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Posted to commits@iotdb.apache.org by hu...@apache.org on 2022/11/01 15:16:11 UTC
[iotdb] branch research/encoding-exp updated: update encoding algorithms (#7864)
This is an automated email from the ASF dual-hosted git repository.
hui pushed a commit to branch research/encoding-exp
in repository https://gitbox.apache.org/repos/asf/iotdb.git
The following commit(s) were added to refs/heads/research/encoding-exp by this push:
new 8777165245 update encoding algorithms (#7864)
8777165245 is described below
commit 8777165245179203e348ed6a06aa4596be04de18
Author: xjz17 <67...@users.noreply.github.com>
AuthorDate: Tue Nov 1 23:16:04 2022 +0800
update encoding algorithms (#7864)
---
.../org/apache/iotdb/db/qp/sql/IoTDBSqlLexer.g4 | 21 +-
client-cpp/src/main/Session.h | 7 +-
client-py/iotdb/utils/IoTDBConstants.py | 5 +
docs/UserGuide/Process-Data/UDF-Library.md | 4700 +++++++++++++++++---
docs/zh/UserGuide/Process-Data/UDF-Library.md | 4662 ++++++++++++++++---
.../iotdb/flink/tsfile/util/TSFileConfigUtil.java | 1 +
.../db/integration/IoTDBRemovePartitionIT.java | 20 +-
mvn | 0
pom.xml | 2 +
.../engine/compaction/CompactionTaskManager.java | 5 +
.../storagegroup/VirtualStorageGroupProcessor.java | 4 +-
.../org/apache/iotdb/db/utils/SchemaUtils.java | 8 +
.../datastructure/FixedPriorityBlockingQueue.java | 9 +-
.../engine/compaction/CompactionSchedulerTest.java | 483 +-
site/src/main/.vuepress/config.js | 5 +
site/src/main/.vuepress/redirects | 2 +
site/src/main/package.json | 3 +-
tsfile/README.md | 2 +-
tsfile/pom.xml | 3 -
.../iotdb/tsfile/common/conf/TSFileConfig.java | 10 +
.../apache/iotdb/tsfile/compress/ICompressor.java | 40 +-
.../iotdb/tsfile/compress/IUnCompressor.java | 12 +-
.../tsfile/encoding/HuffmanTree/Frequency.java | 11 +
.../tsfile/encoding/HuffmanTree/HuffmanCode.java | 12 +
.../iotdb/tsfile/encoding/decoder/Decoder.java | 68 +
.../encoding/decoder/DeltaBinaryDecoder.java | 7 +-
.../encoding/decoder/DoublePrecisionDecoderV2.java | 3 +-
...cisionDecoderV2.java => DoubleRAKEDecoder.java} | 41 +-
.../tsfile/encoding/decoder/DoubleRLBEDecoder.java | 197 +
.../encoding/decoder/DoubleSprintzDecoder.java | 139 +
.../tsfile/encoding/decoder/FloatDecoder.java | 3 +
...ecisionDecoderV2.java => FloatRAKEDecoder.java} | 41 +-
.../tsfile/encoding/decoder/FloatRLBEDecoder.java | 197 +
.../encoding/decoder/FloatSprintzDecoder.java | 141 +
...PrecisionDecoderV2.java => IntRAKEDecoder.java} | 39 +-
.../tsfile/encoding/decoder/IntRLBEDecoder.java | 196 +
.../tsfile/encoding/decoder/IntRleDecoder.java | 4 +-
.../tsfile/encoding/decoder/IntSprintzDecoder.java | 129 +
...recisionDecoderV2.java => LongRAKEDecoder.java} | 41 +-
.../tsfile/encoding/decoder/LongRLBEDecoder.java | 196 +
.../encoding/decoder/LongSprintzDecoder.java | 127 +
.../tsfile/encoding/decoder/PlainDecoder.java | 18 +-
.../iotdb/tsfile/encoding/decoder/RAKEDecoder.java | 207 +
.../encoding/decoder/SinglePrecisionDecoderV2.java | 3 +-
...PrecisionDecoderV2.java => SprintzDecoder.java} | 47 +-
.../tsfile/encoding/decoder/TextRleDecoder.java | 50 +
...cisionEncoderV2.java => DoubleRAKEEncoder.java} | 35 +-
.../iotdb/tsfile/encoding/encoder/DoubleRLBE.java | 272 ++
.../encoding/encoder/DoubleSprintzEncoder.java | 160 +
.../iotdb/tsfile/encoding/encoder/Encoder.java | 79 -
.../tsfile/encoding/encoder/FloatEncoder.java | 16 +
...ecisionEncoderV2.java => FloatRAKEEncoder.java} | 35 +-
.../iotdb/tsfile/encoding/encoder/FloatRLBE.java | 273 ++
.../encoding/encoder/FloatSprintzEncoder.java | 159 +
.../tsfile/encoding/encoder/GorillaEncoderV2.java | 5 +
.../tsfile/encoding/encoder/HuffmanEncoder.java | 235 +
...PrecisionEncoderV2.java => IntRAKEEncoder.java} | 35 +-
.../iotdb/tsfile/encoding/encoder/IntRLBE.java | 263 ++
.../tsfile/encoding/encoder/IntSprintzEncoder.java | 158 +
...recisionEncoderV2.java => LongRAKEEncoder.java} | 35 +-
.../iotdb/tsfile/encoding/encoder/LongRLBE.java | 257 ++
.../encoding/encoder/LongSprintzEncoder.java | 159 +
.../iotdb/tsfile/encoding/encoder/RAKEEncoder.java | 166 +
.../apache/iotdb/tsfile/encoding/encoder/RLBE.java | 61 +
.../iotdb/tsfile/encoding/encoder/RleEncoder.java | 7 +-
.../encoding/encoder/SinglePrecisionEncoderV2.java | 5 +
.../tsfile/encoding/encoder/SprintzEncoder.java | 72 +
.../tsfile/encoding/encoder/TSEncodingBuilder.java | 10 -
.../tsfile/encoding/encoder/TextRleEncoder.java | 90 +
.../apache/iotdb/tsfile/encoding/fire/Fire.java | 56 +
.../apache/iotdb/tsfile/encoding/fire/IntFire.java | 52 +
.../iotdb/tsfile/encoding/fire/LongFire.java | 48 +
.../tsfile/file/metadata/enums/TSEncoding.java | 7 -
.../tsfile/utils/ReadWriteForEncodingUtils.java | 18 +
.../encoding/decoder/HuffmanDecoderTest.java | 101 +
.../tsfile/encoding/decoder/PLAINDecoderTest.java | 217 +
.../tsfile/encoding/decoder/RAKEDecoderTest.java | 626 +++
.../encoding/decoder/TextRleDecoderTest.java | 125 +
78 files changed, 14243 insertions(+), 1515 deletions(-)
diff --git a/antlr/src/main/antlr4/org/apache/iotdb/db/qp/sql/IoTDBSqlLexer.g4 b/antlr/src/main/antlr4/org/apache/iotdb/db/qp/sql/IoTDBSqlLexer.g4
index 024cf78316..603e17a84e 100644
--- a/antlr/src/main/antlr4/org/apache/iotdb/db/qp/sql/IoTDBSqlLexer.g4
+++ b/antlr/src/main/antlr4/org/apache/iotdb/db/qp/sql/IoTDBSqlLexer.g4
@@ -633,7 +633,7 @@ TEXT
// Encoding Type Keywords
ENCODING_VALUE
- : DICTIONARY | DIFF | GORILLA | PLAIN | REGULAR | RLE | TS_2DIFF
+ : DICTIONARY | DIFF | GORILLA | PLAIN | REGULAR | RLE | TS_2DIFF | RLBE | RAKE | SPRINTZ | HUFFMAN | TEXTRLE
;
DICTIONARY
@@ -664,6 +664,25 @@ TS_2DIFF
: T S '_' '2' D I F F
;
+RLBE
+ : R L B E
+ ;
+
+RAKE
+ : R A K E
+ ;
+
+SPRINTZ
+ : S P R I N T Z
+ ;
+
+HUFFMAN
+ : H U F F M A N
+ ;
+
+TEXTRLE
+ : T E X T R L E
+ ;
// Compressor Type Keywords
diff --git a/client-cpp/src/main/Session.h b/client-cpp/src/main/Session.h
index 3a93a8e9af..b3c3ee140f 100644
--- a/client-cpp/src/main/Session.h
+++ b/client-cpp/src/main/Session.h
@@ -143,7 +143,12 @@ namespace TSEncoding {
BITMAP = (char) 5,
GORILLA_V1 = (char) 6,
REGULAR = (char) 7,
- GORILLA = (char) 8
+ GORILLA = (char) 8,
+ SPRINTZ = (char) 9,
+ RAKE = (char) 10,
+ RLBE = (char) 11,
+ TEXTRLE = (char) 12,
+ HUFFMAN = (char) 13
};
}
diff --git a/client-py/iotdb/utils/IoTDBConstants.py b/client-py/iotdb/utils/IoTDBConstants.py
index 50344d1480..bac922b781 100644
--- a/client-py/iotdb/utils/IoTDBConstants.py
+++ b/client-py/iotdb/utils/IoTDBConstants.py
@@ -48,6 +48,11 @@ class TSEncoding(Enum):
GORILLA_V1 = 6
REGULAR = 7
GORILLA = 8
+ SPRINTZ = 9,
+ RAKE = 10,
+ RLBE = 11,
+ TEXTRLE = 12,
+ HUFFMAN = 13
# this method is implemented to avoid the issue reported by:
# https://bugs.python.org/issue30545
diff --git a/docs/UserGuide/Process-Data/UDF-Library.md b/docs/UserGuide/Process-Data/UDF-Library.md
index d06355f474..f76da74c6f 100644
--- a/docs/UserGuide/Process-Data/UDF-Library.md
+++ b/docs/UserGuide/Process-Data/UDF-Library.md
@@ -1,23 +1,26 @@
<!--
- Licensed to the Apache Software Foundation (ASF) under one
- or more contributor license agreements. See the NOTICE file
- distributed with this work for additional information
- regarding copyright ownership. The ASF licenses this file
- to you under the Apache License, Version 2.0 (the
- "License"); you may not use this file except in compliance
- with the License. You may obtain a copy of the License at
-
- http://www.apache.org/licenses/LICENSE-2.0
-
- Unless required by applicable law or agreed to in writing,
- software distributed under the License is distributed on an
- "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
- KIND, either express or implied. See the License for the
- specific language governing permissions and limitations
- under the License.
+ Licensed to the Apache Software Foundation (ASF) under one
+ or more contributor license agreements. See the NOTICE file
+ distributed with this work for additional information
+ regarding copyright ownership. The ASF licenses this file
+ to you under the Apache License, Version 2.0 (the
+ "License"); you may not use this file except in compliance
+ with the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing,
+ software distributed under the License is distributed on an
+ "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ KIND, either express or implied. See the License for the
+ specific language governing permissions and limitations
+ under the License.
-->
+
+
+
# UDF Library
For applications based on time series data, data quality is vital.
@@ -58,29 +61,30 @@ You can download the following files:
</tr>
</table>
-## Data Quality
-### Completeness
-#### Usage
-This function is used to calculate the completeness of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the completeness of each window will be output.
+## Data Profiling
-**Name:** COMPLETENESS
+### ACF
-**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+#### Usage
-**Parameters:**
+This function is used to calculate the auto-correlation factor of the input time series,
+which equals to cross correlation between the same series.
+For more information, please refer to `XCorr` function.
-+ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
-+ `downtime`: Whether the downtime exception is considered in the calculation of completeness. It is 'true' or 'false' (default). When considering the downtime exception, long-term missing data will be considered as downtime exception without any influence on completeness.
+**Name:** ACF
-**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
+**Input Series:** Only support a single input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.
-**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
+**Output Series:** Output a single series. The type is DOUBLE.
+There are $2N-1$ data points in the series, and the values are interpreted in details in `XCorr` function.
-#### Example: Default Parameters
+**Note:**
-With default parameters, this function will regard all input data as the same window.
++ `null` and `NaN` values in the input series will be ignored and treated as 0.
+
+#### Examples
Input series:
@@ -88,120 +92,115 @@ Input series:
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:01.000+08:00| 1|
+|2020-01-01T00:00:02.000+08:00| null|
+|2020-01-01T00:00:03.000+08:00| 3|
+|2020-01-01T00:00:04.000+08:00| NaN|
+|2020-01-01T00:00:05.000+08:00| 5|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select completeness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select acf(s1) from root.test.d1 where time <= 2020-01-01 00:00:05
```
Output series:
```
-+-----------------------------+-----------------------------+
-| Time|completeness(root.test.d1.s1)|
-+-----------------------------+-----------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.875|
-+-----------------------------+-----------------------------+
++-----------------------------+--------------------+
+| Time|acf(root.test.d1.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.001+08:00| 1.0|
+|1970-01-01T08:00:00.002+08:00| 0.0|
+|1970-01-01T08:00:00.003+08:00| 3.6|
+|1970-01-01T08:00:00.004+08:00| 0.0|
+|1970-01-01T08:00:00.005+08:00| 7.0|
+|1970-01-01T08:00:00.006+08:00| 0.0|
+|1970-01-01T08:00:00.007+08:00| 3.6|
+|1970-01-01T08:00:00.008+08:00| 0.0|
+|1970-01-01T08:00:00.009+08:00| 1.0|
++-----------------------------+--------------------+
```
-#### Example: Specific Window Size
+### Distinct
-When the window size is given, this function will divide the input data as multiple windows.
+#### Usage
+
+This function returns all unique values in time series.
+
+**Name:** DISTINCT
+
+**Input Series:** Only support a single input series. The type is arbitrary.
+
+**Output Series:** Output a single series. The type is the same as the input.
+
+**Note:**
+
++ The timestamp of the output series is meaningless. The output order is arbitrary.
++ Missing points and null points in the input series will be ignored, but `NaN` will not.
++ Case Sensitive.
+
+
+#### Examples
Input series:
```
+-----------------------------+---------------+
-| Time|root.test.d1.s1|
+| Time|root.test.d2.s2|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
+|2020-01-01T08:00:00.001+08:00| Hello|
+|2020-01-01T08:00:00.002+08:00| hello|
+|2020-01-01T08:00:00.003+08:00| Hello|
+|2020-01-01T08:00:00.004+08:00| World|
+|2020-01-01T08:00:00.005+08:00| World|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select completeness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select distinct(s2) from root.test.d2
```
Output series:
```
-+-----------------------------+--------------------------------------------+
-| Time|completeness(root.test.d1.s1, "window"="15")|
-+-----------------------------+--------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.875|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+--------------------------------------------+
++-----------------------------+-------------------------+
+| Time|distinct(root.test.d2.s2)|
++-----------------------------+-------------------------+
+|1970-01-01T08:00:00.001+08:00| Hello|
+|1970-01-01T08:00:00.002+08:00| hello|
+|1970-01-01T08:00:00.003+08:00| World|
++-----------------------------+-------------------------+
```
-### Consistency
+### Histogram
#### Usage
-This function is used to calculate the consistency of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the consistency of each window will be output.
-**Name:** CONSISTENCY
+This function is used to calculate the distribution histogram of a single column of numerical data.
-**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+**Name:** HISTOGRAM
+
+**Input Series:** Only supports a single input sequence, the type is INT32 / INT64 / FLOAT / DOUBLE
**Parameters:**
-+ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
++ `min`: The lower limit of the requested data range, the default value is -Double.MAX_VALUE.
++ `max`: The upper limit of the requested data range, the default value is Double.MAX_VALUE, and the value of start must be less than or equal to end.
++ `count`: The number of buckets of the histogram, the default value is 1. It must be a positive integer.
-**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
+**Output Series:** The value of the bucket of the histogram, where the lower bound represented by the i-th bucket (index starts from 1) is $min+ (i-1)\cdot\frac{max-min}{count}$ and the upper bound is $min + i \cdot \frac{max-min}{count}$.
-**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
+**Note:**
-#### Example: Default Parameters
++ If the value is lower than `min`, it will be put into the 1st bucket. If the value is larger than `max`, it will be put into the last bucket.
++ Missing points, null points and `NaN` in the input series will be ignored.
-With default parameters, this function will regard all input data as the same window.
+#### Examples
Input series:
@@ -209,43 +208,85 @@ Input series:
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:00.000+08:00| 1.0|
+|2020-01-01T00:00:01.000+08:00| 2.0|
+|2020-01-01T00:00:02.000+08:00| 3.0|
+|2020-01-01T00:00:03.000+08:00| 4.0|
+|2020-01-01T00:00:04.000+08:00| 5.0|
+|2020-01-01T00:00:05.000+08:00| 6.0|
+|2020-01-01T00:00:06.000+08:00| 7.0|
+|2020-01-01T00:00:07.000+08:00| 8.0|
+|2020-01-01T00:00:08.000+08:00| 9.0|
+|2020-01-01T00:00:09.000+08:00| 10.0|
+|2020-01-01T00:00:10.000+08:00| 11.0|
+|2020-01-01T00:00:11.000+08:00| 12.0|
+|2020-01-01T00:00:12.000+08:00| 13.0|
+|2020-01-01T00:00:13.000+08:00| 14.0|
+|2020-01-01T00:00:14.000+08:00| 15.0|
+|2020-01-01T00:00:15.000+08:00| 16.0|
+|2020-01-01T00:00:16.000+08:00| 17.0|
+|2020-01-01T00:00:17.000+08:00| 18.0|
+|2020-01-01T00:00:18.000+08:00| 19.0|
+|2020-01-01T00:00:19.000+08:00| 20.0|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select consistency(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select histogram(s1,"min"="1","max"="20","count"="10") from root.test.d1
```
Output series:
```
-+-----------------------------+----------------------------+
-| Time|consistency(root.test.d1.s1)|
-+-----------------------------+----------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-+-----------------------------+----------------------------+
++-----------------------------+---------------------------------------------------------------+
+| Time|histogram(root.test.d1.s1, "min"="1", "max"="20", "count"="10")|
++-----------------------------+---------------------------------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 2|
+|1970-01-01T08:00:00.001+08:00| 2|
+|1970-01-01T08:00:00.002+08:00| 2|
+|1970-01-01T08:00:00.003+08:00| 2|
+|1970-01-01T08:00:00.004+08:00| 2|
+|1970-01-01T08:00:00.005+08:00| 2|
+|1970-01-01T08:00:00.006+08:00| 2|
+|1970-01-01T08:00:00.007+08:00| 2|
+|1970-01-01T08:00:00.008+08:00| 2|
+|1970-01-01T08:00:00.009+08:00| 2|
++-----------------------------+---------------------------------------------------------------+
```
-#### Example: Specific Window Size
+### Integral
-When the window size is given, this function will divide the input data as multiple windows.
+#### Usage
+
+This function is used to calculate the integration of time series,
+which equals to the area under the curve with time as X-axis and values as Y-axis.
+
+**Name:** INTEGRAL
+
+**Input Series:** Only support a single input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `unit`: The unit of time used when computing the integral.
+ The value should be chosen from "1S", "1s", "1m", "1H", "1d"(case-sensitive),
+ and each represents taking one millisecond / second / minute / hour / day as 1.0 while calculating the area and integral.
+
+**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 integration.
+
+**Note:**
+
++ The integral value equals to the sum of the areas of right-angled trapezoids consisting of each two adjacent points and the time-axis.
+ Choosing different `unit` implies different scaling of time axis, thus making it apparent to convert the value among those results with constant coefficient.
+
++ `NaN` values in the input series will be ignored. The curve or trapezoids will skip these points and use the next valid point.
+
+#### Examples
+
+##### Default Parameters
+
+With default parameters, this function will take one second as 1.0.
