docs/UserGuide/Operators-Functions/Variation-Trend.md

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# Variation Trend Calculation Functions

Currently, IoTDB supports the following variation trend calculation functions:

| Function Name           | Allowed Input Series Data Types                 | Output Series Data Type       | Description                                                  |
| ----------------------- | ----------------------------------------------- | ----------------------------- | ------------------------------------------------------------ |
| TIME_DIFFERENCE         | INT32 / INT64 / FLOAT / DOUBLE / BOOLEAN / TEXT | INT64                         | Calculates the difference between the time stamp of a data point and the time stamp of the previous data point. There is no corresponding output for the first data point. |
| DIFFERENCE              | INT32 / INT64 / FLOAT / DOUBLE                  | Same type as the input series | Calculates the difference between the value of a data point and the value of the previous data point. There is no corresponding output for the first data point. |
| NON_NEGATIVE_DIFFERENCE | INT32 / INT64 / FLOAT / DOUBLE                  | Same type as the input series | Calculates the absolute value of the difference between the value of a data point and the value of the previous data point. There is no corresponding output for the first data point. |
| DERIVATIVE              | INT32 / INT64 / FLOAT / DOUBLE                  | DOUBLE                        | Calculates the rate of change of a data point compared to the previous data point, the result is equals to DIFFERENCE / TIME_DIFFERENCE. There is no corresponding output for the first data point. |
| NON_NEGATIVE_DERIVATIVE | INT32 / INT64 / FLOAT / DOUBLE                  | DOUBLE                        | Calculates the absolute value of the rate of change of a data point compared to the previous data point, the result is equals to NON_NEGATIVE_DIFFERENCE / TIME_DIFFERENCE. There is no corresponding output for the first data point. |

Example:

```   sql
select s1, time_difference(s1), difference(s1), non_negative_difference(s1), derivative(s1), non_negative_derivative(s1) from root.sg1.d1 limit 5 offset 1000; 
```

Result:

``` 
+-----------------------------+-------------------+-------------------------------+--------------------------+---------------------------------------+--------------------------+---------------------------------------+
|                         Time|     root.sg1.d1.s1|time_difference(root.sg1.d1.s1)|difference(root.sg1.d1.s1)|non_negative_difference(root.sg1.d1.s1)|derivative(root.sg1.d1.s1)|non_negative_derivative(root.sg1.d1.s1)|
+-----------------------------+-------------------+-------------------------------+--------------------------+---------------------------------------+--------------------------+---------------------------------------+
|2020-12-10T17:11:49.037+08:00|7360723084922759782|                              1|      -8431715764844238876|                    8431715764844238876|    -8.4317157648442388E18|                  8.4317157648442388E18|
|2020-12-10T17:11:49.038+08:00|4377791063319964531|                              1|      -2982932021602795251|                    2982932021602795251|     -2.982932021602795E18|                   2.982932021602795E18|
|2020-12-10T17:11:49.039+08:00|7972485567734642915|                              1|       3594694504414678384|                    3594694504414678384|     3.5946945044146785E18|                  3.5946945044146785E18|
|2020-12-10T17:11:49.040+08:00|2508858212791964081|                              1|      -5463627354942678834|                    5463627354942678834|     -5.463627354942679E18|                   5.463627354942679E18|
|2020-12-10T17:11:49.041+08:00|2817297431185141819|                              1|        308439218393177738|                     308439218393177738|     3.0843921839317773E17|                  3.0843921839317773E17|
+-----------------------------+-------------------+-------------------------------+--------------------------+---------------------------------------+--------------------------+---------------------------------------+
Total line number = 5
It costs 0.014s
```

| Function Name | Allowed Input Series Data Types | Attributes                                                                                                                                                                                                                                                                                              | Output Series Data Type | Description                                                                                                                                                                        |
|---------------|---------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| DIFF          | INT32 / INT64 / FLOAT / DOUBLE  | `ignoreNull`：optional，default is true. If is true, the previous data point is ignored when it is null and continues to find the first non-null value forwardly. If the value is false, previous data point is not ignored when it is null, the result is also null because null is used for subtraction | DOUBLE                  | Calculates the difference between the value of a data point and the value of the previous data point. There is no corresponding output for the first data point, so output is null |

### Example

#### RawData

``` 
+-----------------------------+------------+------------+
|                         Time|root.test.s1|root.test.s2|
+-----------------------------+------------+------------+
|1970-01-01T08:00:00.001+08:00|           1|         1.0|
|1970-01-01T08:00:00.002+08:00|           2|        null|
|1970-01-01T08:00:00.003+08:00|        null|         3.0|
|1970-01-01T08:00:00.004+08:00|           4|        null|
|1970-01-01T08:00:00.005+08:00|           5|         5.0|
|1970-01-01T08:00:00.006+08:00|        null|         6.0|
+-----------------------------+------------+------------+
```

#### Not use `ignoreNull` attribute (Ignore Null)

SQL:
```sql
SELECT DIFF(s1), DIFF(s2) from root.test;
```

Result:
```
+-----------------------------+------------------+------------------+
|                         Time|DIFF(root.test.s1)|DIFF(root.test.s2)|
+-----------------------------+------------------+------------------+
|1970-01-01T08:00:00.001+08:00|              null|              null|
|1970-01-01T08:00:00.002+08:00|               1.0|              null|
|1970-01-01T08:00:00.003+08:00|              null|               2.0|
|1970-01-01T08:00:00.004+08:00|               2.0|              null|
|1970-01-01T08:00:00.005+08:00|               1.0|               2.0|
|1970-01-01T08:00:00.006+08:00|              null|               1.0|
+-----------------------------+------------------+------------------+
```

#### Use `ignoreNull` attribute

SQL:
```sql
SELECT DIFF(s1, 'ignoreNull'='false'), DIFF(s2, 'ignoreNull'='false') from root.test;
```

Result:
```
+-----------------------------+----------------------------------------+----------------------------------------+
|                         Time|DIFF(root.test.s1, "ignoreNull"="false")|DIFF(root.test.s2, "ignoreNull"="false")|
+-----------------------------+----------------------------------------+----------------------------------------+
|1970-01-01T08:00:00.001+08:00|                                    null|                                    null|
|1970-01-01T08:00:00.002+08:00|                                     1.0|                                    null|
|1970-01-01T08:00:00.003+08:00|                                    null|                                    null|
|1970-01-01T08:00:00.004+08:00|                                    null|                                    null|
|1970-01-01T08:00:00.005+08:00|                                     1.0|                                    null|
|1970-01-01T08:00:00.006+08:00|                                    null|                                     1.0|
+-----------------------------+----------------------------------------+----------------------------------------+
```