# Mathematical function

Vectors support the following mathematical functions:

## SQRT

### **Function Description**

The `sqrt` function is used to calculate the square root of each element in a vector.

### **Function Syntax**

```sql
SELECT sqrt(vector_column) FROM table_name;
```

#### Return type

Returns a new vector of type vecf64 that contains the square root of each element in the original vector.

### **Example**

```text
drop table if exists vec_table;
create table vec_table(a int, b vecf32(3), c vecf64(3));
insert into vec_table values(1, "[1,2,3]", "[4,5,6]");
mysql> select * from vec_table;
+-------+--------------------------+
| a | b | c |
+-------+--------------------------+
| 1 | [1, 2, 3] | [4, 5, 6] |
+-------+--------------------------+
1 row in set (0.00 sec)

mysql> select sqrt(b) from vec_table;
+-----------------------------------------------------+
| sqrt(b) |
+-----------------------------------------------------+
| [1, 1.4142135623730951, 1.7320508075688772] |
+-----------------------------------------------------+
1 row in set (0.00 sec)
```

### **limit**

- The elements of a vector cannot be negative.

## ABS

### **Function Description**

The `abs` function is used to calculate the absolute value of a vector.

### **Function Syntax**

```sql
SELECT ABS(vector_column) FROM table_name;
```

#### Return type

Returns a new vector of the same type that contains the absolute value of each element in the original vector.

### **Example**

```text
drop table if exists vec_table;
create table vec_table(a int, b vecf32(3), c vecf64(3));
insert into vec_table values(1, "[-1,-2,3]", "[4,5,6]");
  mysql> select * from vec_table;
  +-------+--------------------------+
  | a | b | c |
  +-------+--------------------------+
  | 1 | [-1, -2, 3] | [4, 5, 6] |
  +-------+--------------------------+
  1 row in set (0.00 sec)

mysql> select abs(b) from vec_table;
+---------------+
| abs(b) |
+---------------+
| [1, 2, 3] |
+---------------+
1 row in set (0.01 sec)
```

## CAST

### **Function Description**

The cast function is used to explicitly convert a vector from one vector type to another.

### **Function Syntax**

```sql
SELECT CAST(vector AS vector_type) FROM table_name;
```

#### Parameters

- `vector`: Input vector.
- `vector_type`: New vector type.

#### Return type

New `vector_type` vector.

### **Example**

```text
drop table if exists vec_table;
create table vec_table(a int, b vecf32(3), c vecf64(3));
insert into vec_table values(1, "[1,2,3]", "[4,5,6]");
mysql> select * from vec_table;
+-------+--------------------------+
| a | b | c |
+-------+--------------------------+
| 1 | [1, 2, 3] | [4, 5, 6] |
+-------+--------------------------+
1 row in set (0.00 sec)

mysql> select b + cast("[1,2,3]" as vecf32(3)) from vec_table;
+------------------------------------+
| b + cast([1,2,3] as vecf32(3)) |
+------------------------------------+
| [2, 4, 6] |
+------------------------------------+
1 row in set (0.00 sec)
```

## SUMMATION

### **Function Description**

The `summation` function returns the sum of all elements in the vector.

### **Function Syntax**

```sql
SELECT SUMMATION(vector_column) FROM table_name;
```

#### Return type

Returns a FLOAT64 value, which is the sum of all elements in the vector.

### **Example**

```text
drop table if exists vec_table;
create table vec_table(a int, b vecf32(3), c vecf64(3));
insert into vec_table values(1, "[1,2,3]", "[4,5,6]");
mysql> select * from vec_table;
+-------+--------------------------+
| a | b | c |
+-------+--------------------------+
| 1 | [1, 2, 3] | [4, 5, 6] |
+-------+--------------------------+
1 row in set (0.00 sec)

mysql> select summation(b) from vec_table;
+-------------------+
| summation(b) |
+-------------------+
| 6 |
+-------------------+
1 row in set (0.00 sec)
```