Input series:
@@ -253,76 +294,83 @@ Input series:
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
+|2020-01-01T00:00:01.000+08:00| 1|
+|2020-01-01T00:00:02.000+08:00| 2|
+|2020-01-01T00:00:03.000+08:00| 5|
+|2020-01-01T00:00:04.000+08:00| 6|
+|2020-01-01T00:00:05.000+08:00| 7|
+|2020-01-01T00:00:08.000+08:00| 8|
+|2020-01-01T00:00:09.000+08:00| NaN|
+|2020-01-01T00:00:10.000+08:00| 10|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select consistency(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select integral(s1) from root.test.d1 where time <= 2020-01-01 00:00:10
```
Output series:
```
-+-----------------------------+-------------------------------------------+
-| Time|consistency(root.test.d1.s1, "window"="15")|
-+-----------------------------+-------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+-------------------------------------------+
++-----------------------------+-------------------------+
+| Time|integral(root.test.d1.s1)|
++-----------------------------+-------------------------+
+|1970-01-01T08:00:00.000+08:00| 57.5|
++-----------------------------+-------------------------+
```
-### Timeliness
+Calculation expression:
+$$\frac{1}{2}[(1+2) \times 1 + (2+5) \times 1 + (5+6) \times 1 + (6+7) \times 1 + (7+8) \times 3 + (8+10) \times 2] = 57.5$$
+
+##### Specific time unit
+
+With time unit specified as "1m", this function will take one minute as 1.0.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select integral(s1, "unit"="1m") from root.test.d1 where time <= 2020-01-01 00:00:10
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------+
+| Time|integral(root.test.d1.s1)|
++-----------------------------+-------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.958|
++-----------------------------+-------------------------+
+```
+
+Calculation expression:
+$$\frac{1}{2\times 60}[(1+2) \times 1 + (2+5) \times 1 + (5+6) \times 1 + (6+7) \times 1 + (7+8) \times 3 + (8+10) \times 2] = 0.958$$
+
+### IntegralAvg
#### Usage
-This function is used to calculate the timeliness of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the timeliness of each window will be output.
-**Name:** TIMELINESS
+This function is used to calculate the function average of time series.
+The output equals to the area divided by the time interval using the same time `unit`.
+For more information of the area under the curve, please refer to `Integral` function.
-**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+**Name:** INTEGRALAVG
-**Parameters:**
+**Input Series:** Only support a single input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.
-+ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
+**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 time-weighted average.
-**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
+**Note:**
-**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
++ The time-weighted value equals to the integral value with any `unit` divided by the time interval of input series.
+ The result is irrelevant to the time unit used in integral, and it's consistent with the timestamp precision of IoTDB by default.
-#### Example: Default Parameters
++ `NaN` values in the input series will be ignored. The curve or trapezoids will skip these points and use the next valid point.
-With default parameters, this function will regard all input data as the same window.
++ If the input series is empty, the output value will be 0.0, but if there is only one data point, the value will equal to the input value.
+
+#### Examples
Input series:
@@ -330,120 +378,3384 @@ Input series:
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:01.000+08:00| 1|
+|2020-01-01T00:00:02.000+08:00| 2|
+|2020-01-01T00:00:03.000+08:00| 5|
+|2020-01-01T00:00:04.000+08:00| 6|
+|2020-01-01T00:00:05.000+08:00| 7|
+|2020-01-01T00:00:08.000+08:00| 8|
+|2020-01-01T00:00:09.000+08:00| NaN|
+|2020-01-01T00:00:10.000+08:00| 10|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select timeliness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select integralavg(s1) from root.test.d1 where time <= 2020-01-01 00:00:10
```
Output series:
```
-+-----------------------------+---------------------------+
-| Time|timeliness(root.test.d1.s1)|
-+-----------------------------+---------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-+-----------------------------+---------------------------+
++-----------------------------+----------------------------+
+| Time|integralavg(root.test.d1.s1)|
++-----------------------------+----------------------------+
+|1970-01-01T08:00:00.000+08:00| 5.75|
++-----------------------------+----------------------------+
```
-#### Example: Specific Window Size
+Calculation expression:
+$$\frac{1}{2}[(1+2) \times 1 + (2+5) \times 1 + (5+6) \times 1 + (6+7) \times 1 + (7+8) \times 3 + (8+10) \times 2] / 10 = 5.75$$
-When the window size is given, this function will divide the input data as multiple windows.
+### Mad
+
+#### Usage
+
+The function is used to compute the exact or approximate median absolute deviation (MAD) of a numeric time series. MAD is the median of the deviation of each element from the elements' median.
+
+Take a dataset $\{1,3,3,5,5,6,7,8,9\}$ as an instance. Its median is 5 and the deviation of each element from the median is $\{0,0,1,2,2,2,3,4,4\}$, whose median is 2. Therefore, the MAD of the original dataset is 2.
+
+**Name:** MAD
+
+**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameter:**
+
++ `error`: The relative error of the approximate MAD. It should be within [0,1) and the default value is 0. Taking `error`=0.01 as an instance, suppose the exact MAD is $a$ and the approximate MAD is $b$, we have $0.99a \le b \le 1.01a$. With `error`=0, the output is the exact MAD.
+
+**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 MAD.
+
+**Note:** Missing points, null points and `NaN` in the input series will be ignored.
+
+#### Examples
+
+##### Exact Query
+
+With the default `error`(`error`=0), the function queries the exact MAD.
Input series:
```
-+-----------------------------+---------------+
-| Time|root.test.d1.s1|
-+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|2021-03-17T10:32:17.054+08:00| 0.5319929|
+|2021-03-17T10:32:18.054+08:00| 0.9304316|
+|2021-03-17T10:32:19.054+08:00| -1.4800133|
+|2021-03-17T10:32:20.054+08:00| 0.6114087|
+|2021-03-17T10:32:21.054+08:00| 2.5163336|
+|2021-03-17T10:32:22.054+08:00| -1.0845392|
+|2021-03-17T10:32:23.054+08:00| 1.0562582|
+|2021-03-17T10:32:24.054+08:00| 1.3867859|
+|2021-03-17T10:32:25.054+08:00| -0.45429882|
+|2021-03-17T10:32:26.054+08:00| 1.0353678|
+|2021-03-17T10:32:27.054+08:00| 0.7307929|
+|2021-03-17T10:32:28.054+08:00| 2.3167255|
+|2021-03-17T10:32:29.054+08:00| 2.342443|
+|2021-03-17T10:32:30.054+08:00| 1.5809103|
+|2021-03-17T10:32:31.054+08:00| 1.4829416|
+|2021-03-17T10:32:32.054+08:00| 1.5800357|
+|2021-03-17T10:32:33.054+08:00| 0.7124368|
+|2021-03-17T10:32:34.054+08:00| -0.78597564|
+|2021-03-17T10:32:35.054+08:00| 1.2058644|
+|2021-03-17T10:32:36.054+08:00| 1.4215064|
+|2021-03-17T10:32:37.054+08:00| 1.2808295|
+|2021-03-17T10:32:38.054+08:00| -0.6173715|
+|2021-03-17T10:32:39.054+08:00| 0.06644377|
+|2021-03-17T10:32:40.054+08:00| 2.349338|
+|2021-03-17T10:32:41.054+08:00| 1.7335888|
+|2021-03-17T10:32:42.054+08:00| 1.5872132|
+............
+Total line number = 10000
+```
+
+SQL for query:
+
+```sql
+select mad(s0) from root.test
+```
+
+Output series:
+
+```
++-----------------------------+------------------+
+| Time| mad(root.test.s0)|
++-----------------------------+------------------+
+|1970-01-01T08:00:00.000+08:00|0.6806197166442871|
++-----------------------------+------------------+
+```
+
+##### Approximate Query
+
+By setting `error` within (0,1), the function queries the approximate MAD.
+
+SQL for query:
+
+```sql
+select mad(s0, "error"="0.01") from root.test
+```
+
+Output series:
+
+```
++-----------------------------+---------------------------------+
+| Time|mad(root.test.s0, "error"="0.01")|
++-----------------------------+---------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.6806616245859518|
++-----------------------------+---------------------------------+
+```
+
+### Median
+
+#### Usage
+
+The function is used to compute the exact or approximate median of a numeric time series. Median is the value separating the higher half from the lower half of a data sample.
+
+**Name:** MEDIAN
+
+**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameter:**
+
++ `error`: The rank error of the approximate median. It should be within [0,1) and the default value is 0. For instance, a median with `error`=0.01 is the value of the element with rank percentage 0.49~0.51. With `error`=0, the output is the exact median.
+
+**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 median.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|2021-03-17T10:32:17.054+08:00| 0.5319929|
+|2021-03-17T10:32:18.054+08:00| 0.9304316|
+|2021-03-17T10:32:19.054+08:00| -1.4800133|
+|2021-03-17T10:32:20.054+08:00| 0.6114087|
+|2021-03-17T10:32:21.054+08:00| 2.5163336|
+|2021-03-17T10:32:22.054+08:00| -1.0845392|
+|2021-03-17T10:32:23.054+08:00| 1.0562582|
+|2021-03-17T10:32:24.054+08:00| 1.3867859|
+|2021-03-17T10:32:25.054+08:00| -0.45429882|
+|2021-03-17T10:32:26.054+08:00| 1.0353678|
+|2021-03-17T10:32:27.054+08:00| 0.7307929|
+|2021-03-17T10:32:28.054+08:00| 2.3167255|
+|2021-03-17T10:32:29.054+08:00| 2.342443|
+|2021-03-17T10:32:30.054+08:00| 1.5809103|
+|2021-03-17T10:32:31.054+08:00| 1.4829416|
+|2021-03-17T10:32:32.054+08:00| 1.5800357|
+|2021-03-17T10:32:33.054+08:00| 0.7124368|
+|2021-03-17T10:32:34.054+08:00| -0.78597564|
+|2021-03-17T10:32:35.054+08:00| 1.2058644|
+|2021-03-17T10:32:36.054+08:00| 1.4215064|
+|2021-03-17T10:32:37.054+08:00| 1.2808295|
+|2021-03-17T10:32:38.054+08:00| -0.6173715|
+|2021-03-17T10:32:39.054+08:00| 0.06644377|
+|2021-03-17T10:32:40.054+08:00| 2.349338|
+|2021-03-17T10:32:41.054+08:00| 1.7335888|
+|2021-03-17T10:32:42.054+08:00| 1.5872132|
+............
+Total line number = 10000
+```
+
+SQL for query:
+
+```sql
+select median(s0, "error"="0.01") from root.test
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------+
+| Time|median(root.test.s0, "error"="0.01")|
++-----------------------------+------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.021884560585022|
++-----------------------------+------------------------------------+
+```
+
+### MinMax
+
+#### Usage
+
+This function is used to standardize the input series with min-max. Minimum value is transformed to 0; maximum value is transformed to 1.
+
+**Name:** MINMAX
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `compute`: When set to "batch", anomaly test is conducted after importing all data points; when set to "stream", it is required to provide minimum and maximum values. The default method is "batch".
++ `min`: The maximum value when method is set to "stream".
++ `max`: The minimum value when method is set to "stream".
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+#### Examples
+
+##### Batch computing
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+SQL for query:
+
+```sql
+select minmax(s1) from root.test
+```
+
+Output series:
+
+```
++-----------------------------+--------------------+
+| Time|minmax(root.test.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.100+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.200+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.300+08:00| 0.25|
+|1970-01-01T08:00:00.400+08:00| 0.08333333333333333|
+|1970-01-01T08:00:00.500+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.600+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.700+08:00| 0.0|
+|1970-01-01T08:00:00.800+08:00| 0.3333333333333333|
+|1970-01-01T08:00:00.900+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.000+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.100+08:00| 0.25|
+|1970-01-01T08:00:01.200+08:00| 0.08333333333333333|
+|1970-01-01T08:00:01.300+08:00| 0.08333333333333333|
+|1970-01-01T08:00:01.400+08:00| 0.25|
+|1970-01-01T08:00:01.500+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.600+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.700+08:00| 1.0|
+|1970-01-01T08:00:01.800+08:00| 0.3333333333333333|
+|1970-01-01T08:00:01.900+08:00| 0.0|
+|1970-01-01T08:00:02.000+08:00| 0.16666666666666666|
++-----------------------------+--------------------+
+```
+
+### Mode
+
+#### Usage
+
+This function is used to calculate the mode of time series, that is, the value that occurs most frequently.
+
+**Name:** MODE
+
+**Input Series:** Only support a single input series. The type is arbitrary.
+
+**Output Series:** Output a single series. The type is the same as the input. There is only one data point in the series, whose timestamp is the same as which the first mode value has and value is the mode.
+
+**Note:**
+
++ If there are multiple values with the most occurrences, the arbitrary one will be output.
++ Missing points and null points in the input series will be ignored, but `NaN` will not.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s2|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.001+08:00| Hello|
+|1970-01-01T08:00:00.002+08:00| hello|
+|1970-01-01T08:00:00.003+08:00| Hello|
+|1970-01-01T08:00:00.004+08:00| World|
+|1970-01-01T08:00:00.005+08:00| World|
+|1970-01-01T08:00:01.600+08:00| World|
+|1970-01-15T09:37:34.451+08:00| Hello|
+|1970-01-15T09:37:34.452+08:00| hello|
+|1970-01-15T09:37:34.453+08:00| Hello|
+|1970-01-15T09:37:34.454+08:00| World|
+|1970-01-15T09:37:34.455+08:00| World|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select mode(s2) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+---------------------+
+| Time|mode(root.test.d2.s2)|
++-----------------------------+---------------------+
+|1970-01-01T08:00:00.004+08:00| World|
++-----------------------------+---------------------+
+```
+
+### MvAvg
+
+#### Usage
+
+This function is used to calculate moving average of input series.
+
+**Name:** MVAVG
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `window`: Length of the moving window. Default value is 10.
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+#### Examples
+
+##### Batch computing
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+SQL for query:
+
+```sql
+select mvavg(s1, "window"="3") from root.test
+```
+
+Output series:
+
+```
++-----------------------------+---------------------------------+
+| Time|mvavg(root.test.s1, "window"="3")|
++-----------------------------+---------------------------------+
+|1970-01-01T08:00:00.300+08:00| 0.3333333333333333|
+|1970-01-01T08:00:00.400+08:00| 0.0|
+|1970-01-01T08:00:00.500+08:00| -0.3333333333333333|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -0.6666666666666666|
+|1970-01-01T08:00:00.800+08:00| 0.0|
+|1970-01-01T08:00:00.900+08:00| 0.6666666666666666|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 0.3333333333333333|
+|1970-01-01T08:00:01.200+08:00| 0.0|
+|1970-01-01T08:00:01.300+08:00| -0.6666666666666666|
+|1970-01-01T08:00:01.400+08:00| 0.0|
+|1970-01-01T08:00:01.500+08:00| 0.3333333333333333|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 3.3333333333333335|
+|1970-01-01T08:00:01.800+08:00| 4.0|
+|1970-01-01T08:00:01.900+08:00| 0.0|
+|1970-01-01T08:00:02.000+08:00| -0.6666666666666666|
++-----------------------------+---------------------------------+
+```
+
+### PACF
+
+#### Usage
+
+This function is used to calculate partial autocorrelation of input series by solving Yule-Walker equation. For some cases, the equation may not be solved, and NaN will be output.
+
+**Name:** PACF
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `lag`: Maximum lag of pacf to calculate. The default value is $\min(10\log_{10}n,n-1)$, where $n$ is the number of data points.
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+#### Examples
+
+##### Assigning maximum lag
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|2019-12-27T00:00:00.000+08:00| 5.0|
+|2019-12-27T00:05:00.000+08:00| 5.0|
+|2019-12-27T00:10:00.000+08:00| 5.0|
+|2019-12-27T00:15:00.000+08:00| 5.0|
+|2019-12-27T00:20:00.000+08:00| 6.0|
+|2019-12-27T00:25:00.000+08:00| 5.0|
+|2019-12-27T00:30:00.000+08:00| 6.0|
+|2019-12-27T00:35:00.000+08:00| 6.0|
+|2019-12-27T00:40:00.000+08:00| 6.0|
+|2019-12-27T00:45:00.000+08:00| 6.0|
+|2019-12-27T00:50:00.000+08:00| 6.0|
+|2019-12-27T00:55:00.000+08:00| 5.982609|
+|2019-12-27T01:00:00.000+08:00| 5.9652176|
+|2019-12-27T01:05:00.000+08:00| 5.947826|
+|2019-12-27T01:10:00.000+08:00| 5.9304347|
+|2019-12-27T01:15:00.000+08:00| 5.9130435|
+|2019-12-27T01:20:00.000+08:00| 5.8956523|
+|2019-12-27T01:25:00.000+08:00| 5.878261|
+|2019-12-27T01:30:00.000+08:00| 5.8608694|
+|2019-12-27T01:35:00.000+08:00| 5.843478|
+............
+Total line number = 18066
+```
+
+SQL for query:
+
+```sql
+select pacf(s1, "lag"="5") from root.test
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------------+
+| Time|pacf(root.test.s1, "lag"="5")|
++-----------------------------+-----------------------------+
+|2019-12-27T00:00:00.000+08:00| 1.0|
+|2019-12-27T00:05:00.000+08:00| 0.3528915091942786|
+|2019-12-27T00:10:00.000+08:00| 0.1761346122516304|
+|2019-12-27T00:15:00.000+08:00| 0.1492391973294682|
+|2019-12-27T00:20:00.000+08:00| 0.03560059645868398|
+|2019-12-27T00:25:00.000+08:00| 0.0366222998995286|
++-----------------------------+-----------------------------+
+```
+
+### Percentile
+
+#### Usage
+
+The function is used to compute the exact or approximate percentile of a numeric time series. A percentile is value of element in the certain rank of the sorted series.
+
+**Name:** PERCENTILE
+
+**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameter:**
+
++ `rank`: The rank percentage of the percentile. It should be (0,1] and the default value is 0.5. For instance, a percentile with `rank`=0.5 is the median.
++ `error`: The rank error of the approximate percentile. It should be within [0,1) and the default value is 0. For instance, a 0.5-percentile with `error`=0.01 is the value of the element with rank percentage 0.49~0.51. With `error`=0, the output is the exact percentile.
+
+**Output Series:** Output a single series. The type is the same as input series. If `error`=0, there is only one data point in the series, whose timestamp is the same has which the first percentile value has, and value is the percentile, otherwise the timestamp of the only data point is 0.
+
+**Note:** Missing points, null points and `NaN` in the input series will be ignored.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|2021-03-17T10:32:17.054+08:00| 0.5319929|
+|2021-03-17T10:32:18.054+08:00| 0.9304316|
+|2021-03-17T10:32:19.054+08:00| -1.4800133|
+|2021-03-17T10:32:20.054+08:00| 0.6114087|
+|2021-03-17T10:32:21.054+08:00| 2.5163336|
+|2021-03-17T10:32:22.054+08:00| -1.0845392|
+|2021-03-17T10:32:23.054+08:00| 1.0562582|
+|2021-03-17T10:32:24.054+08:00| 1.3867859|
+|2021-03-17T10:32:25.054+08:00| -0.45429882|
+|2021-03-17T10:32:26.054+08:00| 1.0353678|
+|2021-03-17T10:32:27.054+08:00| 0.7307929|
+|2021-03-17T10:32:28.054+08:00| 2.3167255|
+|2021-03-17T10:32:29.054+08:00| 2.342443|
+|2021-03-17T10:32:30.054+08:00| 1.5809103|
+|2021-03-17T10:32:31.054+08:00| 1.4829416|
+|2021-03-17T10:32:32.054+08:00| 1.5800357|
+|2021-03-17T10:32:33.054+08:00| 0.7124368|
+|2021-03-17T10:32:34.054+08:00| -0.78597564|
+|2021-03-17T10:32:35.054+08:00| 1.2058644|
+|2021-03-17T10:32:36.054+08:00| 1.4215064|
+|2021-03-17T10:32:37.054+08:00| 1.2808295|
+|2021-03-17T10:32:38.054+08:00| -0.6173715|
+|2021-03-17T10:32:39.054+08:00| 0.06644377|
+|2021-03-17T10:32:40.054+08:00| 2.349338|
+|2021-03-17T10:32:41.054+08:00| 1.7335888|
+|2021-03-17T10:32:42.054+08:00| 1.5872132|
+............
