +1623,7 @@ formated
 formatschema
 formatter
 formatters
+frac
 freezed
 fromDaysSinceYearZero
 fromModifiedJulianDay
@ -1735,8 +1750,8 @@ hdfs
 hdfsCluster
 heredoc
 heredocs
-hilbertEncode
 hilbertDecode
+hilbertEncode
 hiveHash
 holistics
 homebrew
@ -2666,16 +2681,16 @@ toStartOfFiveMinutes
 toStartOfHour
 toStartOfISOYear
 toStartOfInterval
+toStartOfMicrosecond
+toStartOfMillisecond
 toStartOfMinute
 toStartOfMonth
+toStartOfNanosecond
 toStartOfQuarter
 toStartOfSecond
 toStartOfTenMinutes
 toStartOfWeek
 toStartOfYear
-toStartOfMicrosecond
-toStartOfMillisecond
-toStartOfNanosecond
 toString
 toStringCutToZero
 toTime
@ -2805,7 +2820,6 @@ urls
 usearch
 userspace
 userver
-UTCTimestamp
 utils
 uuid
 uuidv