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# Machine Learning

## AR

### Usage

This function is used to learn the coefficients of the autoregressive models for a time series.

**Name:** AR

**Input Series:** Only support a single input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.

**Parameters:** 

- `p`: The order of the autoregressive model. Its default value is 1.

**Output Series:** Output a single series. The type is DOUBLE. The first line corresponds to the first order coefficient, and so on. 

**Note:** 

- Parameter `p` should be a positive integer. 
- Most points in the series should be sampled at a constant time interval. 
- Linear interpolation is applied for the missing points in the series.

### Examples

#### Assigning Model Order

Input Series: 

```
+-----------------------------+---------------+
|                         Time|root.test.d0.s0|
+-----------------------------+---------------+
|2020-01-01T00:00:01.000+08:00|           -4.0|
|2020-01-01T00:00:02.000+08:00|           -3.0|
|2020-01-01T00:00:03.000+08:00|           -2.0|
|2020-01-01T00:00:04.000+08:00|           -1.0|
|2020-01-01T00:00:05.000+08:00|            0.0|
|2020-01-01T00:00:06.000+08:00|            1.0|
|2020-01-01T00:00:07.000+08:00|            2.0|
|2020-01-01T00:00:08.000+08:00|            3.0|
|2020-01-01T00:00:09.000+08:00|            4.0|
+-----------------------------+---------------+
```

SQL for query: 

```sql
select ar(s0,"p"="2") from root.test.d0
```

Output Series:

```
+-----------------------------+---------------------------+
|                         Time|ar(root.test.d0.s0,"p"="2")|
+-----------------------------+---------------------------+
|1970-01-01T08:00:00.001+08:00|                     0.9429|
|1970-01-01T08:00:00.002+08:00|                    -0.2571|
+-----------------------------+---------------------------+
```

### Representation

#### Usage

This function is used to represent a time series.

**Name:** Representation

**Input Series:** Only support a single input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.

**Parameters:** 

- `tb`: The number of timestamp blocks. Its default value is 10.
- `vb`: The number of value blocks. Its default value is 10.

**Output Series:** Output a single series. The type is INT32. The length is `tb*vb`. The timestamps starting from 0 only indicate the order.

**Note:** 

- Parameters `tb` and `vb` should be positive integers.

#### Examples

##### Assigning Window Size and Dimension

Input Series: 

```
+-----------------------------+---------------+
|                         Time|root.test.d0.s0|
+-----------------------------+---------------+
|2020-01-01T00:00:01.000+08:00|           -4.0|
|2020-01-01T00:00:02.000+08:00|           -3.0|
|2020-01-01T00:00:03.000+08:00|           -2.0|
|2020-01-01T00:00:04.000+08:00|           -1.0|
|2020-01-01T00:00:05.000+08:00|            0.0|
|2020-01-01T00:00:06.000+08:00|            1.0|
|2020-01-01T00:00:07.000+08:00|            2.0|
|2020-01-01T00:00:08.000+08:00|            3.0|
|2020-01-01T00:00:09.000+08:00|            4.0|
+-----------------------------+---------------+
```

SQL for query: 

```sql
select representation(s0,"tb"="3","vb"="2") from root.test.d0
```

Output Series:

```
+-----------------------------+-------------------------------------------------+
|                         Time|representation(root.test.d0.s0,"tb"="3","vb"="2")|
+-----------------------------+-------------------------------------------------+
|1970-01-01T08:00:00.001+08:00|                                                1|
|1970-01-01T08:00:00.002+08:00|                                                1|
|1970-01-01T08:00:00.003+08:00|                                                0|
|1970-01-01T08:00:00.004+08:00|                                                0|
|1970-01-01T08:00:00.005+08:00|                                                1|
|1970-01-01T08:00:00.006+08:00|                                                1|
+-----------------------------+-------------------------------------------------+
```

### RM

#### Usage

This function is used to calculate the matching score of two time series according to the representation.

**Name:** RM

**Input Series:** Only support two input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.

**Parameters:** 

- `tb`: The number of timestamp blocks. Its default value is 10.
- `vb`: The number of value blocks. Its default value is 10.

**Output Series:** Output a single series. The type is DOUBLE. There is only one data point in the series, whose timestamp is 0 and value is the matching score.

**Note:** 

- Parameters `tb` and `vb` should be positive integers.

#### Examples

##### Assigning Window Size and Dimension

Input Series: 

```
+-----------------------------+---------------+---------------+
|                         Time|root.test.d0.s0|root.test.d0.s1
+-----------------------------+---------------+---------------+
|2020-01-01T00:00:01.000+08:00|           -4.0|           -4.0|
|2020-01-01T00:00:02.000+08:00|           -3.0|           -3.0|
|2020-01-01T00:00:03.000+08:00|           -3.0|           -3.0|
|2020-01-01T00:00:04.000+08:00|           -1.0|           -1.0|
|2020-01-01T00:00:05.000+08:00|            0.0|            0.0|
|2020-01-01T00:00:06.000+08:00|            1.0|            1.0|
|2020-01-01T00:00:07.000+08:00|            2.0|            2.0|
|2020-01-01T00:00:08.000+08:00|            3.0|            3.0|
|2020-01-01T00:00:09.000+08:00|            4.0|            4.0|
+-----------------------------+---------------+---------------+
```

SQL for query: 

```sql
select rm(s0, s1,"tb"="3","vb"="2") from root.test.d0
```

Output Series:

```
+-----------------------------+-----------------------------------------------------+
|                         Time|rm(root.test.d0.s0,root.test.d0.s1,"tb"="3","vb"="2")|
+-----------------------------+-----------------------------------------------------+
|1970-01-01T08:00:00.001+08:00|                                                 1.00|
+-----------------------------+-----------------------------------------------------+
```