+Total line number = 10000
+```
+
+SQL for query:
+
+```sql
+select percentile(s0, "rank"="0.2", "error"="0.01") from root.test
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|percentile(root.test.s0, "rank"="0.2", "error"="0.01")|
++-----------------------------+------------------------------------------------------+
+|2021-03-17T10:35:02.054+08:00| 0.1801469624042511|
++-----------------------------+------------------------------------------------------+
+```
+
+### Period
+
+#### Usage
+
+The function is used to compute the period of a numeric time series.
+
+**Name:** PERIOD
+
+**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Output Series:** Output a single series. The type is INT32. There is only one data point in the series, whose timestamp is 0 and value is the period.
+
+#### Examples
+
+Input series:
+
+
+```
++-----------------------------+---------------+
+| Time|root.test.d3.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.001+08:00| 1.0|
+|1970-01-01T08:00:00.002+08:00| 2.0|
+|1970-01-01T08:00:00.003+08:00| 3.0|
+|1970-01-01T08:00:00.004+08:00| 1.0|
+|1970-01-01T08:00:00.005+08:00| 2.0|
+|1970-01-01T08:00:00.006+08:00| 3.0|
+|1970-01-01T08:00:00.007+08:00| 1.0|
+|1970-01-01T08:00:00.008+08:00| 2.0|
+|1970-01-01T08:00:00.009+08:00| 3.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select period(s1) from root.test.d3
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------+
+| Time|period(root.test.d3.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| 3|
++-----------------------------+-----------------------+
+```
+
+### QLB
+
+#### Usage
+
+This function is used to calculate Ljung-Box statistics $Q_{LB}$ for time series, and convert it to p value.
+
+**Name:** QLB
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters**:
+
+`lag`: max lag to calculate. Legal input shall be integer from 1 to n-2, where n is the sample number. Default value is n-2.
+
+**Output Series:** Output a single series. The type is DOUBLE. The output series is p value, and timestamp means lag.
+
+**Note:** If you want to calculate Ljung-Box statistics $Q_{LB}$ instead of p value, you may use ACF function.
+
+#### Examples
+
+##### Using Default Parameter
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T00:00:00.100+08:00| 1.22|
+|1970-01-01T00:00:00.200+08:00| -2.78|
+|1970-01-01T00:00:00.300+08:00| 1.53|
+|1970-01-01T00:00:00.400+08:00| 0.70|
+|1970-01-01T00:00:00.500+08:00| 0.75|
+|1970-01-01T00:00:00.600+08:00| -0.72|
+|1970-01-01T00:00:00.700+08:00| -0.22|
+|1970-01-01T00:00:00.800+08:00| 0.28|
+|1970-01-01T00:00:00.900+08:00| 0.57|
+|1970-01-01T00:00:01.000+08:00| -0.22|
+|1970-01-01T00:00:01.100+08:00| -0.72|
+|1970-01-01T00:00:01.200+08:00| 1.34|
+|1970-01-01T00:00:01.300+08:00| -0.25|
+|1970-01-01T00:00:01.400+08:00| 0.17|
+|1970-01-01T00:00:01.500+08:00| 2.51|
+|1970-01-01T00:00:01.600+08:00| 1.42|
+|1970-01-01T00:00:01.700+08:00| -1.34|
+|1970-01-01T00:00:01.800+08:00| -0.01|
+|1970-01-01T00:00:01.900+08:00| -0.49|
+|1970-01-01T00:00:02.000+08:00| 1.63|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select QLB(s1) from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+--------------------+
+| Time|QLB(root.test.d1.s1)|
++-----------------------------+--------------------+
+|1970-01-01T00:00:00.001+08:00| 0.2168702295315677|
+|1970-01-01T00:00:00.002+08:00| 0.3068948509261751|
+|1970-01-01T00:00:00.003+08:00| 0.4217859150918444|
+|1970-01-01T00:00:00.004+08:00| 0.5114539874276656|
+|1970-01-01T00:00:00.005+08:00| 0.6560619525616759|
+|1970-01-01T00:00:00.006+08:00| 0.7722398654053280|
+|1970-01-01T00:00:00.007+08:00| 0.8532491661465290|
+|1970-01-01T00:00:00.008+08:00| 0.9028575017542528|
+|1970-01-01T00:00:00.009+08:00| 0.9434989988192729|
+|1970-01-01T00:00:00.010+08:00| 0.8950280161464689|
+|1970-01-01T00:00:00.011+08:00| 0.7701048398839656|
+|1970-01-01T00:00:00.012+08:00| 0.7845536060001281|
+|1970-01-01T00:00:00.013+08:00| 0.5943030981705825|
+|1970-01-01T00:00:00.014+08:00| 0.4618413512531093|
+|1970-01-01T00:00:00.015+08:00| 0.2645948244673964|
+|1970-01-01T00:00:00.016+08:00| 0.3167530476666645|
+|1970-01-01T00:00:00.017+08:00| 0.2330010780351453|
+|1970-01-01T00:00:00.018+08:00| 0.0666611237622325|
++-----------------------------+--------------------+
+```
+
+### Resample
+
+#### Usage
+
+This function is used to resample the input series according to a given frequency,
+including up-sampling and down-sampling.
+Currently, the supported up-sampling methods are
+NaN (filling with `NaN`),
+FFill (filling with previous value),
+BFill (filling with next value) and
+Linear (filling with linear interpolation).
+Down-sampling relies on group aggregation,
+which supports Max, Min, First, Last, Mean and Median.
+
+**Name:** RESAMPLE
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
+
++ `every`: The frequency of resampling, which is a positive number with an unit. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. This parameter cannot be lacked.
++ `interp`: The interpolation method of up-sampling, which is 'NaN', 'FFill', 'BFill' or 'Linear'. By default, NaN is used.
++ `aggr`: The aggregation method of down-sampling, which is 'Max', 'Min', 'First', 'Last', 'Mean' or 'Median'. By default, Mean is used.
++ `start`: The start time (inclusive) of resampling with the format 'yyyy-MM-dd HH:mm:ss'. By default, it is the timestamp of the first valid data point.
++ `end`: The end time (exclusive) of resampling with the format 'yyyy-MM-dd HH:mm:ss'. By default, it is the timestamp of the last valid data point.
+
+**Output Series:** Output a single series. The type is DOUBLE. It is strictly equispaced with the frequency `every`.
+
+**Note:** `NaN` in the input series will be ignored.
+
+#### Examples
+
+##### Up-sampling
+
+When the frequency of resampling is higher than the original frequency, up-sampling starts.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2021-03-06T16:00:00.000+08:00| 3.09|
+|2021-03-06T16:15:00.000+08:00| 3.53|
+|2021-03-06T16:30:00.000+08:00| 3.5|
+|2021-03-06T16:45:00.000+08:00| 3.51|
+|2021-03-06T17:00:00.000+08:00| 3.41|
++-----------------------------+---------------+
+```
+
+
+SQL for query:
+
+```sql
+select resample(s1,'every'='5m','interp'='linear') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+----------------------------------------------------------+
+| Time|resample(root.test.d1.s1, "every"="5m", "interp"="linear")|
++-----------------------------+----------------------------------------------------------+
+|2021-03-06T16:00:00.000+08:00| 3.0899999141693115|
+|2021-03-06T16:05:00.000+08:00| 3.2366665999094644|
+|2021-03-06T16:10:00.000+08:00| 3.3833332856496177|
+|2021-03-06T16:15:00.000+08:00| 3.5299999713897705|
+|2021-03-06T16:20:00.000+08:00| 3.5199999809265137|
+|2021-03-06T16:25:00.000+08:00| 3.509999990463257|
+|2021-03-06T16:30:00.000+08:00| 3.5|
+|2021-03-06T16:35:00.000+08:00| 3.503333330154419|
+|2021-03-06T16:40:00.000+08:00| 3.506666660308838|
+|2021-03-06T16:45:00.000+08:00| 3.509999990463257|
+|2021-03-06T16:50:00.000+08:00| 3.4766666889190674|
+|2021-03-06T16:55:00.000+08:00| 3.443333387374878|
+|2021-03-06T17:00:00.000+08:00| 3.4100000858306885|
++-----------------------------+----------------------------------------------------------+
+```
+
+##### Down-sampling
+
+When the frequency of resampling is lower than the original frequency, down-sampling starts.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select resample(s1,'every'='30m','aggr'='first') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+--------------------------------------------------------+
+| Time|resample(root.test.d1.s1, "every"="30m", "aggr"="first")|
++-----------------------------+--------------------------------------------------------+
+|2021-03-06T16:00:00.000+08:00| 3.0899999141693115|
+|2021-03-06T16:30:00.000+08:00| 3.5|
+|2021-03-06T17:00:00.000+08:00| 3.4100000858306885|
++-----------------------------+--------------------------------------------------------+
+```
+
+
+
+##### Specify the time period
+
+The time period of resampling can be specified with `start` and `end`.
+The period outside the actual time range will be interpolated.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select resample(s1,'every'='30m','start'='2021-03-06 15:00:00') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------------------------------------------------------+
+| Time|resample(root.test.d1.s1, "every"="30m", "start"="2021-03-06 15:00:00")|
++-----------------------------+-----------------------------------------------------------------------+
+|2021-03-06T15:00:00.000+08:00| NaN|
+|2021-03-06T15:30:00.000+08:00| NaN|
+|2021-03-06T16:00:00.000+08:00| 3.309999942779541|
+|2021-03-06T16:30:00.000+08:00| 3.5049999952316284|
+|2021-03-06T17:00:00.000+08:00| 3.4100000858306885|
++-----------------------------+-----------------------------------------------------------------------+
+```
+
+### Sample
+
+#### Usage
+
+This function is used to sample the input series,
+that is, select a specified number of data points from the input series and output them.
+Currently, two sampling methods are supported:
+**Reservoir sampling** randomly selects data points.
+All of the points have the same probability of being sampled.
+**Isometric sampling** selects data points at equal index intervals.
+
+
+**Name:** SAMPLE
+
+**Input Series:** Only support a single input series. The type is arbitrary.
+
+**Parameters:**
+
++ `method`: The method of sampling, which is 'reservoir' or 'isometric'. By default, reservoir sampling is used.
++ `k`: The number of sampling, which is a positive integer. By default, it's 1.
+
+**Output Series:** Output a single series. The type is the same as the input. The length of the output series is `k`. Each data point in the output series comes from the input series.
+
+**Note:** If `k` is greater than the length of input series, all data points in the input series will be output.
+
+#### Examples
+
+##### Reservoir Sampling
+
+When `method` is 'reservoir' or the default, reservoir sampling is used.
+Due to the randomness of this method, the output series shown below is only a possible result.
+
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:01.000+08:00| 1.0|
+|2020-01-01T00:00:02.000+08:00| 2.0|
+|2020-01-01T00:00:03.000+08:00| 3.0|
+|2020-01-01T00:00:04.000+08:00| 4.0|
+|2020-01-01T00:00:05.000+08:00| 5.0|
+|2020-01-01T00:00:06.000+08:00| 6.0|
+|2020-01-01T00:00:07.000+08:00| 7.0|
+|2020-01-01T00:00:08.000+08:00| 8.0|
+|2020-01-01T00:00:09.000+08:00| 9.0|
+|2020-01-01T00:00:10.000+08:00| 10.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select sample(s1,'method'='reservoir','k'='5') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|sample(root.test.d1.s1, "method"="reservoir", "k"="5")|
++-----------------------------+------------------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 2.0|
+|2020-01-01T00:00:03.000+08:00| 3.0|
+|2020-01-01T00:00:05.000+08:00| 5.0|
+|2020-01-01T00:00:08.000+08:00| 8.0|
+|2020-01-01T00:00:10.000+08:00| 10.0|
++-----------------------------+------------------------------------------------------+
+```
+
+##### Isometric Sampling
+
+When `method` is 'isometric', isometric sampling is used.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select sample(s1,'method'='isometric','k'='5') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|sample(root.test.d1.s1, "method"="isometric", "k"="5")|
++-----------------------------+------------------------------------------------------+
+|2020-01-01T00:00:01.000+08:00| 1.0|
+|2020-01-01T00:00:03.000+08:00| 3.0|
+|2020-01-01T00:00:05.000+08:00| 5.0|
+|2020-01-01T00:00:07.000+08:00| 7.0|
+|2020-01-01T00:00:09.000+08:00| 9.0|
++-----------------------------+------------------------------------------------------+
+```
+
+### Segment
+
+#### Usage
+
+This function is used to segment a time series into subsequences according to linear trend, and returns linear fitted values of first values in each subsequence or every data point.
+
+**Name:** SEGMENT
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `output` :"all" to output all fitted points; "first" to output first fitted points in each subsequence.
+
++ `error`: error allowed at linear regression. It is defined as mean absolute error of a subsequence.
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+**Note:** This function treat input series as equal-interval sampled. All data are loaded, so downsample input series first if there are too many data points.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 5.0|
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 1.0|
+|1970-01-01T08:00:00.300+08:00| 2.0|
+|1970-01-01T08:00:00.400+08:00| 3.0|
+|1970-01-01T08:00:00.500+08:00| 4.0|
+|1970-01-01T08:00:00.600+08:00| 5.0|
+|1970-01-01T08:00:00.700+08:00| 6.0|
+|1970-01-01T08:00:00.800+08:00| 7.0|
+|1970-01-01T08:00:00.900+08:00| 8.0|
+|1970-01-01T08:00:01.000+08:00| 9.0|
+|1970-01-01T08:00:01.100+08:00| 9.1|
+|1970-01-01T08:00:01.200+08:00| 9.2|
+|1970-01-01T08:00:01.300+08:00| 9.3|
+|1970-01-01T08:00:01.400+08:00| 9.4|
+|1970-01-01T08:00:01.500+08:00| 9.5|
+|1970-01-01T08:00:01.600+08:00| 9.6|
+|1970-01-01T08:00:01.700+08:00| 9.7|
+|1970-01-01T08:00:01.800+08:00| 9.8|
+|1970-01-01T08:00:01.900+08:00| 9.9|
+|1970-01-01T08:00:02.000+08:00| 10.0|
+|1970-01-01T08:00:02.100+08:00| 8.0|
+|1970-01-01T08:00:02.200+08:00| 6.0|
+|1970-01-01T08:00:02.300+08:00| 4.0|
+|1970-01-01T08:00:02.400+08:00| 2.0|
+|1970-01-01T08:00:02.500+08:00| 0.0|
+|1970-01-01T08:00:02.600+08:00| -2.0|
+|1970-01-01T08:00:02.700+08:00| -4.0|
+|1970-01-01T08:00:02.800+08:00| -6.0|
+|1970-01-01T08:00:02.900+08:00| -8.0|
+|1970-01-01T08:00:03.000+08:00| -10.0|
+|1970-01-01T08:00:03.100+08:00| 10.0|
+|1970-01-01T08:00:03.200+08:00| 10.0|
+|1970-01-01T08:00:03.300+08:00| 10.0|
+|1970-01-01T08:00:03.400+08:00| 10.0|
+|1970-01-01T08:00:03.500+08:00| 10.0|
+|1970-01-01T08:00:03.600+08:00| 10.0|
+|1970-01-01T08:00:03.700+08:00| 10.0|
+|1970-01-01T08:00:03.800+08:00| 10.0|
+|1970-01-01T08:00:03.900+08:00| 10.0|
++-----------------------------+------------+
+```
+
+SQL for query:
+
+```sql
+select segment(s1, "error"="0.1") from root.test
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------+
+| Time|segment(root.test.s1, "error"="0.1")|
++-----------------------------+------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 5.0|
+|1970-01-01T08:00:00.200+08:00| 1.0|
+|1970-01-01T08:00:01.000+08:00| 9.0|
+|1970-01-01T08:00:02.000+08:00| 10.0|
+|1970-01-01T08:00:03.000+08:00| -10.0|
+|1970-01-01T08:00:03.200+08:00| 10.0|
++-----------------------------+------------------------------------+
+```
+
+### Skew
+
+#### Usage
+
+This function is used to calculate the population skewness.
+
+**Name:** SKEW
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**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 population skewness.
+
+**Note:** Missing points, null points and `NaN` in the input series will be ignored.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0|
+|2020-01-01T00:00:01.000+08:00| 2.0|
+|2020-01-01T00:00:02.000+08:00| 3.0|
+|2020-01-01T00:00:03.000+08:00| 4.0|
+|2020-01-01T00:00:04.000+08:00| 5.0|
+|2020-01-01T00:00:05.000+08:00| 6.0|
+|2020-01-01T00:00:06.000+08:00| 7.0|
+|2020-01-01T00:00:07.000+08:00| 8.0|
+|2020-01-01T00:00:08.000+08:00| 9.0|
+|2020-01-01T00:00:09.000+08:00| 10.0|
+|2020-01-01T00:00:10.000+08:00| 10.0|
+|2020-01-01T00:00:11.000+08:00| 10.0|
+|2020-01-01T00:00:12.000+08:00| 10.0|
+|2020-01-01T00:00:13.000+08:00| 10.0|
+|2020-01-01T00:00:14.000+08:00| 10.0|
+|2020-01-01T00:00:15.000+08:00| 10.0|
+|2020-01-01T00:00:16.000+08:00| 10.0|
+|2020-01-01T00:00:17.000+08:00| 10.0|
+|2020-01-01T00:00:18.000+08:00| 10.0|
+|2020-01-01T00:00:19.000+08:00| 10.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select skew(s1) from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------+
+| Time| skew(root.test.d1.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| -0.9998427402292644|
++-----------------------------+-----------------------+
+```
+
+### Spline
+
+#### Usage
+
+This function is used to calculate cubic spline interpolation of input series.
+
+**Name:** SPLINE
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `points`: Number of resampling points.
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+**Note**: Output series retains the first and last timestamps of input series. Interpolation points are selected at equal intervals. The function tries to calculate only when there are no less than 4 points in input series.
+
+#### Examples
+
+##### Assigning number of interpolation points
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.2|
+|1970-01-01T08:00:00.500+08:00| 1.7|
+|1970-01-01T08:00:00.700+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 2.1|
+|1970-01-01T08:00:01.100+08:00| 2.0|
+|1970-01-01T08:00:01.200+08:00| 1.8|
+|1970-01-01T08:00:01.300+08:00| 1.2|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 1.6|
++-----------------------------+------------+
+```
+
+SQL for query:
+
+```sql
+select spline(s1, "points"="151") from root.test
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------+
+| Time|spline(root.test.s1, "points"="151")|
++-----------------------------+------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.010+08:00| 0.04870000251134237|
+|1970-01-01T08:00:00.020+08:00| 0.09680000495910646|
+|1970-01-01T08:00:00.030+08:00| 0.14430000734329226|
+|1970-01-01T08:00:00.040+08:00| 0.19120000966389972|
+|1970-01-01T08:00:00.050+08:00| 0.23750001192092896|
+|1970-01-01T08:00:00.060+08:00| 0.2832000141143799|
+|1970-01-01T08:00:00.070+08:00| 0.32830001624425253|
+|1970-01-01T08:00:00.080+08:00| 0.3728000183105469|
+|1970-01-01T08:00:00.090+08:00| 0.416700020313263|
+|1970-01-01T08:00:00.100+08:00| 0.4600000222524008|
+|1970-01-01T08:00:00.110+08:00| 0.5027000241279602|
+|1970-01-01T08:00:00.120+08:00| 0.5448000259399414|
+|1970-01-01T08:00:00.130+08:00| 0.5863000276883443|
+|1970-01-01T08:00:00.140+08:00| 0.627200029373169|
+|1970-01-01T08:00:00.150+08:00| 0.6675000309944153|
+|1970-01-01T08:00:00.160+08:00| 0.7072000325520833|
+|1970-01-01T08:00:00.170+08:00| 0.7463000340461731|
+|1970-01-01T08:00:00.180+08:00| 0.7848000354766846|
+|1970-01-01T08:00:00.190+08:00| 0.8227000368436178|
+|1970-01-01T08:00:00.200+08:00| 0.8600000381469728|
+|1970-01-01T08:00:00.210+08:00| 0.8967000393867494|
+|1970-01-01T08:00:00.220+08:00| 0.9328000405629477|
+|1970-01-01T08:00:00.230+08:00| 0.9683000416755676|
+|1970-01-01T08:00:00.240+08:00| 1.0032000427246095|
+|1970-01-01T08:00:00.250+08:00| 1.037500043710073|
+|1970-01-01T08:00:00.260+08:00| 1.071200044631958|
+|1970-01-01T08:00:00.270+08:00| 1.1043000454902647|
+|1970-01-01T08:00:00.280+08:00| 1.1368000462849934|
+|1970-01-01T08:00:00.290+08:00| 1.1687000470161437|
+|1970-01-01T08:00:00.300+08:00| 1.2000000476837158|
+|1970-01-01T08:00:00.310+08:00| 1.2307000483103594|
+|1970-01-01T08:00:00.320+08:00| 1.2608000489139557|
+|1970-01-01T08:00:00.330+08:00| 1.2903000494873524|
+|1970-01-01T08:00:00.340+08:00| 1.3192000500233967|
+|1970-01-01T08:00:00.350+08:00| 1.3475000505149364|
+|1970-01-01T08:00:00.360+08:00| 1.3752000509548186|
+|1970-01-01T08:00:00.370+08:00| 1.402300051335891|
+|1970-01-01T08:00:00.380+08:00| 1.4288000516510009|
+|1970-01-01T08:00:00.390+08:00| 1.4547000518929958|
+|1970-01-01T08:00:00.400+08:00| 1.480000052054723|
+|1970-01-01T08:00:00.410+08:00| 1.5047000521290301|
+|1970-01-01T08:00:00.420+08:00| 1.5288000521087646|
+|1970-01-01T08:00:00.430+08:00| 1.5523000519867738|
+|1970-01-01T08:00:00.440+08:00| 1.575200051755905|
+|1970-01-01T08:00:00.450+08:00| 1.597500051409006|
+|1970-01-01T08:00:00.460+08:00| 1.619200050938924|
+|1970-01-01T08:00:00.470+08:00| 1.6403000503385066|
+|1970-01-01T08:00:00.480+08:00| 1.660800049600601|
+|1970-01-01T08:00:00.490+08:00| 1.680700048718055|
+|1970-01-01T08:00:00.500+08:00| 1.7000000476837158|
+|1970-01-01T08:00:00.510+08:00| 1.7188475466453037|
+|1970-01-01T08:00:00.520+08:00| 1.7373800457262996|
+|1970-01-01T08:00:00.530+08:00| 1.7555825448831923|
+|1970-01-01T08:00:00.540+08:00| 1.7734400440724702|
+|1970-01-01T08:00:00.550+08:00| 1.790937543250622|
+|1970-01-01T08:00:00.560+08:00| 1.8080600423741364|
+|1970-01-01T08:00:00.570+08:00| 1.8247925413995016|
+|1970-01-01T08:00:00.580+08:00| 1.8411200402832066|
+|1970-01-01T08:00:00.590+08:00| 1.8570275389817397|
+|1970-01-01T08:00:00.600+08:00| 1.8725000374515897|
+|1970-01-01T08:00:00.610+08:00| 1.8875225356492449|
+|1970-01-01T08:00:00.620+08:00| 1.902080033531194|
+|1970-01-01T08:00:00.630+08:00| 1.9161575310539258|
+|1970-01-01T08:00:00.640+08:00| 1.9297400281739288|
+|1970-01-01T08:00:00.650+08:00| 1.9428125248476913|
+|1970-01-01T08:00:00.660+08:00| 1.9553600210317021|
+|1970-01-01T08:00:00.670+08:00| 1.96736751668245|
+|1970-01-01T08:00:00.680+08:00| 1.9788200117564232|
+|1970-01-01T08:00:00.690+08:00| 1.9897025062101101|
+|1970-01-01T08:00:00.700+08:00| 2.0|
+|1970-01-01T08:00:00.710+08:00| 2.0097024933913334|
+|1970-01-01T08:00:00.720+08:00| 2.0188199867081615|
+|1970-01-01T08:00:00.730+08:00| 2.027367479995188|
+|1970-01-01T08:00:00.740+08:00| 2.0353599732971155|
+|1970-01-01T08:00:00.750+08:00| 2.0428124666586482|
+|1970-01-01T08:00:00.760+08:00| 2.049739960124489|
+|1970-01-01T08:00:00.770+08:00| 2.056157453739342|
+|1970-01-01T08:00:00.780+08:00| 2.06207994754791|
+|1970-01-01T08:00:00.790+08:00| 2.067522441594897|
+|1970-01-01T08:00:00.800+08:00| 2.072499935925006|
+|1970-01-01T08:00:00.810+08:00| 2.07702743058294|
+|1970-01-01T08:00:00.820+08:00| 2.081119925613404|
+|1970-01-01T08:00:00.830+08:00| 2.0847924210611|
+|1970-01-01T08:00:00.840+08:00| 2.0880599169707317|
+|1970-01-01T08:00:00.850+08:00| 2.0909374133870027|
+|1970-01-01T08:00:00.860+08:00| 2.0934399103546166|
+|1970-01-01T08:00:00.870+08:00| 2.0955824079182768|
+|1970-01-01T08:00:00.880+08:00| 2.0973799061226863|
+|1970-01-01T08:00:00.890+08:00| 2.098847405012549|
+|1970-01-01T08:00:00.900+08:00| 2.0999999046325684|
+|1970-01-01T08:00:00.910+08:00| 2.1005574051201332|
+|1970-01-01T08:00:00.920+08:00| 2.1002599065303778|
+|1970-01-01T08:00:00.930+08:00| 2.0991524087846245|
+|1970-01-01T08:00:00.940+08:00| 2.0972799118041947|
+|1970-01-01T08:00:00.950+08:00| 2.0946874155104105|
+|1970-01-01T08:00:00.960+08:00| 2.0914199198245944|
+|1970-01-01T08:00:00.970+08:00| 2.0875224246680673|
+|1970-01-01T08:00:00.980+08:00| 2.083039929962151|
+|1970-01-01T08:00:00.990+08:00| 2.0780174356281687|
+|1970-01-01T08:00:01.000+08:00| 2.0724999415874406|
+|1970-01-01T08:00:01.010+08:00| 2.06653244776129|
+|1970-01-01T08:00:01.020+08:00| 2.060159954071038|
+|1970-01-01T08:00:01.030+08:00| 2.053427460438006|
+|1970-01-01T08:00:01.040+08:00| 2.046379966783517|
+|1970-01-01T08:00:01.050+08:00| 2.0390624730288924|
+|1970-01-01T08:00:01.060+08:00| 2.031519979095454|
+|1970-01-01T08:00:01.070+08:00| 2.0237974849045237|
+|1970-01-01T08:00:01.080+08:00| 2.015939990377423|
+|1970-01-01T08:00:01.090+08:00| 2.0079924954354746|
+|1970-01-01T08:00:01.100+08:00| 2.0|
+|1970-01-01T08:00:01.110+08:00| 1.9907018211101906|
+|1970-01-01T08:00:01.120+08:00| 1.9788509124245144|
+|1970-01-01T08:00:01.130+08:00| 1.9645127287932083|
+|1970-01-01T08:00:01.140+08:00| 1.9477527250665083|
+|1970-01-01T08:00:01.150+08:00| 1.9286363560946513|
+|1970-01-01T08:00:01.160+08:00| 1.9072290767278735|
+|1970-01-01T08:00:01.170+08:00| 1.8835963418164114|
+|1970-01-01T08:00:01.180+08:00| 1.8578036062105014|
+|1970-01-01T08:00:01.190+08:00| 1.8299163247603802|
+|1970-01-01T08:00:01.200+08:00| 1.7999999523162842|
+|1970-01-01T08:00:01.210+08:00| 1.7623635841923329|
+|1970-01-01T08:00:01.220+08:00| 1.7129696477516976|
+|1970-01-01T08:00:01.230+08:00| 1.6543635959181928|
+|1970-01-01T08:00:01.240+08:00| 1.5890908816156328|
+|1970-01-01T08:00:01.250+08:00| 1.5196969577678319|
+|1970-01-01T08:00:01.260+08:00| 1.4487272772986044|
+|1970-01-01T08:00:01.270+08:00| 1.3787272931317647|
+|1970-01-01T08:00:01.280+08:00| 1.3122424581911272|
+|1970-01-01T08:00:01.290+08:00| 1.251818225400506|
+|1970-01-01T08:00:01.300+08:00| 1.2000000476837158|
+|1970-01-01T08:00:01.310+08:00| 1.1548000470995912|
+|1970-01-01T08:00:01.320+08:00| 1.1130667107899999|
+|1970-01-01T08:00:01.330+08:00| 1.0756000393033045|
+|1970-01-01T08:00:01.340+08:00| 1.043200033187868|
+|1970-01-01T08:00:01.350+08:00| 1.016666692992053|
+|1970-01-01T08:00:01.360+08:00| 0.9968000192642223|
+|1970-01-01T08:00:01.370+08:00| 0.9844000125527389|
+|1970-01-01T08:00:01.380+08:00| 0.9802666734059655|
+|1970-01-01T08:00:01.390+08:00| 0.9852000023722649|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.410+08:00| 1.023999999165535|
+|1970-01-01T08:00:01.420+08:00| 1.0559999990463256|
+|1970-01-01T08:00:01.430+08:00| 1.0959999996423722|
+|1970-01-01T08:00:01.440+08:00| 1.1440000009536744|
+|1970-01-01T08:00:01.450+08:00| 1.2000000029802322|
+|1970-01-01T08:00:01.460+08:00| 1.264000005722046|
+|1970-01-01T08:00:01.470+08:00| 1.3360000091791153|
+|1970-01-01T08:00:01.480+08:00| 1.4160000133514405|
+|1970-01-01T08:00:01.490+08:00| 1.5040000182390214|
+|1970-01-01T08:00:01.500+08:00| 1.600000023841858|
++-----------------------------+------------------------------------+
+```
+
+### Spread
+
+#### Usage
+
+This function is used to calculate the spread of time series, that is, the maximum value minus the minimum value.
+
+**Name:** SPREAD
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Output Series:** Output a single series. The type is the same as the input. There is only one data point in the series, whose timestamp is 0 and value is the spread.
+
+**Note:** Missing points, null points and `NaN` in the input series will be ignored.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select spread(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------+
+| Time|spread(root.test.d1.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| 26.0|
++-----------------------------+-----------------------+
+```
+
+### Stddev
+
+#### Usage
+
+This function is used to calculate the population standard deviation.
+
+**Name:** STDDEV
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**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 population standard deviation.
+
+**Note:** Missing points, null points and `NaN` in the input series will be ignored.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0|
+|2020-01-01T00:00:01.000+08:00| 2.0|
+|2020-01-01T00:00:02.000+08:00| 3.0|
+|2020-01-01T00:00:03.000+08:00| 4.0|
+|2020-01-01T00:00:04.000+08:00| 5.0|
+|2020-01-01T00:00:05.000+08:00| 6.0|
+|2020-01-01T00:00:06.000+08:00| 7.0|
+|2020-01-01T00:00:07.000+08:00| 8.0|
+|2020-01-01T00:00:08.000+08:00| 9.0|
+|2020-01-01T00:00:09.000+08:00| 10.0|
+|2020-01-01T00:00:10.000+08:00| 11.0|
+|2020-01-01T00:00:11.000+08:00| 12.0|
+|2020-01-01T00:00:12.000+08:00| 13.0|
+|2020-01-01T00:00:13.000+08:00| 14.0|
+|2020-01-01T00:00:14.000+08:00| 15.0|
+|2020-01-01T00:00:15.000+08:00| 16.0|
+|2020-01-01T00:00:16.000+08:00| 17.0|
+|2020-01-01T00:00:17.000+08:00| 18.0|
+|2020-01-01T00:00:18.000+08:00| 19.0|
+|2020-01-01T00:00:19.000+08:00| 20.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select stddev(s1) from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------+
+| Time|stddev(root.test.d1.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| 5.7662812973353965|
++-----------------------------+-----------------------+
+```
+
+### ZScore
+
+#### Usage
+
+This function is used to standardize the input series with z-score.
+
+**Name:** ZSCORE
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `compute`: When set to "batch", anomaly test is conducted after importing all data points; when set to "stream", it is required to provide mean and standard deviation. The default method is "batch".
++ `avg`: Mean value when method is set to "stream".
++ `sd`: Standard deviation when method is set to "stream".
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+#### Examples
+
+##### Batch computing
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+SQL for query:
+
+```sql
+select zscore(s1) from root.test
+```
+
+Output series:
+
+```
++-----------------------------+--------------------+
+| Time|zscore(root.test.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.100+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.200+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.300+08:00| 0.20672455764868078|
+|1970-01-01T08:00:00.400+08:00| -0.6201736729460423|
+|1970-01-01T08:00:00.500+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.600+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.700+08:00| -1.033622788243404|
+|1970-01-01T08:00:00.800+08:00| 0.6201736729460423|
+|1970-01-01T08:00:00.900+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.000+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.100+08:00| 0.20672455764868078|
+|1970-01-01T08:00:01.200+08:00| -0.6201736729460423|
+|1970-01-01T08:00:01.300+08:00| -0.6201736729460423|
+|1970-01-01T08:00:01.400+08:00| 0.20672455764868078|
+|1970-01-01T08:00:01.500+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.600+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.700+08:00| 3.9277665953249348|
+|1970-01-01T08:00:01.800+08:00| 0.6201736729460423|
+|1970-01-01T08:00:01.900+08:00| -1.033622788243404|
+|1970-01-01T08:00:02.000+08:00|-0.20672455764868078|
++-----------------------------+--------------------+
+```
+
+
+
+## Data Quality
+
+### Completeness
+
+#### Usage
+
+This function is used to calculate the completeness of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the completeness of each window will be output.
+
+**Name:** COMPLETENESS
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
++ `downtime`: Whether the downtime exception is considered in the calculation of completeness. It is 'true' or 'false' (default). When considering the downtime exception, long-term missing data will be considered as downtime exception without any influence on completeness.
+
+**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
+
+**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
+
+#### Examples
+
+##### Default Parameters
+
+With default parameters, this function will regard all input data as the same window.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select completeness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------------+
+| Time|completeness(root.test.d1.s1)|
++-----------------------------+-----------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.875|
++-----------------------------+-----------------------------+
+```
+
+##### Specific Window Size
+
+When the window size is given, this function will divide the input data as multiple windows.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select completeness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+Output series:
+
+```
++-----------------------------+--------------------------------------------+
+| Time|completeness(root.test.d1.s1, "window"="15")|
++-----------------------------+--------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.875|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+--------------------------------------------+
+```
+
+### Consistency
+
+#### Usage
+
+This function is used to calculate the consistency of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the consistency of each window will be output.
+
+**Name:** CONSISTENCY
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
+
+**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
+
+**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
+
+#### Examples
+
+##### Default Parameters
+
+With default parameters, this function will regard all input data as the same window.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select consistency(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+Output series:
+
+```
++-----------------------------+----------------------------+
+| Time|consistency(root.test.d1.s1)|
++-----------------------------+----------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
++-----------------------------+----------------------------+
+```
+
+##### Specific Window Size
+
+When the window size is given, this function will divide the input data as multiple windows.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select consistency(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------------------------+
+| Time|consistency(root.test.d1.s1, "window"="15")|
++-----------------------------+-------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+-------------------------------------------+
+```
+
+### Timeliness
+
+#### Usage
+
+This function is used to calculate the timeliness of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the timeliness of each window will be output.
+
+**Name:** TIMELINESS
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
+
+**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
+
+**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
+
+#### Examples
+
+##### Default Parameters
+
+With default parameters, this function will regard all input data as the same window.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select timeliness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+Output series:
+
+```
++-----------------------------+---------------------------+
+| Time|timeliness(root.test.d1.s1)|
++-----------------------------+---------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
++-----------------------------+---------------------------+
+```
+
+##### Specific Window Size
+
+When the window size is given, this function will divide the input data as multiple windows.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select timeliness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------+
+| Time|timeliness(root.test.d1.s1, "window"="15")|
++-----------------------------+------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+------------------------------------------+
+```
+
+### Validity
+
+#### Usage
+
+This function is used to calculate the Validity of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the Validity of each window will be output.
+
+**Name:** VALIDITY
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
+
+**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
+
+**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
+
+#### Examples
+
+##### Default Parameters
+
+With default parameters, this function will regard all input data as the same window.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select Validity(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------+
+| Time|validity(root.test.d1.s1)|
++-----------------------------+-------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
++-----------------------------+-------------------------+
+```
+
+##### Specific Window Size
+
+When the window size is given, this function will divide the input data as multiple windows.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select Validity(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+Output series:
+
+```
++-----------------------------+----------------------------------------+
+| Time|validity(root.test.d1.s1, "window"="15")|
++-----------------------------+----------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+----------------------------------------+
+```
+
+
+
+## Data Repairing
+
+### TimestampRepair
+
+This function is used for timestamp repair.
+According to the given standard time interval,
+the method of minimizing the repair cost is adopted.
+By fine-tuning the timestamps,
+the original data with unstable timestamp interval is repaired to strictly equispaced data.
+If no standard time interval is given,
+this function will use the **median**, **mode** or **cluster** of the time interval to estimate the standard time interval.
+
+**Name:** TIMESTAMPREPAIR
+
+**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `interval`: The standard time interval whose unit is millisecond. It is a positive integer. By default, it will be estimated according to the given method.
++ `method`: The method to estimate the standard time interval, which is 'median', 'mode' or 'cluster'. This parameter is only valid when `interval` is not given. By default, median will be used.
+
+**Output Series:** Output a single series. The type is the same as the input. This series is the input after repairing.
+
+#### Examples
+
+##### Manually Specify the Standard Time Interval
+
+When `interval` is given, this function repairs according to the given standard time interval.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s1|
++-----------------------------+---------------+
+|2021-07-01T12:00:00.000+08:00| 1.0|
+|2021-07-01T12:00:10.000+08:00| 2.0|
+|2021-07-01T12:00:19.000+08:00| 3.0|
+|2021-07-01T12:00:30.000+08:00| 4.0|
+|2021-07-01T12:00:40.000+08:00| 5.0|
+|2021-07-01T12:00:50.000+08:00| 6.0|
+|2021-07-01T12:01:01.000+08:00| 7.0|
+|2021-07-01T12:01:11.000+08:00| 8.0|
+|2021-07-01T12:01:21.000+08:00| 9.0|
+|2021-07-01T12:01:31.000+08:00| 10.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select timestamprepair(s1,'interval'='10000') from root.test.d2
+```
+
+Output series:
+
+
+```
++-----------------------------+----------------------------------------------------+
+| Time|timestamprepair(root.test.d2.s1, "interval"="10000")|
++-----------------------------+----------------------------------------------------+
+|2021-07-01T12:00:00.000+08:00| 1.0|
+|2021-07-01T12:00:10.000+08:00| 2.0|
+|2021-07-01T12:00:20.000+08:00| 3.0|
+|2021-07-01T12:00:30.000+08:00| 4.0|
+|2021-07-01T12:00:40.000+08:00| 5.0|
+|2021-07-01T12:00:50.000+08:00| 6.0|
+|2021-07-01T12:01:00.000+08:00| 7.0|
+|2021-07-01T12:01:10.000+08:00| 8.0|
+|2021-07-01T12:01:20.000+08:00| 9.0|
+|2021-07-01T12:01:30.000+08:00| 10.0|
++-----------------------------+----------------------------------------------------+
+```
+
+##### Automatically Estimate the Standard Time Interval
+
+When `interval` is default, this function estimates the standard time interval.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select timestamprepair(s1) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+--------------------------------+
+| Time|timestamprepair(root.test.d2.s1)|
++-----------------------------+--------------------------------+
+|2021-07-01T12:00:00.000+08:00| 1.0|
+|2021-07-01T12:00:10.000+08:00| 2.0|
+|2021-07-01T12:00:20.000+08:00| 3.0|
+|2021-07-01T12:00:30.000+08:00| 4.0|
+|2021-07-01T12:00:40.000+08:00| 5.0|
+|2021-07-01T12:00:50.000+08:00| 6.0|
+|2021-07-01T12:01:00.000+08:00| 7.0|
+|2021-07-01T12:01:10.000+08:00| 8.0|
+|2021-07-01T12:01:20.000+08:00| 9.0|
+|2021-07-01T12:01:30.000+08:00| 10.0|
++-----------------------------+--------------------------------+
+```
+
+### ValueFill
+
+#### Usage
+
+This function is used to impute time series. Several methods are supported.
+
+**Name**: ValueFill
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `method`: {"mean", "previous", "linear", "likelihood", "AR", "MA", "SCREEN"}, default "linear".
+ Method to use for imputation in series. "mean": use global mean value to fill holes; "previous": propagate last valid observation forward to next valid. "linear": simplest interpolation method; "likelihood":Maximum likelihood estimation based on the normal distribution of speed; "AR": auto regression; "MA": moving average; "SCREEN": speed constraint.
+
+**Output Series:** Output a single series. The type is the same as the input. This series is the input after repairing.
+
+**Note:** AR method use AR(1) model. Input value should be auto-correlated, or the function would output a single point (0, 0.0).
+
+#### Examples
+
+##### Fill with linear
+
+When `method` is "linear" or the default, Screen method is used to impute.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| NaN|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| NaN|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| NaN|
+|2020-01-01T00:00:22.000+08:00| NaN|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select valuefill(s1) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------+
+| Time|valuefill(root.test.d2)|
++-----------------------------+-----------------------+
+|2020-01-01T00:00:02.000+08:00| NaN|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 108.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.7|
+|2020-01-01T00:00:22.000+08:00| 121.3|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+-----------------------+
+```
+
+##### Previous Fill
+
+When `method` is "previous", previous method is used.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select valuefill(s1,"method"="previous") from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------------------------+
+| Time|valuefill(root.test.d2,"method"="previous")|
++-----------------------------+-------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| NaN|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 110.5|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 116.0|
+|2020-01-01T00:00:22.000+08:00| 116.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+-------------------------------------------+
+```
+
+### ValueRepair
+
+#### Usage
+
+This function is used to repair the value of the time series.
+Currently, two methods are supported:
+**Screen** is a method based on speed threshold, which makes all speeds meet the threshold requirements under the premise of minimum changes;
+**LsGreedy** is a method based on speed change likelihood, which models speed changes as Gaussian distribution, and uses a greedy algorithm to maximize the likelihood.
+
+
+**Name:** VALUEREPAIR
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `method`: The method used to repair, which is 'Screen' or 'LsGreedy'. By default, Screen is used.
++ `minSpeed`: This parameter is only valid with Screen. It is the speed threshold. Speeds below it will be regarded as outliers. By default, it is the median minus 3 times of median absolute deviation.
++ `maxSpeed`: This parameter is only valid with Screen. It is the speed threshold. Speeds above it will be regarded as outliers. By default, it is the median plus 3 times of median absolute deviation.
++ `center`: This parameter is only valid with LsGreedy. It is the center of the Gaussian distribution of speed changes. By default, it is 0.
++ `sigma`: This parameter is only valid with LsGreedy. It is the standard deviation of the Gaussian distribution of speed changes. By default, it is the median absolute deviation.
+
+**Output Series:** Output a single series. The type is the same as the input. This series is the input after repairing.
+
+**Note:** `NaN` will be filled with linear interpolation before repairing.
+
+#### Examples
+
+##### Repair with Screen
+
+When `method` is 'Screen' or the default, Screen method is used.
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 100.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select valuerepair(s1) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+----------------------------+
+| Time|valuerepair(root.test.d2.s1)|
++-----------------------------+----------------------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 106.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+----------------------------+
+```
+
+##### Repair with LsGreedy
+
+When `method` is 'LsGreedy', LsGreedy method is used.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select valuerepair(s1,'method'='LsGreedy') from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------------------------------+
+| Time|valuerepair(root.test.d2.s1, "method"="LsGreedy")|
++-----------------------------+-------------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 106.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+-------------------------------------------------+
+```
+
+
+
+## Data Matching
+
+### Cov
+
+#### Usage
+
+This function is used to calculate the population covariance.
+
+**Name:** COV
+
+**Input Series:** Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.
+
+**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 population covariance.
+
+**Note:**
+
++ If a row contains missing points, null points or `NaN`, it will be ignored;
++ If all rows are ignored, `NaN` will be output.
+
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0| 101.0|
+|2020-01-01T00:00:03.000+08:00| 101.0| null|
+|2020-01-01T00:00:04.000+08:00| 102.0| 101.0|
+|2020-01-01T00:00:06.000+08:00| 104.0| 102.0|
+|2020-01-01T00:00:08.000+08:00| 126.0| 102.0|
+|2020-01-01T00:00:10.000+08:00| 108.0| 103.0|
+|2020-01-01T00:00:12.000+08:00| null| 103.0|
+|2020-01-01T00:00:14.000+08:00| 112.0| 104.0|
+|2020-01-01T00:00:15.000+08:00| 113.0| null|
+|2020-01-01T00:00:16.000+08:00| 114.0| 104.0|
+|2020-01-01T00:00:18.000+08:00| 116.0| 105.0|
+|2020-01-01T00:00:20.000+08:00| 118.0| 105.0|
+|2020-01-01T00:00:22.000+08:00| 100.0| 106.0|
+|2020-01-01T00:00:26.000+08:00| 124.0| 108.0|
+|2020-01-01T00:00:28.000+08:00| 126.0| 108.0|
+|2020-01-01T00:00:30.000+08:00| NaN| 108.0|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select cov(s1,s2) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------------------+
+| Time|cov(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 12.291666666666666|
++-----------------------------+-------------------------------------+
+```
+
+### DTW
+
+#### Usage
+
+This function is used to calculate the DTW distance between two input series.
+
+**Name:** DTW
+
+**Input Series:** Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.
+
+**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 DTW distance.
+
+**Note:**
+
++ If a row contains missing points, null points or `NaN`, it will be ignored;
++ If all rows are ignored, `0` will be output.
+
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.001+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.002+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.003+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.004+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.005+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.006+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.007+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.008+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.009+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.010+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.011+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.012+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.013+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.014+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.015+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.016+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.017+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.018+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.019+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.020+08:00| 1.0| 2.0|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select dtw(s1,s2) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------------------+
+| Time|dtw(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 20.0|
++-----------------------------+-------------------------------------+
+```
+
+### Pearson
+
+#### Usage
+
+This function is used to calculate the Pearson Correlation Coefficient.
+
+**Name:** PEARSON
+
+**Input Series:** Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.
+
+**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 Pearson Correlation Coefficient.
+
+**Note:**
+
++ If a row contains missing points, null points or `NaN`, it will be ignored;
++ If all rows are ignored, `NaN` will be output.
+
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0| 101.0|
+|2020-01-01T00:00:03.000+08:00| 101.0| null|
+|2020-01-01T00:00:04.000+08:00| 102.0| 101.0|
+|2020-01-01T00:00:06.000+08:00| 104.0| 102.0|
+|2020-01-01T00:00:08.000+08:00| 126.0| 102.0|
+|2020-01-01T00:00:10.000+08:00| 108.0| 103.0|
+|2020-01-01T00:00:12.000+08:00| null| 103.0|
+|2020-01-01T00:00:14.000+08:00| 112.0| 104.0|
+|2020-01-01T00:00:15.000+08:00| 113.0| null|
+|2020-01-01T00:00:16.000+08:00| 114.0| 104.0|
+|2020-01-01T00:00:18.000+08:00| 116.0| 105.0|
+|2020-01-01T00:00:20.000+08:00| 118.0| 105.0|
+|2020-01-01T00:00:22.000+08:00| 100.0| 106.0|
+|2020-01-01T00:00:26.000+08:00| 124.0| 108.0|
+|2020-01-01T00:00:28.000+08:00| 126.0| 108.0|
+|2020-01-01T00:00:30.000+08:00| NaN| 108.0|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select pearson(s1,s2) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------------------------+
+| Time|pearson(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+-----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.5630881927754872|
++-----------------------------+-----------------------------------------+
+```
+
+### PtnSym
+
+#### Usage
+
+This function is used to find all symmetric subseries in the input whose degree of symmetry is less than the threshold.
+The degree of symmetry is calculated by DTW.
+The smaller the degree, the more symmetrical the series is.
+
+**Name:** PATTERNSYMMETRIC
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE
+
+**Parameter:**
+
++ `window`: The length of the symmetric subseries. It's a positive integer and the default value is 10.
++ `threshold`: The threshold of the degree of symmetry. It's non-negative. Only the subseries whose degree of symmetry is below it will be output. By default, all subseries will be output.
+
+
+**Output Series:** Output a single series. The type is DOUBLE. Each data point in the output series corresponds to a symmetric subseries. The output timestamp is the starting timestamp of the subseries and the output value is the degree of symmetry.
+
+#### Example
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s4|
++-----------------------------+---------------+
+|2021-01-01T12:00:00.000+08:00| 1.0|
+|2021-01-01T12:00:01.000+08:00| 2.0|
+|2021-01-01T12:00:02.000+08:00| 3.0|
+|2021-01-01T12:00:03.000+08:00| 2.0|
+|2021-01-01T12:00:04.000+08:00| 1.0|
+|2021-01-01T12:00:05.000+08:00| 1.0|
+|2021-01-01T12:00:06.000+08:00| 1.0|
+|2021-01-01T12:00:07.000+08:00| 1.0|
+|2021-01-01T12:00:08.000+08:00| 2.0|
+|2021-01-01T12:00:09.000+08:00| 3.0|
+|2021-01-01T12:00:10.000+08:00| 2.0|
+|2021-01-01T12:00:11.000+08:00| 1.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select ptnsym(s4, 'window'='5', 'threshold'='0') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|ptnsym(root.test.d1.s4, "window"="5", "threshold"="0")|
++-----------------------------+------------------------------------------------------+
+|2021-01-01T12:00:00.000+08:00| 0.0|
+|2021-01-01T12:00:07.000+08:00| 0.0|
++-----------------------------+------------------------------------------------------+
+```
+
+### XCorr
+
+#### Usage
+
+This function is used to calculate the cross correlation function of given two time series.
+For discrete time series, cross correlation is given by
+$$CR(n) = \frac{1}{N} \sum_{m=1}^N S_1[m]S_2[m+n]$$
+which represent the similarities between two series with different index shifts.
+
+**Name:** XCORR
+
+**Input Series:** Only support two input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Output Series:** Output a single series with DOUBLE as datatype.
+There are $2N-1$ data points in the series, the center of which represents the cross correlation
+calculated with pre-aligned series(that is $CR(0)$ in the formula above),
+and the previous(or post) values represent those with shifting the latter series forward(or backward otherwise)
+until the two series are no longer overlapped(not included).
+In short, the values of output series are given by(index starts from 1)
+$$OS[i] = CR(-N+i) = \frac{1}{N} \sum_{m=1}^{i} S_1[m]S_2[N-i+m],\ if\ i <= N$$
+$$OS[i] = CR(i-N) = \frac{1}{N} \sum_{m=1}^{2N-i} S_1[i-N+m]S_2[m],\ if\ i > N$$
+
+**Note:**
+
++ `null` and `NaN` values in the input series will be ignored and treated as 0.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:01.000+08:00| null| 6|
+|2020-01-01T00:00:02.000+08:00| 2| 7|
+|2020-01-01T00:00:03.000+08:00| 3| NaN|
+|2020-01-01T00:00:04.000+08:00| 4| 9|
+|2020-01-01T00:00:05.000+08:00| 5| 10|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select xcorr(s1, s2) from root.test.d1 where time <= 2020-01-01 00:00:05
+```
+
+Output series:
+
+```
++-----------------------------+---------------------------------------+
+| Time|xcorr(root.test.d1.s1, root.test.d1.s2)|
++-----------------------------+---------------------------------------+
+|1970-01-01T08:00:00.001+08:00| 0.0|
+|1970-01-01T08:00:00.002+08:00| 4.0|
+|1970-01-01T08:00:00.003+08:00| 9.6|
+|1970-01-01T08:00:00.004+08:00| 13.4|
+|1970-01-01T08:00:00.005+08:00| 20.0|
+|1970-01-01T08:00:00.006+08:00| 15.6|
+|1970-01-01T08:00:00.007+08:00| 9.2|
+|1970-01-01T08:00:00.008+08:00| 11.8|
+|1970-01-01T08:00:00.009+08:00| 6.0|
++-----------------------------+---------------------------------------+
+```
+
+
+
+## Anomaly Detection
+
+### IQR
+
+#### Usage
+
+This function is used to detect anomalies based on IQR. Points distributing beyond 1.5 times IQR are selected.
+
+**Name:** IQR
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `method`: When set to "batch", anomaly test is conducted after importing all data points; when set to "stream", it is required to provide upper and lower quantiles. The default method is "batch".
++ `q1`: The lower quantile when method is set to "stream".
++ `q3`: The upper quantile when method is set to "stream".
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+**Note:** $IQR=Q_3-Q_1$
+
+#### Examples
+
+##### Batch computing
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+SQL for query:
+
+```sql
+select iqr(s1) from root.test
+```
+
+Output series:
+
+```
++-----------------------------+-----------------+
+| Time|iqr(root.test.s1)|
++-----------------------------+-----------------+
+|1970-01-01T08:00:01.700+08:00| 10.0|
++-----------------------------+-----------------+
+```
+
+### KSigma
+
+#### Usage
+
+This function is used to detect anomalies based on the Dynamic K-Sigma Algorithm.
+Within a sliding window, the input value with a deviation of more than k times the standard deviation from the average will be output as anomaly.
+
+**Name:** KSIGMA
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `k`: How many times to multiply on standard deviation to define anomaly, the default value is 3.
++ `window`: The window size of Dynamic K-Sigma Algorithm, the default value is 10000.
+
+**Output Series:** Output a single series. The type is same as input series.
+
+**Note:** Only when is larger than 0, the anomaly detection will be performed. Otherwise, nothing will be output.
+
+#### Examples
+
+##### Assigning k
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 0.0|
+|2020-01-01T00:00:03.000+08:00| 50.0|
+|2020-01-01T00:00:04.000+08:00| 100.0|
+|2020-01-01T00:00:06.000+08:00| 150.0|
+|2020-01-01T00:00:08.000+08:00| 200.0|
+|2020-01-01T00:00:10.000+08:00| 200.0|
+|2020-01-01T00:00:14.000+08:00| 200.0|
+|2020-01-01T00:00:15.000+08:00| 200.0|
+|2020-01-01T00:00:16.000+08:00| 200.0|
+|2020-01-01T00:00:18.000+08:00| 200.0|
+|2020-01-01T00:00:20.000+08:00| 150.0|
+|2020-01-01T00:00:22.000+08:00| 100.0|
+|2020-01-01T00:00:26.000+08:00| 50.0|
+|2020-01-01T00:00:28.000+08:00| 0.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select ksigma(s1,"k"="1.0") from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+Output series:
+
+```
++-----------------------------+---------------------------------+
+|Time |ksigma(root.test.d1.s1,"k"="3.0")|
++-----------------------------+---------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.0|
+|2020-01-01T00:00:03.000+08:00| 50.0|
+|2020-01-01T00:00:26.000+08:00| 50.0|
+|2020-01-01T00:00:28.000+08:00| 0.0|
++-----------------------------+---------------------------------+
+```
+
+### LOF
+
+#### Usage
+
+This function is used to detect density anomaly of time series. According to k-th distance calculation parameter and local outlier factor (lof) threshold, the function judges if a set of input values is an density anomaly, and a bool mark of anomaly values will be output.
+
+**Name:** LOF
+
+**Input Series:** Multiple input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `method`:assign a detection method. The default value is "default", when input data has multiple dimensions. The alternative is "series", when a input series will be transformed to high dimension.
++ `k`:use the k-th distance to calculate lof. Default value is 3.
++ `window`: size of window to split origin data points. Default value is 10000.
++ `windowsize`:dimension that will be transformed into when method is "series". The default value is 5.
+
+**Output Series:** Output a single series. The type is DOUBLE.
+
+**Note:** Incomplete rows will be ignored. They are neither calculated nor marked as anomaly.
+
+#### Examples
+
+##### Using default parameters
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.100+08:00| 0.0| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0| 1.0|
+|1970-01-01T08:00:00.300+08:00| 1.0| 1.0|
+|1970-01-01T08:00:00.400+08:00| 1.0| 0.0|
+|1970-01-01T08:00:00.500+08:00| 0.0| -1.0|
+|1970-01-01T08:00:00.600+08:00| -1.0| -1.0|
+|1970-01-01T08:00:00.700+08:00| -1.0| 0.0|
+|1970-01-01T08:00:00.800+08:00| 2.0| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0| null|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select lof(s1,s2) from root.test.d1 where time<1000
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------------------+
+| Time|lof(root.test.d1.s1, root.test.d1.s2)|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.100+08:00| 3.8274824267668244|
+|1970-01-01T08:00:00.200+08:00| 3.0117631741126156|
+|1970-01-01T08:00:00.300+08:00| 2.838155437762879|
+|1970-01-01T08:00:00.400+08:00| 3.0117631741126156|
+|1970-01-01T08:00:00.500+08:00| 2.73518261244453|
+|1970-01-01T08:00:00.600+08:00| 2.371440975708148|
+|1970-01-01T08:00:00.700+08:00| 2.73518261244453|
+|1970-01-01T08:00:00.800+08:00| 1.7561416374270742|
++-----------------------------+-------------------------------------+
+```
+
+##### Diagnosing 1d timeseries
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.100+08:00| 1.0|
+|1970-01-01T08:00:00.200+08:00| 2.0|
+|1970-01-01T08:00:00.300+08:00| 3.0|
+|1970-01-01T08:00:00.400+08:00| 4.0|
+|1970-01-01T08:00:00.500+08:00| 5.0|
+|1970-01-01T08:00:00.600+08:00| 6.0|
+|1970-01-01T08:00:00.700+08:00| 7.0|
+|1970-01-01T08:00:00.800+08:00| 8.0|
+|1970-01-01T08:00:00.900+08:00| 9.0|
+|1970-01-01T08:00:01.000+08:00| 10.0|
+|1970-01-01T08:00:01.100+08:00| 11.0|
+|1970-01-01T08:00:01.200+08:00| 12.0|
+|1970-01-01T08:00:01.300+08:00| 13.0|
+|1970-01-01T08:00:01.400+08:00| 14.0|
+|1970-01-01T08:00:01.500+08:00| 15.0|
+|1970-01-01T08:00:01.600+08:00| 16.0|
+|1970-01-01T08:00:01.700+08:00| 17.0|
+|1970-01-01T08:00:01.800+08:00| 18.0|
+|1970-01-01T08:00:01.900+08:00| 19.0|
+|1970-01-01T08:00:02.000+08:00| 20.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select lof(s1, "method"="series") from root.test.d1 where time<1000
+```
+
+Output series:
+
+```
++-----------------------------+--------------------+
+| Time|lof(root.test.d1.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.100+08:00| 3.77777777777778|
+|1970-01-01T08:00:00.200+08:00| 4.32727272727273|
+|1970-01-01T08:00:00.300+08:00| 4.85714285714286|
+|1970-01-01T08:00:00.400+08:00| 5.40909090909091|
+|1970-01-01T08:00:00.500+08:00| 5.94999999999999|
+|1970-01-01T08:00:00.600+08:00| 6.43243243243243|
+|1970-01-01T08:00:00.700+08:00| 6.79999999999999|
+|1970-01-01T08:00:00.800+08:00| 7.0|
+|1970-01-01T08:00:00.900+08:00| 7.0|
+|1970-01-01T08:00:01.000+08:00| 6.79999999999999|
+|1970-01-01T08:00:01.100+08:00| 6.43243243243243|
+|1970-01-01T08:00:01.200+08:00| 5.94999999999999|
+|1970-01-01T08:00:01.300+08:00| 5.40909090909091|
+|1970-01-01T08:00:01.400+08:00| 4.85714285714286|
+|1970-01-01T08:00:01.500+08:00| 4.32727272727273|
+|1970-01-01T08:00:01.600+08:00| 3.77777777777778|
++-----------------------------+--------------------+
+```
+
+### MissDetect
+
+#### Usage
+
+This function is used to detect missing anomalies.
+In some datasets, missing values are filled by linear interpolation.
+Thus, there are several long perfect linear segments.
+By discovering these perfect linear segments,
+missing anomalies are detected.
+
+**Name:** MISSDETECT
+
+**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameter:**
+
+`error`: The minimum length of the detected missing anomalies, which is an integer greater than or equal to 10. By default, it is 10.
+
+**Output Series:** Output a single series. The type is BOOLEAN. Each data point which is miss anomaly will be labeled as true.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s2|
++-----------------------------+---------------+
+|2021-07-01T12:00:00.000+08:00| 0.0|
+|2021-07-01T12:00:01.000+08:00| 1.0|
+|2021-07-01T12:00:02.000+08:00| 0.0|
+|2021-07-01T12:00:03.000+08:00| 1.0|
+|2021-07-01T12:00:04.000+08:00| 0.0|
+|2021-07-01T12:00:05.000+08:00| 0.0|
+|2021-07-01T12:00:06.000+08:00| 0.0|
+|2021-07-01T12:00:07.000+08:00| 0.0|
+|2021-07-01T12:00:08.000+08:00| 0.0|
+|2021-07-01T12:00:09.000+08:00| 0.0|
+|2021-07-01T12:00:10.000+08:00| 0.0|
+|2021-07-01T12:00:11.000+08:00| 0.0|
+|2021-07-01T12:00:12.000+08:00| 0.0|
+|2021-07-01T12:00:13.000+08:00| 0.0|
+|2021-07-01T12:00:14.000+08:00| 0.0|
+|2021-07-01T12:00:15.000+08:00| 0.0|
+|2021-07-01T12:00:16.000+08:00| 1.0|
+|2021-07-01T12:00:17.000+08:00| 0.0|
+|2021-07-01T12:00:18.000+08:00| 1.0|
+|2021-07-01T12:00:19.000+08:00| 0.0|
+|2021-07-01T12:00:20.000+08:00| 1.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select missdetect(s2,'minlen'='10') from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------+
+| Time|missdetect(root.test.d2.s2, "minlen"="10")|
++-----------------------------+------------------------------------------+
+|2021-07-01T12:00:00.000+08:00| false|
+|2021-07-01T12:00:01.000+08:00| false|
+|2021-07-01T12:00:02.000+08:00| false|
+|2021-07-01T12:00:03.000+08:00| false|
+|2021-07-01T12:00:04.000+08:00| true|
+|2021-07-01T12:00:05.000+08:00| true|
+|2021-07-01T12:00:06.000+08:00| true|
+|2021-07-01T12:00:07.000+08:00| true|
+|2021-07-01T12:00:08.000+08:00| true|
+|2021-07-01T12:00:09.000+08:00| true|
+|2021-07-01T12:00:10.000+08:00| true|
+|2021-07-01T12:00:11.000+08:00| true|
+|2021-07-01T12:00:12.000+08:00| true|
+|2021-07-01T12:00:13.000+08:00| true|
+|2021-07-01T12:00:14.000+08:00| true|
+|2021-07-01T12:00:15.000+08:00| true|
+|2021-07-01T12:00:16.000+08:00| false|
+|2021-07-01T12:00:17.000+08:00| false|
+|2021-07-01T12:00:18.000+08:00| false|
+|2021-07-01T12:00:19.000+08:00| false|
+|2021-07-01T12:00:20.000+08:00| false|
++-----------------------------+------------------------------------------+
+```
+
+### Range
+
+#### Usage
+
+This function is used to detect range anomaly of time series. According to upper bound and lower bound parameters, the function judges if a input value is beyond range, aka range anomaly, and a new time series of anomaly will be output.
+
+**Name:** RANGE
+
+**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
++ `lower_bound`:lower bound of range anomaly detection.
++ `upper_bound`:upper bound of range anomaly detection.
+
+**Output Series:** Output a single series. The type is the same as the input.
+
+**Note:** Only when `upper_bound` is larger than `lower_bound`, the anomaly detection will be performed. Otherwise, nothing will be output.
+
+
+
+#### Examples
+
+##### Assigning Lower and Upper Bound
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
|2020-01-01T00:00:28.000+08:00| 126.0|
|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select range(s1,"lower_bound"="101.0","upper_bound"="125.0") from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------------------------------+
+|Time |range(root.test.d1.s1,"lower_bound"="101.0","upper_bound"="125.0")|
++-----------------------------+------------------------------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
++-----------------------------+------------------------------------------------------------------+
+```
+
+### TwoSidedFilter
+
+#### Usage
+
+The function is used to filter anomalies of a numeric time series based on two-sided window detection.
+
+**Name:** TWOSIDEDFILTER
+
+**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE
+
+**Output Series:** Output a single series. The type is the same as the input. It is the input without anomalies.
+
+**Parameter:**
+
+- `len`: The size of the window, which is a positive integer. By default, it's 5. When `len`=3, the algorithm detects forward window and backward window with length 3 and calculates the outlierness of the current point.
+
+- `threshold`: The threshold of outlierness, which is a floating number in (0,1). By default, it's 0.3. The strict standard of detecting anomalies is in proportion to the threshold.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 2002.0|
+|1970-01-01T08:00:01.000+08:00| 1946.0|
+|1970-01-01T08:00:02.000+08:00| 1958.0|
+|1970-01-01T08:00:03.000+08:00| 2012.0|
+|1970-01-01T08:00:04.000+08:00| 2051.0|
+|1970-01-01T08:00:05.000+08:00| 1898.0|
+|1970-01-01T08:00:06.000+08:00| 2014.0|
+|1970-01-01T08:00:07.000+08:00| 2052.0|
+|1970-01-01T08:00:08.000+08:00| 1935.0|
+|1970-01-01T08:00:09.000+08:00| 1901.0|
+|1970-01-01T08:00:10.000+08:00| 1972.0|
+|1970-01-01T08:00:11.000+08:00| 1969.0|
+|1970-01-01T08:00:12.000+08:00| 1984.0|
+|1970-01-01T08:00:13.000+08:00| 2018.0|
+|1970-01-01T08:00:37.000+08:00| 1484.0|
+|1970-01-01T08:00:38.000+08:00| 1055.0|
+|1970-01-01T08:00:39.000+08:00| 1050.0|
+|1970-01-01T08:01:05.000+08:00| 1023.0|
+|1970-01-01T08:01:06.000+08:00| 1056.0|
+|1970-01-01T08:01:07.000+08:00| 978.0|
+|1970-01-01T08:01:08.000+08:00| 1050.0|
+|1970-01-01T08:01:09.000+08:00| 1123.0|
+|1970-01-01T08:01:10.000+08:00| 1150.0|
+|1970-01-01T08:01:11.000+08:00| 1034.0|
+|1970-01-01T08:01:12.000+08:00| 950.0|
+|1970-01-01T08:01:13.000+08:00| 1059.0|
++-----------------------------+------------+
+```
+
+SQL for query:
+
+```sql
+select TwoSidedFilter(s0, 'len'='5', 'threshold'='0.3') from root.test
+```
+
+Output series:
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 2002.0|
+|1970-01-01T08:00:01.000+08:00| 1946.0|
+|1970-01-01T08:00:02.000+08:00| 1958.0|
+|1970-01-01T08:00:03.000+08:00| 2012.0|
+|1970-01-01T08:00:04.000+08:00| 2051.0|
+|1970-01-01T08:00:05.000+08:00| 1898.0|
+|1970-01-01T08:00:06.000+08:00| 2014.0|
+|1970-01-01T08:00:07.000+08:00| 2052.0|
+|1970-01-01T08:00:08.000+08:00| 1935.0|
+|1970-01-01T08:00:09.000+08:00| 1901.0|
+|1970-01-01T08:00:10.000+08:00| 1972.0|
+|1970-01-01T08:00:11.000+08:00| 1969.0|
+|1970-01-01T08:00:12.000+08:00| 1984.0|
+|1970-01-01T08:00:13.000+08:00| 2018.0|
+|1970-01-01T08:01:05.000+08:00| 1023.0|
+|1970-01-01T08:01:06.000+08:00| 1056.0|
+|1970-01-01T08:01:07.000+08:00| 978.0|
+|1970-01-01T08:01:08.000+08:00| 1050.0|
+|1970-01-01T08:01:09.000+08:00| 1123.0|
+|1970-01-01T08:01:10.000+08:00| 1150.0|
+|1970-01-01T08:01:11.000+08:00| 1034.0|
+|1970-01-01T08:01:12.000+08:00| 950.0|
+|1970-01-01T08:01:13.000+08:00| 1059.0|
++-----------------------------+------------+
+```
+
+
+
+
+## Frequency Domain
+
+### Conv
+
+#### Usage
+
+This function is used to calculate the convolution, i.e. polynomial multiplication.
+
+**Name:** CONV
+
+**Input:** Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.
+
+**Output:** Output a single series. The type is DOUBLE. It is the result of convolution whose timestamps starting from 0 only indicate the order.
+
+**Note:** `NaN` in the input series will be ignored.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 1.0| 7.0|
+|1970-01-01T08:00:00.001+08:00| 0.0| 2.0|
+|1970-01-01T08:00:00.002+08:00| 1.0| null|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select conv(s1,s2) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+--------------------------------------+
+| Time|conv(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+--------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 7.0|
+|1970-01-01T08:00:00.001+08:00| 2.0|
+|1970-01-01T08:00:00.002+08:00| 7.0|
+|1970-01-01T08:00:00.003+08:00| 2.0|
++-----------------------------+--------------------------------------+
+```
+
+### Deconv
+
+#### Usage
+
+This function is used to calculate the deconvolution, i.e. polynomial division.
+
+**Name:** DECONV
+
+**Input:** Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `result`: The result of deconvolution, which is 'quotient' or 'remainder'. By default, the quotient will be output.
+
+**Output:** Output a single series. The type is DOUBLE. It is the result of deconvolving the second series from the first series (dividing the first series by the second series) whose timestamps starting from 0 only indicate the order.
+
+**Note:** `NaN` in the input series will be ignored.
+
+#### Examples
+
+
+##### Calculate the quotient
+
+When `result` is 'quotient' or the default, this function calculates the quotient of the deconvolution.
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s3|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 8.0| 7.0|
+|1970-01-01T08:00:00.001+08:00| 2.0| 2.0|
+|1970-01-01T08:00:00.002+08:00| 7.0| null|
+|1970-01-01T08:00:00.003+08:00| 2.0| null|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select deconv(s3,s2) from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+----------------------------------------+
+| Time|deconv(root.test.d2.s3, root.test.d2.s2)|
++-----------------------------+----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.0|
+|1970-01-01T08:00:00.001+08:00| 0.0|
+|1970-01-01T08:00:00.002+08:00| 1.0|
++-----------------------------+----------------------------------------+
+```
+
+##### Calculate the remainder
+
+When `result` is 'remainder', this function calculates the remainder of the deconvolution.
+
+Input series is the same as above, the SQL for query is shown below:
+
+
+```sql
+select deconv(s3,s2,'result'='remainder') from root.test.d2
+```
+
+Output series:
+
+```
++-----------------------------+--------------------------------------------------------------+
+| Time|deconv(root.test.d2.s3, root.test.d2.s2, "result"="remainder")|
++-----------------------------+--------------------------------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.0|
+|1970-01-01T08:00:00.001+08:00| 0.0|
+|1970-01-01T08:00:00.002+08:00| 0.0|
+|1970-01-01T08:00:00.003+08:00| 0.0|
++-----------------------------+--------------------------------------------------------------+
+```
+
+### DWT
+
+#### Usage
+
+This function is used to calculate 1d discrete wavelet transform of a numerical series.
+
+**Name:** DWT
+
+**Input:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `method`: The type of wavelet. May select 'Haar', 'DB4', 'DB6', 'DB8', where DB means Daubechies. User may offer coefficients of wavelet transform and ignore this parameter. Case ignored.
++ `coef`: Coefficients of wavelet transform. When providing this parameter, use comma ',' to split them, and leave no spaces or other punctuations.
++ `layer`: Times to transform. The number of output vectors equals $layer+1$. Default is 1.
+
+**Output:** Output a single series. The type is DOUBLE. The length is the same as the input.
+
+**Note:** The length of input series must be an integer number power of 2.
+
+#### Examples
+
+
+##### Haar wavelet transform
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.100+08:00| 0.2|
+|1970-01-01T08:00:00.200+08:00| 1.5|
+|1970-01-01T08:00:00.300+08:00| 1.2|
+|1970-01-01T08:00:00.400+08:00| 0.6|
+|1970-01-01T08:00:00.500+08:00| 1.7|
+|1970-01-01T08:00:00.600+08:00| 0.8|
+|1970-01-01T08:00:00.700+08:00| 2.0|
+|1970-01-01T08:00:00.800+08:00| 2.5|
+|1970-01-01T08:00:00.900+08:00| 2.1|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 2.0|
+|1970-01-01T08:00:01.200+08:00| 1.8|
+|1970-01-01T08:00:01.300+08:00| 1.2|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 1.6|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select timeliness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select dwt(s1,"method"="haar") from root.test.d1
```
Output series:
```
-+-----------------------------+------------------------------------------+
-| Time|timeliness(root.test.d1.s1, "window"="15")|
-+-----------------------------+------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+------------------------------------------+
++-----------------------------+-------------------------------------+
+| Time|dwt(root.test.d1.s1, "method"="haar")|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.14142135834465192|
+|1970-01-01T08:00:00.100+08:00| 1.909188342921157|
+|1970-01-01T08:00:00.200+08:00| 1.6263456473052773|
+|1970-01-01T08:00:00.300+08:00| 1.9798989957517026|
+|1970-01-01T08:00:00.400+08:00| 3.252691126023161|
+|1970-01-01T08:00:00.500+08:00| 1.414213562373095|
+|1970-01-01T08:00:00.600+08:00| 2.1213203435596424|
+|1970-01-01T08:00:00.700+08:00| 1.8384776479437628|
+|1970-01-01T08:00:00.800+08:00| -0.14142135834465192|
+|1970-01-01T08:00:00.900+08:00| 0.21213200063848547|
+|1970-01-01T08:00:01.000+08:00| -0.7778174761639416|
+|1970-01-01T08:00:01.100+08:00| -0.8485281289944873|
+|1970-01-01T08:00:01.200+08:00| 0.2828427799095765|
+|1970-01-01T08:00:01.300+08:00| -1.414213562373095|
+|1970-01-01T08:00:01.400+08:00| 0.42426400127697095|
+|1970-01-01T08:00:01.500+08:00| -0.42426408557066786|
++-----------------------------+-------------------------------------+
```
-### Validity
+### FFT
#### Usage
-This function is used to calculate the Validity of time series. The input series are divided into several continuous and non overlapping windows. The timestamp of the first data point and the Validity of each window will be output.
-**Name:** VALIDITY
+This function is used to calculate the fast Fourier transform (FFT) of a numerical series.
-**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+**Name:** FFT
+
+**Input:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
**Parameters:**
-+ `window`: The size of each window. It is a positive integer or a positive number with an unit. The former is the number of data points in each window. The number of data points in the last window may be less than it. The latter is the time of the window. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, all input data belongs to the same window.
++ `method`: The type of FFT, which is 'uniform' (by default) or 'nonuniform'. If the value is 'uniform', the timestamps will be ignored and all data points will be regarded as equidistant. Thus, the equidistant fast Fourier transform algorithm will be applied. If the value is 'nonuniform' (TODO), the non-equidistant fast Fourier transform algorithm will be applied based on timestamps.
++ `result`: The result of FFT, which is 'real', 'imag', 'abs' or 'angle', corresponding to the real part, imaginary part, magnitude and phase angle. By default, the magnitude will be output.
++ `compress`: The parameter of compression, which is within (0,1]. It is the reserved energy ratio of lossy compression. By default, there is no compression.
-**Output Series:** Output a single series. The type is DOUBLE. The range of each value is [0,1].
-**Note:** Only when the number of data points in the window exceeds 10, the calculation will be performed. Otherwise, the window will be ignored and nothing will be output.
+**Output:** Output a single series. The type is DOUBLE. The length is the same as the input. The timestamps starting from 0 only indicate the order.
-#### Example: Default Parameters
+**Note:** `NaN` in the input series will be ignored.
-With default parameters, this function will regard all input data as the same window.
+#### Examples
+
+
+##### Uniform FFT
+
+With the default `type`, uniform FFT is applied.
Input series:
@@ -451,43 +3763,116 @@ Input series:
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|1970-01-01T08:00:00.000+08:00| 2.902113|
+|1970-01-01T08:00:01.000+08:00| 1.1755705|
+|1970-01-01T08:00:02.000+08:00| -2.1755705|
+|1970-01-01T08:00:03.000+08:00| -1.9021131|
+|1970-01-01T08:00:04.000+08:00| 1.0|
+|1970-01-01T08:00:05.000+08:00| 1.9021131|
+|1970-01-01T08:00:06.000+08:00| 0.1755705|
+|1970-01-01T08:00:07.000+08:00| -1.1755705|
+|1970-01-01T08:00:08.000+08:00| -0.902113|
+|1970-01-01T08:00:09.000+08:00| 0.0|
+|1970-01-01T08:00:10.000+08:00| 0.902113|
+|1970-01-01T08:00:11.000+08:00| 1.1755705|
+|1970-01-01T08:00:12.000+08:00| -0.1755705|
+|1970-01-01T08:00:13.000+08:00| -1.9021131|
+|1970-01-01T08:00:14.000+08:00| -1.0|
+|1970-01-01T08:00:15.000+08:00| 1.9021131|
+|1970-01-01T08:00:16.000+08:00| 2.1755705|
+|1970-01-01T08:00:17.000+08:00| -1.1755705|
+|1970-01-01T08:00:18.000+08:00| -2.902113|
+|1970-01-01T08:00:19.000+08:00| 0.0|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select Validity(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select fft(s1) from root.test.d1
```
Output series:
```
-+-----------------------------+-------------------------+
-| Time|validity(root.test.d1.s1)|
-+-----------------------------+-------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
-+-----------------------------+-------------------------+
++-----------------------------+----------------------+
+| Time| fft(root.test.d1.s1)|
++-----------------------------+----------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.001+08:00| 1.2727111142703152E-8|
+|1970-01-01T08:00:00.002+08:00| 2.385520799101839E-7|
+|1970-01-01T08:00:00.003+08:00| 8.723291723972645E-8|
+|1970-01-01T08:00:00.004+08:00| 19.999999960195904|
+|1970-01-01T08:00:00.005+08:00| 9.999999850988388|
+|1970-01-01T08:00:00.006+08:00| 3.2260694930700566E-7|
+|1970-01-01T08:00:00.007+08:00| 8.723291605373329E-8|
+|1970-01-01T08:00:00.008+08:00| 1.108657103979944E-7|
+|1970-01-01T08:00:00.009+08:00| 1.2727110997246171E-8|
+|1970-01-01T08:00:00.010+08:00|1.9852334701272664E-23|
+|1970-01-01T08:00:00.011+08:00| 1.2727111194499847E-8|
+|1970-01-01T08:00:00.012+08:00| 1.108657103979944E-7|
+|1970-01-01T08:00:00.013+08:00| 8.723291785769131E-8|
+|1970-01-01T08:00:00.014+08:00| 3.226069493070057E-7|
+|1970-01-01T08:00:00.015+08:00| 9.999999850988388|
+|1970-01-01T08:00:00.016+08:00| 19.999999960195904|
+|1970-01-01T08:00:00.017+08:00| 8.723291747109068E-8|
+|1970-01-01T08:00:00.018+08:00| 2.3855207991018386E-7|
+|1970-01-01T08:00:00.019+08:00| 1.2727112069910878E-8|
++-----------------------------+----------------------+
```
-#### Example: Specific Window Size
+Note: The input is $y=sin(2\pi t/4)+2sin(2\pi t/5)$ with a length of 20. Thus, there are peaks in $k=4$ and $k=5$ of the output.
-When the window size is given, this function will divide the input data as multiple windows.
+##### Uniform FFT with Compression
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select fft(s1, 'result'='real', 'compress'='0.99'), fft(s1, 'result'='imag','compress'='0.99') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+----------------------+----------------------+
+| Time| fft(root.test.d1.s1,| fft(root.test.d1.s1,|
+| | "result"="real",| "result"="imag",|
+| | "compress"="0.99")| "compress"="0.99")|
++-----------------------------+----------------------+----------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0| 0.0|
+|1970-01-01T08:00:00.001+08:00| -3.932894010461041E-9| 1.2104201863039066E-8|
+|1970-01-01T08:00:00.002+08:00|-1.4021739447490164E-7| 1.9299268669082926E-7|
+|1970-01-01T08:00:00.003+08:00| -7.057291240286645E-8| 5.127422242345858E-8|
+|1970-01-01T08:00:00.004+08:00| 19.021130288047125| -6.180339875198807|
+|1970-01-01T08:00:00.005+08:00| 9.999999850988388| 3.501852745067114E-16|
+|1970-01-01T08:00:00.019+08:00| -3.932894898639461E-9|-1.2104202549376264E-8|
++-----------------------------+----------------------+----------------------+
+```
+
+Note: Based on the conjugation of the Fourier transform result, only the first half of the compression result is reserved.
+According to the given parameter, data points are reserved from low frequency to high frequency until the reserved energy ratio exceeds it.
+The last data point is reserved to indicate the length of the series.
+
+### HighPass
+
+#### Usage
+
+This function performs low-pass filtering on the input series and extracts components above the cutoff frequency.
+The timestamps of input will be ignored and all data points will be regarded as equidistant.
+
+**Name:** HIGHPASS
+
+**Input:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `wpass`: The normalized cutoff frequency which values (0,1). This parameter cannot be lacked.
+
+**Output:** Output a single series. The type is DOUBLE. It is the input after filtering. The length and timestamps of output are the same as the input.
+
+**Note:** `NaN` in the input series will be ignored.
+
+#### Examples
Input series:
@@ -495,378 +3880,663 @@ Input series:
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
+|1970-01-01T08:00:00.000+08:00| 2.902113|
+|1970-01-01T08:00:01.000+08:00| 1.1755705|
+|1970-01-01T08:00:02.000+08:00| -2.1755705|
+|1970-01-01T08:00:03.000+08:00| -1.9021131|
+|1970-01-01T08:00:04.000+08:00| 1.0|
+|1970-01-01T08:00:05.000+08:00| 1.9021131|
+|1970-01-01T08:00:06.000+08:00| 0.1755705|
+|1970-01-01T08:00:07.000+08:00| -1.1755705|
+|1970-01-01T08:00:08.000+08:00| -0.902113|
+|1970-01-01T08:00:09.000+08:00| 0.0|
+|1970-01-01T08:00:10.000+08:00| 0.902113|
+|1970-01-01T08:00:11.000+08:00| 1.1755705|
+|1970-01-01T08:00:12.000+08:00| -0.1755705|
+|1970-01-01T08:00:13.000+08:00| -1.9021131|
+|1970-01-01T08:00:14.000+08:00| -1.0|
+|1970-01-01T08:00:15.000+08:00| 1.9021131|
+|1970-01-01T08:00:16.000+08:00| 2.1755705|
+|1970-01-01T08:00:17.000+08:00| -1.1755705|
+|1970-01-01T08:00:18.000+08:00| -2.902113|
+|1970-01-01T08:00:19.000+08:00| 0.0|
++-----------------------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select highpass(s1,'wpass'='0.45') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+-----------------------------------------+
+| Time|highpass(root.test.d1.s1, "wpass"="0.45")|
++-----------------------------+-----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.9999999534830373|
+|1970-01-01T08:00:01.000+08:00| 1.7462829277628608E-8|
+|1970-01-01T08:00:02.000+08:00| -0.9999999593178128|
+|1970-01-01T08:00:03.000+08:00| -4.1115269056426626E-8|
+|1970-01-01T08:00:04.000+08:00| 0.9999999925494194|
+|1970-01-01T08:00:05.000+08:00| 3.328126513330016E-8|
+|1970-01-01T08:00:06.000+08:00| -1.0000000183304454|
+|1970-01-01T08:00:07.000+08:00| 6.260191433311374E-10|
+|1970-01-01T08:00:08.000+08:00| 1.0000000018134796|
+|1970-01-01T08:00:09.000+08:00| -3.097210911744423E-17|
+|1970-01-01T08:00:10.000+08:00| -1.0000000018134794|
+|1970-01-01T08:00:11.000+08:00| -6.260191627862097E-10|
+|1970-01-01T08:00:12.000+08:00| 1.0000000183304454|
+|1970-01-01T08:00:13.000+08:00| -3.328126501424346E-8|
+|1970-01-01T08:00:14.000+08:00| -0.9999999925494196|
+|1970-01-01T08:00:15.000+08:00| 4.111526915498874E-8|
+|1970-01-01T08:00:16.000+08:00| 0.9999999593178128|
+|1970-01-01T08:00:17.000+08:00| -1.7462829341296528E-8|
+|1970-01-01T08:00:18.000+08:00| -0.9999999534830369|
+|1970-01-01T08:00:19.000+08:00| -1.035237222742873E-16|
++-----------------------------+-----------------------------------------+
+```
+
+Note: The input is $y=sin(2\pi t/4)+2sin(2\pi t/5)$ with a length of 20. Thus, the output is $y=sin(2\pi t/4)$ after high-pass filtering.
+
+### IFFT
+
+#### Usage
+
+This function treats the two input series as the real and imaginary part of a complex series, performs an inverse fast Fourier transform (IFFT), and outputs the real part of the result.
+For the input format, please refer to the output format of `FFT` function.
+Moreover, the compressed output of `FFT` function is also supported.
+
+**Name:** IFFT
+
+**Input:** Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `start`: The start time of the output series with the format 'yyyy-MM-dd HH:mm:ss'. By default, it is '1970-01-01 08:00:00'.
++ `interval`: The interval of the output series, which is a positive number with an unit. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, it is 1s.
+
+**Output:** Output a single series. The type is DOUBLE. It is strictly equispaced. The values are the results of IFFT.
+
+**Note:** If a row contains null points or `NaN`, it will be ignored.
+
+#### Examples
+
+
+Input series:
+
+```
++-----------------------------+----------------------+----------------------+
+| Time| root.test.d1.re| root.test.d1.im|
++-----------------------------+----------------------+----------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0| 0.0|
+|1970-01-01T08:00:00.001+08:00| -3.932894010461041E-9| 1.2104201863039066E-8|
+|1970-01-01T08:00:00.002+08:00|-1.4021739447490164E-7| 1.9299268669082926E-7|
+|1970-01-01T08:00:00.003+08:00| -7.057291240286645E-8| 5.127422242345858E-8|
+|1970-01-01T08:00:00.004+08:00| 19.021130288047125| -6.180339875198807|
+|1970-01-01T08:00:00.005+08:00| 9.999999850988388| 3.501852745067114E-16|
+|1970-01-01T08:00:00.019+08:00| -3.932894898639461E-9|-1.2104202549376264E-8|
++-----------------------------+----------------------+----------------------+
+```
+
+
+SQL for query:
+
+```sql
+select ifft(re, im, 'interval'='1m', 'start'='2021-01-01 00:00:00') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+-------------------------------------------------------+
+| Time|ifft(root.test.d1.re, root.test.d1.im, "interval"="1m",|
+| | "start"="2021-01-01 00:00:00")|
++-----------------------------+-------------------------------------------------------+
+|2021-01-01T00:00:00.000+08:00| 2.902112992431231|
+|2021-01-01T00:01:00.000+08:00| 1.1755704705132448|
+|2021-01-01T00:02:00.000+08:00| -2.175570513757101|
+|2021-01-01T00:03:00.000+08:00| -1.9021130389094498|
+|2021-01-01T00:04:00.000+08:00| 0.9999999925494194|
+|2021-01-01T00:05:00.000+08:00| 1.902113046743454|
+|2021-01-01T00:06:00.000+08:00| 0.17557053610884188|
+|2021-01-01T00:07:00.000+08:00| -1.1755704886020932|
+|2021-01-01T00:08:00.000+08:00| -0.9021130371347148|
+|2021-01-01T00:09:00.000+08:00| 3.552713678800501E-16|
+|2021-01-01T00:10:00.000+08:00| 0.9021130371347154|
+|2021-01-01T00:11:00.000+08:00| 1.1755704886020932|
+|2021-01-01T00:12:00.000+08:00| -0.17557053610884144|
+|2021-01-01T00:13:00.000+08:00| -1.902113046743454|
+|2021-01-01T00:14:00.000+08:00| -0.9999999925494196|
+|2021-01-01T00:15:00.000+08:00| 1.9021130389094498|
+|2021-01-01T00:16:00.000+08:00| 2.1755705137571004|
+|2021-01-01T00:17:00.000+08:00| -1.1755704705132448|
+|2021-01-01T00:18:00.000+08:00| -2.902112992431231|
+|2021-01-01T00:19:00.000+08:00| -3.552713678800501E-16|
++-----------------------------+-------------------------------------------------------+
+```
+
+### LowPass
+
+#### Usage
+
+This function performs low-pass filtering on the input series and extracts components below the cutoff frequency.
+The timestamps of input will be ignored and all data points will be regarded as equidistant.
+
+**Name:** LOWPASS
+
+**Input:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+
+**Parameters:**
+
++ `wpass`: The normalized cutoff frequency which values (0,1). This parameter cannot be lacked.
+
+**Output:** Output a single series. The type is DOUBLE. It is the input after filtering. The length and timestamps of output are the same as the input.
+
+**Note:** `NaN` in the input series will be ignored.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 2.902113|
+|1970-01-01T08:00:01.000+08:00| 1.1755705|
+|1970-01-01T08:00:02.000+08:00| -2.1755705|
+|1970-01-01T08:00:03.000+08:00| -1.9021131|
+|1970-01-01T08:00:04.000+08:00| 1.0|
+|1970-01-01T08:00:05.000+08:00| 1.9021131|
+|1970-01-01T08:00:06.000+08:00| 0.1755705|
+|1970-01-01T08:00:07.000+08:00| -1.1755705|
+|1970-01-01T08:00:08.000+08:00| -0.902113|
+|1970-01-01T08:00:09.000+08:00| 0.0|
+|1970-01-01T08:00:10.000+08:00| 0.902113|
+|1970-01-01T08:00:11.000+08:00| 1.1755705|
+|1970-01-01T08:00:12.000+08:00| -0.1755705|
+|1970-01-01T08:00:13.000+08:00| -1.9021131|
+|1970-01-01T08:00:14.000+08:00| -1.0|
+|1970-01-01T08:00:15.000+08:00| 1.9021131|
+|1970-01-01T08:00:16.000+08:00| 2.1755705|
+|1970-01-01T08:00:17.000+08:00| -1.1755705|
+|1970-01-01T08:00:18.000+08:00| -2.902113|
+|1970-01-01T08:00:19.000+08:00| 0.0|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select Validity(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select lowpass(s1,'wpass'='0.45') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+----------------------------------------+
+| Time|lowpass(root.test.d1.s1, "wpass"="0.45")|
++-----------------------------+----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.9021130073323922|
+|1970-01-01T08:00:01.000+08:00| 1.1755704705132448|
+|1970-01-01T08:00:02.000+08:00| -1.1755705286582614|
+|1970-01-01T08:00:03.000+08:00| -1.9021130389094498|
+|1970-01-01T08:00:04.000+08:00| 7.450580419288145E-9|
+|1970-01-01T08:00:05.000+08:00| 1.902113046743454|
+|1970-01-01T08:00:06.000+08:00| 1.1755705212076808|
+|1970-01-01T08:00:07.000+08:00| -1.1755704886020932|
+|1970-01-01T08:00:08.000+08:00| -1.9021130222335536|
+|1970-01-01T08:00:09.000+08:00| 3.552713678800501E-16|
+|1970-01-01T08:00:10.000+08:00| 1.9021130222335536|
+|1970-01-01T08:00:11.000+08:00| 1.1755704886020932|
+|1970-01-01T08:00:12.000+08:00| -1.1755705212076801|
+|1970-01-01T08:00:13.000+08:00| -1.902113046743454|
+|1970-01-01T08:00:14.000+08:00| -7.45058112983088E-9|
+|1970-01-01T08:00:15.000+08:00| 1.9021130389094498|
+|1970-01-01T08:00:16.000+08:00| 1.1755705286582616|
+|1970-01-01T08:00:17.000+08:00| -1.1755704705132448|
+|1970-01-01T08:00:18.000+08:00| -1.9021130073323924|
+|1970-01-01T08:00:19.000+08:00| -2.664535259100376E-16|
++-----------------------------+----------------------------------------+
+```
+
+Note: The input is $y=sin(2\pi t/4)+2sin(2\pi t/5)$ with a length of 20. Thus, the output is $y=2sin(2\pi t/5)$ after low-pass filtering.
+
+
+
+
+## Series Discovery
+
+### ConsecutiveSequences
+
+#### Usage
+
+This function is used to find locally longest consecutive subsequences in strictly equispaced multidimensional data.
+
+Strictly equispaced data is the data whose time intervals are strictly equal. Missing data, including missing rows and missing values, is allowed in it, while data redundancy and timestamp drift is not allowed.
+
+Consecutive subsequence is the subsequence that is strictly equispaced with the standard time interval without any missing data. If a consecutive subsequence is not a proper subsequence of any consecutive subsequence, it is locally longest.
+
+**Name:** CONSECUTIVESEQUENCES
+
+**Input Series:** Support multiple input series. The type is arbitrary but the data is strictly equispaced.
+
+**Parameters:**
+
++ `gap`: The standard time interval which is a positive number with an unit. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, it will be estimated by the mode of time intervals.
+
+**Output Series:** Output a single series. The type is INT32. Each data point in the output series corresponds to a locally longest consecutive subsequence. The output timestamp is the starting timestamp of the subsequence and the output value is the number of data points in the subsequence.
+
+**Note:** For input series that is not strictly equispaced, there is no guarantee on the output.
+
+#### Examples
+
+##### Manually Specify the Standard Time Interval
+
+It's able to manually specify the standard time interval by the parameter `gap`. It's notable that false parameter leads to false output.
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:05:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:10:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:20:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:25:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:30:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:35:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:40:00.000+08:00| 1.0| null|
+|2020-01-01T00:45:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:50:00.000+08:00| 1.0| 1.0|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select consecutivesequences(s1,s2,'gap'='5m') from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------------------------------+
+| Time|consecutivesequences(root.test.d1.s1, root.test.d1.s2, "gap"="5m")|
++-----------------------------+------------------------------------------------------------------+
+|2020-01-01T00:00:00.000+08:00| 3|
+|2020-01-01T00:20:00.000+08:00| 4|
+|2020-01-01T00:45:00.000+08:00| 2|
++-----------------------------+------------------------------------------------------------------+
+```
+
+
+##### Automatically Estimate the Standard Time Interval
+
+When `gap` is default, this function estimates the standard time interval by the mode of time intervals and gets the same results. Therefore, this usage is more recommended.
+
+Input series is the same as above, the SQL for query is shown below:
+
+```sql
+select consecutivesequences(s1,s2) from root.test.d1
+```
+
+Output series:
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|consecutivesequences(root.test.d1.s1, root.test.d1.s2)|
++-----------------------------+------------------------------------------------------+
+|2020-01-01T00:00:00.000+08:00| 3|
+|2020-01-01T00:20:00.000+08:00| 4|
+|2020-01-01T00:45:00.000+08:00| 2|
++-----------------------------+------------------------------------------------------+
+```
+
+### ConsecutiveWindows
+
+#### Usage
+
+This function is used to find consecutive windows of specified length in strictly equispaced multidimensional data.
+
+Strictly equispaced data is the data whose time intervals are strictly equal. Missing data, including missing rows and missing values, is allowed in it, while data redundancy and timestamp drift is not allowed.
+
+Consecutive window is the subsequence that is strictly equispaced with the standard time interval without any missing data.
+
+**Name:** CONSECUTIVEWINDOWS
+
+**Input Series:** Support multiple input series. The type is arbitrary but the data is strictly equispaced.
+
+**Parameters:**
+
++ `gap`: The standard time interval which is a positive number with an unit. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. By default, it will be estimated by the mode of time intervals.
++ `length`: The length of the window which is a positive number with an unit. The unit is 'ms' for millisecond, 's' for second, 'm' for minute, 'h' for hour and 'd' for day. This parameter cannot be lacked.
+
+**Output Series:** Output a single series. The type is INT32. Each data point in the output series corresponds to a consecutive window. The output timestamp is the starting timestamp of the window and the output value is the number of data points in the window.
+
+**Note:** For input series that is not strictly equispaced, there is no guarantee on the output.
+
+#### Examples
+
+
+Input series:
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:05:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:10:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:20:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:25:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:30:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:35:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:40:00.000+08:00| 1.0| null|
+|2020-01-01T00:45:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:50:00.000+08:00| 1.0| 1.0|
++-----------------------------+---------------+---------------+
+```
+
+SQL for query:
+
+```sql
+select consecutivewindows(s1,s2,'length'='10m') from root.test.d1
```
Output series:
```
-+-----------------------------+----------------------------------------+
-| Time|validity(root.test.d1.s1, "window"="15")|
-+-----------------------------+----------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+----------------------------------------+
++-----------------------------+--------------------------------------------------------------------+
+| Time|consecutivewindows(root.test.d1.s1, root.test.d1.s2, "length"="10m")|
++-----------------------------+--------------------------------------------------------------------+
+|2020-01-01T00:00:00.000+08:00| 3|
+|2020-01-01T00:20:00.000+08:00| 3|
+|2020-01-01T00:25:00.000+08:00| 3|
++-----------------------------+--------------------------------------------------------------------+
```
-## Data Repair
-### TimestampRepair
-This function is used for timestamp repair.
-According to the given standard time interval,
-the method of minimizing the repair cost is adopted.
-By fine-tuning the timestamps,
-the original data with unstable timestamp interval is repaired to strictly equispaced data.
-If no standard time interval is given,
-this function will use the **median**, **mode** or **cluster** of the time interval to estimate the standard time interval.
+## String Processing
-**Name:** TIMESTAMPREPAIR
+### RegexMatch
-**Input Series:** Only support a single input series. The data type is INT32 / INT64 / FLOAT / DOUBLE.
+#### Usage
-**Parameters:**
+The function is used to fetch matched contents from text with given regular expression.
-+ `interval`: The standard time interval whose unit is millisecond. It is a positive integer. By default, it will be estimated according to the given method.
-+ `method`: The method to estimate the standard time interval, which is 'median', 'mode' or 'cluster'. This parameter is only valid when `interval` is not given. By default, median will be used.
+**Name:** REGEXMATCH
-**Output Series:** Output a single series. The type is the same as the input. This series is the input after repairing.
+**Input Series:** Only support a single input series. The data type is TEXT.
-#### Example: Manually Specify the Standard Time Interval
+**Parameter:**
-When `interval` is given, this function repairs according to the given standard time interval.
++ `regex`: The regular expression to match in the text. All grammars supported by Java are acceptable,
+ for example, `\d+\.\d+\.\d+\.\d+` is expected to match any IPv4 addresses.
++ `group`: The wanted group index in the matched result.
+ Reference to java.util.regex, group 0 is the whole pattern and
+ the next ones are numbered with the appearance order of left parentheses.
+ For example, the groups in `A(B(CD))` are: 0-`A(B(CD))`, 1-`B(CD)`, 2-`CD`.
+
+**Output Series:** Output a single series. The type is TEXT.
+
+**Note:** Those points with null values or not matched with the given pattern will not return any results.
+
+#### Examples
Input series:
```
-+-----------------------------+---------------+
-| Time|root.test.d2.s1|
-+-----------------------------+---------------+
-|2021-07-01T12:00:00.000+08:00| 1.0|
-|2021-07-01T12:00:10.000+08:00| 2.0|
-|2021-07-01T12:00:19.000+08:00| 3.0|
-|2021-07-01T12:00:30.000+08:00| 4.0|
-|2021-07-01T12:00:40.000+08:00| 5.0|
-|2021-07-01T12:00:50.000+08:00| 6.0|
-|2021-07-01T12:01:01.000+08:00| 7.0|
-|2021-07-01T12:01:11.000+08:00| 8.0|
-|2021-07-01T12:01:21.000+08:00| 9.0|
-|2021-07-01T12:01:31.000+08:00| 10.0|
-+-----------------------------+---------------+
++-----------------------------+-------------------------------+
+| Time| root.test.d1.s1|
++-----------------------------+-------------------------------+
+|2021-01-01T00:00:01.000+08:00| [192.168.0.1] [SUCCESS]|
+|2021-01-01T00:00:02.000+08:00| [192.168.0.24] [SUCCESS]|
+|2021-01-01T00:00:03.000+08:00| [192.168.0.2] [FAIL]|
+|2021-01-01T00:00:04.000+08:00| [192.168.0.5] [SUCCESS]|
+|2021-01-01T00:00:05.000+08:00| [192.168.0.124] [SUCCESS]|
++-----------------------------+-------------------------------+
```
SQL for query:
```sql
-select timestamprepair(s1,'interval'='10000') from root.test.d2
+select regexmatch(s1, "regex"="\d+\.\d+\.\d+\.\d+", "group"="0") from root.test.d1
```
Output series:
-
```
-+-----------------------------+----------------------------------------------------+
-| Time|timestamprepair(root.test.d2.s1, "interval"="10000")|
-+-----------------------------+----------------------------------------------------+
-|2021-07-01T12:00:00.000+08:00| 1.0|
-|2021-07-01T12:00:10.000+08:00| 2.0|
-|2021-07-01T12:00:20.000+08:00| 3.0|
-|2021-07-01T12:00:30.000+08:00| 4.0|
-|2021-07-01T12:00:40.000+08:00| 5.0|
-|2021-07-01T12:00:50.000+08:00| 6.0|
-|2021-07-01T12:01:00.000+08:00| 7.0|
-|2021-07-01T12:01:10.000+08:00| 8.0|
-|2021-07-01T12:01:20.000+08:00| 9.0|
-|2021-07-01T12:01:30.000+08:00| 10.0|
-+-----------------------------+----------------------------------------------------+
++-----------------------------+----------------------------------------------------------------------+
+| Time|regexmatch(root.test.d1.s1, "regex"="\d+\.\d+\.\d+\.\d+", "group"="0")|
++-----------------------------+----------------------------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| 192.168.0.1|
+|2021-01-01T00:00:02.000+08:00| 192.168.0.24|
+|2021-01-01T00:00:03.000+08:00| 192.168.0.2|
+|2021-01-01T00:00:04.000+08:00| 192.168.0.5|
+|2021-01-01T00:00:05.000+08:00| 192.168.0.124|
++-----------------------------+----------------------------------------------------------------------+
```
-#### Example: Automatically Estimate the Standard Time Interval
+### RegexReplace
-When `interval` is default, this function estimates the standard time interval.
+#### Usage
-Input series is the same as above, the SQL for query is shown below:
+The function is used to replace the specific regular expression matches with given string.
+
+**Name:** REGEXREPLACE
+
+**Input Series:** Only support a single input series. The data type is TEXT.
+
+**Parameter:**
+
++ `regex`: The target regular expression to be replaced. All grammars supported by Java are acceptable.
++ `replace`: The string to be put on and back reference notes in Java is also supported,
+ for example, '$1' refers to group 1 in the `regex` which will be filled with corresponding matched results.
++ `limit`: The number of matches to be replaced which should be an integer no less than -1,
+ default to -1 which means all matches will be replaced.
++ `offset`: The number of matches to be skipped, which means the first `offset` matches will not be replaced, default to 0.
++ `reverse`: Whether to count all the matches reversely, default to 'false'.
+
+**Output Series:** Output a single series. The type is TEXT.
+
+#### Examples
+
+Input series:
+
+```
++-----------------------------+-------------------------------+
+| Time| root.test.d1.s1|
++-----------------------------+-------------------------------+
+|2021-01-01T00:00:01.000+08:00| [192.168.0.1] [SUCCESS]|
+|2021-01-01T00:00:02.000+08:00| [192.168.0.24] [SUCCESS]|
+|2021-01-01T00:00:03.000+08:00| [192.168.0.2] [FAIL]|
+|2021-01-01T00:00:04.000+08:00| [192.168.0.5] [SUCCESS]|
+|2021-01-01T00:00:05.000+08:00| [192.168.0.124] [SUCCESS]|
++-----------------------------+-------------------------------+
+```
+
+SQL for query:
```sql
-select timestamprepair(s1) from root.test.d2
+select regexreplace(s1, "regex"="192\.168\.0\.(\d+)", "replace"="cluster-$1", "limit"="1") from root.test.d1
```
Output series:
```
-+-----------------------------+--------------------------------+
-| Time|timestamprepair(root.test.d2.s1)|
-+-----------------------------+--------------------------------+
-|2021-07-01T12:00:00.000+08:00| 1.0|
-|2021-07-01T12:00:10.000+08:00| 2.0|
-|2021-07-01T12:00:20.000+08:00| 3.0|
-|2021-07-01T12:00:30.000+08:00| 4.0|
-|2021-07-01T12:00:40.000+08:00| 5.0|
-|2021-07-01T12:00:50.000+08:00| 6.0|
-|2021-07-01T12:01:00.000+08:00| 7.0|
-|2021-07-01T12:01:10.000+08:00| 8.0|
-|2021-07-01T12:01:20.000+08:00| 9.0|
-|2021-07-01T12:01:30.000+08:00| 10.0|
-+-----------------------------+--------------------------------+
++-----------------------------+-----------------------------------------------------------+
+| Time|regexreplace(root.test.d1.s1, "regex"="192\.168\.0\.(\d+)",|
+| | "replace"="cluster-$1", "limit"="1")|
++-----------------------------+-----------------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| [cluster-1] [SUCCESS]|
+|2021-01-01T00:00:02.000+08:00| [cluster-24] [SUCCESS]|
+|2021-01-01T00:00:03.000+08:00| [cluster-2] [FAIL]|
+|2021-01-01T00:00:04.000+08:00| [cluster-5] [SUCCESS]|
+|2021-01-01T00:00:05.000+08:00| [cluster-124] [SUCCESS]|
++-----------------------------+-----------------------------------------------------------+
```
-### ValueFill
+### RegexSplit
#### Usage
-This function is used to impute time series. Several methods are supported.
-**Name**: ValueFill
-**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+The function is used to split text with given regular expression and return specific element.
-**Parameters:**
+**Name:** REGEXSPLIT
-+ `method`: {"mean", "previous", "linear", "likelihood", "AR", "MA", "SCREEN"}, default "linear".
- Method to use for imputation in series. "mean": use global mean value to fill holes; "previous": propagate last valid observation forward to next valid. "linear": simplest interpolation method; "likelihood":Maximum likelihood estimation based on the normal distribution of speed; "AR": auto regression; "MA": moving average; "SCREEN": speed constraint.
+**Input Series:** Only support a single input series. The data type is TEXT.
-**Output Series:** Output a single series. The type is the same as the input. This series is the input after repairing.
+**Parameter:**
-**Note:** AR method use AR(1) model. Input value should be auto-correlated, or the function would output a single point (0, 0.0).
++ `regex`: The regular expression used to split the text.
+ All grammars supported by Java are acceptable, for example, `['"]` is expected to match `'` and `"`.
++ `index`: The wanted index of elements in the split result.
+ It should be an integer no less than -1, default to -1 which means the length of the result array is returned
+ and any non-negative integer is used to fetch the text of the specific index starting from 0.
-#### Example: Fill with linear
+**Output Series:** Output a single series. The type is INT32 when `index` is -1 and TEXT when it's an valid index.
-When `method` is "linear" or the default, Screen method is used to impute.
+**Note:** When `index` is out of the range of the result array, for example `0,1,2` split with `,` and `index` is set to 3,
+no result are returned for that record.
+
+#### Examples
Input series:
```
+-----------------------------+---------------+
-| Time|root.test.d2.s1|
+| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| NaN|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| NaN|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| NaN|
-|2020-01-01T00:00:22.000+08:00| NaN|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| 128.0|
+|2021-01-01T00:00:01.000+08:00| A,B,A+,B-|
+|2021-01-01T00:00:02.000+08:00| A,A+,A,B+|
+|2021-01-01T00:00:03.000+08:00| B+,B,B|
+|2021-01-01T00:00:04.000+08:00| A+,A,A+,A|
+|2021-01-01T00:00:05.000+08:00| A,B-,B,B|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select valuefill(s1) from root.test.d2
+select regexsplit(s1, "regex"=",", "index"="-1") from root.test.d1
```
Output series:
```
-+-----------------------------+-----------------------+
-| Time|valuefill(root.test.d2)|
-+-----------------------------+-----------------------+
-|2020-01-01T00:00:02.000+08:00| NaN|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 108.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.7|
-|2020-01-01T00:00:22.000+08:00| 121.3|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| 128.0|
-+-----------------------------+-----------------------+
++-----------------------------+------------------------------------------------------+
+| Time|regexsplit(root.test.d1.s1, "regex"=",", "index"="-1")|
++-----------------------------+------------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| 4|
+|2021-01-01T00:00:02.000+08:00| 4|
+|2021-01-01T00:00:03.000+08:00| 3|
+|2021-01-01T00:00:04.000+08:00| 4|
+|2021-01-01T00:00:05.000+08:00| 4|
++-----------------------------+------------------------------------------------------+
```
-#### Example: Previous Fill
-
-When `method` is "previous", previous method is used.
+Another SQL for query:
-Input series is the same as above, the SQL for query is shown below:
+SQL for query:
```sql
-select valuefill(s1,"method"="previous") from root.test.d2
+select regexsplit(s1, "regex"=",", "index"="3") from root.test.d1
```
Output series:
```
-+-----------------------------+-------------------------------------------+
-| Time|valuefill(root.test.d2,"method"="previous")|
-+-----------------------------+-------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| NaN|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 110.5|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 116.0|
-|2020-01-01T00:00:22.000+08:00| 116.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| 128.0|
-+-----------------------------+-------------------------------------------+
++-----------------------------+-----------------------------------------------------+
+| Time|regexsplit(root.test.d1.s1, "regex"=",", "index"="3")|
++-----------------------------+-----------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| B-|
+|2021-01-01T00:00:02.000+08:00| B+|
+|2021-01-01T00:00:04.000+08:00| A|
+|2021-01-01T00:00:05.000+08:00| B|
++-----------------------------+-----------------------------------------------------+
```
-### ValueRepair
+### StrReplace
#### Usage
-This function is used to repair the value of the time series.
-Currently, two methods are supported:
-**Screen** is a method based on speed threshold, which makes all speeds meet the threshold requirements under the premise of minimum changes;
-**LsGreedy** is a method based on speed change likelihood, which models speed changes as Gaussian distribution, and uses a greedy algorithm to maximize the likelihood.
-
-
-**Name:** VALUEREPAIR
-**Input Series:** Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE.
+The function is used to replace the specific substring with given string.
-**Parameters:**
+**Name:** STRREPLACE
-+ `method`: The method used to repair, which is 'Screen' or 'LsGreedy'. By default, Screen is used.
-+ `minSpeed`: This parameter is only valid with Screen. It is the speed threshold. Speeds below it will be regarded as outliers. By default, it is the median minus 3 times of median absolute deviation.
-+ `maxSpeed`: This parameter is only valid with Screen. It is the speed threshold. Speeds above it will be regarded as outliers. By default, it is the median plus 3 times of median absolute deviation.
-+ `center`: This parameter is only valid with LsGreedy. It is the center of the Gaussian distribution of speed changes. By default, it is 0.
-+ `sigma`: This parameter is only valid with LsGreedy. It is the standard deviation of the Gaussian distribution of speed changes. By default, it is the median absolute deviation.
+**Input Series:** Only support a single input series. The data type is TEXT.
-**Output Series:** Output a single series. The type is the same as the input. This series is the input after repairing.
+**Parameter:**
-**Note:** `NaN` will be filled with linear interpolation before repairing.
++ `target`: The target substring to be replaced.
++ `replace`: The string to be put on.
++ `limit`: The number of matches to be replaced which should be an integer no less than -1,
+ default to -1 which means all matches will be replaced.
++ `offset`: The number of matches to be skipped, which means the first `offset` matches will not be replaced, default to 0.
++ `reverse`: Whether to count all the matches reversely, default to 'false'.
-#### Example: Repair with Screen
+**Output Series:** Output a single series. The type is TEXT.
-When `method` is 'Screen' or the default, Screen method is used.
+#### Examples
Input series:
```
+-----------------------------+---------------+
-| Time|root.test.d2.s1|
+| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 100.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|2021-01-01T00:00:01.000+08:00| A,B,A+,B-|
+|2021-01-01T00:00:02.000+08:00| A,A+,A,B+|
+|2021-01-01T00:00:03.000+08:00| B+,B,B|
+|2021-01-01T00:00:04.000+08:00| A+,A,A+,A|
+|2021-01-01T00:00:05.000+08:00| A,B-,B,B|
+-----------------------------+---------------+
```
SQL for query:
```sql
-select valuerepair(s1) from root.test.d2
+select strreplace(s1, "target"=",", "replace"="/", "limit"="2") from root.test.d1
```
Output series:
```
-+-----------------------------+----------------------------+
-| Time|valuerepair(root.test.d2.s1)|
-+-----------------------------+----------------------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 106.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| 128.0|
-+-----------------------------+----------------------------+
++-----------------------------+-----------------------------------------+
+| Time|strreplace(root.test.d1.s1, "target"=",",|
+| | "replace"="/", "limit"="2")|
++-----------------------------+-----------------------------------------+
+|2021-01-01T00:00:01.000+08:00| A/B/A+,B-|
+|2021-01-01T00:00:02.000+08:00| A/A+/A,B+|
+|2021-01-01T00:00:03.000+08:00| B+/B/B|
+|2021-01-01T00:00:04.000+08:00| A+/A/A+,A|
+|2021-01-01T00:00:05.000+08:00| A/B-/B,B|
++-----------------------------+-----------------------------------------+
```
-#### Example: Repair with LsGreedy
-When `method` is 'LsGreedy', LsGreedy method is used.
-
-Input series is the same as above, the SQL for query is shown below:
+Another SQL for query:
```sql
-select valuerepair(s1,'method'='LsGreedy') from root.test.d2
+select strreplace(s1, "target"=",", "replace"="/", "limit"="1", "offset"="1", "reverse"="true") from root.test.d1
```
Output series:
```
-+-----------------------------+-------------------------------------------------+
-| Time|valuerepair(root.test.d2.s1, "method"="LsGreedy")|
-+-----------------------------+-------------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 106.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| 128.0|
-+-----------------------------+-------------------------------------------------+
-```
++-----------------------------+-----------------------------------------------------+
+| Time|strreplace(root.test.d1.s1, "target"=",", "replace"= |
+| | "|", "limit"="1", "offset"="1", "reverse"="true")|
++-----------------------------+-----------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| A,B/A+,B-|
+|2021-01-01T00:00:02.000+08:00| A,A+/A,B+|
+|2021-01-01T00:00:03.000+08:00| B+/B,B|
+|2021-01-01T00:00:04.000+08:00| A+,A/A+,A|
+|2021-01-01T00:00:05.000+08:00| A,B-/B,B|
++-----------------------------+-----------------------------------------------------+
+```
\ No newline at end of file
diff --git a/docs/zh/UserGuide/Process-Data/UDF-Library.md b/docs/zh/UserGuide/Process-Data/UDF-Library.md
index 89a7fcac2f..5229a28bd4 100644
--- a/docs/zh/UserGuide/Process-Data/UDF-Library.md
+++ b/docs/zh/UserGuide/Process-Data/UDF-Library.md
@@ -1,23 +1,26 @@
<!--
- Licensed to the Apache Software Foundation (ASF) under one
- or more contributor license agreements. See the NOTICE file
- distributed with this work for additional information
- regarding copyright ownership. The ASF licenses this file
- to you under the Apache License, Version 2.0 (the
- "License"); you may not use this file except in compliance
- with the License. You may obtain a copy of the License at
-
- http://www.apache.org/licenses/LICENSE-2.0
-
- Unless required by applicable law or agreed to in writing,
- software distributed under the License is distributed on an
- "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
- KIND, either express or implied. See the License for the
- specific language governing permissions and limitations
- under the License.
+ Licensed to the Apache Software Foundation (ASF) under one
+ or more contributor license agreements. See the NOTICE file
+ distributed with this work for additional information
+ regarding copyright ownership. The ASF licenses this file
+ to you under the Apache License, Version 2.0 (the
+ "License"); you may not use this file except in compliance
+ with the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing,
+ software distributed under the License is distributed on an
+ "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ KIND, either express or implied. See the License for the
+ specific language governing permissions and limitations
+ under the License.
-->
+
+
+
# UDF 函数库
### 什么是 UDF 函数库
@@ -25,6 +28,7 @@
对基于时序数据的应用而言，数据质量至关重要。**UDF 函数库** 基于 IoTDB 用户自定义函数 (UDF)，实现了一系列关于数据质量的函数，包括数据画像、数据质量评估与修复等，有效满足了工业领域对数据质量的需求。
### 快速开始
+
1. 下载包含全部依赖的 jar 包和注册脚本；
2. 将 jar 包复制到 IoTDB 程序目录的`ext\udf`目录下；
3. 运行`sbin\start-server.bat`（在 Windows 下）或`sbin\start-server.sh`（在 Linux 或 MacOS 下）以启动 IoTDB 服务器；
@@ -57,317 +61,3330 @@
</tr>
</table>
-## 数据质量
-### 完整性(Completeness)
-#### 函数简介
-本函数用于计算时间序列的完整性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的完整性，并输出窗口第一个数据点的时间戳和窗口的完整性。
+## 数据画像
-**函数名：** COMPLETENESS
+### ACF
-**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+#### 函数简介
-**参数：**
+本函数用于计算时间序列的自相关函数值，即序列与自身之间的互相关函数，详情参见`XCorr`函数文档。
-+ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
-+ `downtime`：完整性计算是否考虑停机异常。它的取值为 'true' 或 'false'，默认值为 'true'. 在考虑停机异常时，长时间的数据缺失将被视作停机，不对完整性产生影响。
+**函数名：** ACF
-**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
-**提示：** 只有当窗口内的数据点数目超过10时，才会进行完整性计算。否则，该窗口将被忽略，不做任何输出。
+**输出序列：** 输出单个序列，类型为 DOUBLE。序列中共包含$2N-1$个数据点，每个值的具体含义参见`XCorr`函数文档。
-#### 示例：参数缺省
+**提示：**
-在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算完整性。
++ 序列中的`NaN`值会被忽略，在计算中表现为0。
+
+#### 使用示例
输入序列：
+
```
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:01.000+08:00| 1|
+|2020-01-01T00:00:02.000+08:00| NaN|
+|2020-01-01T00:00:03.000+08:00| 3|
+|2020-01-01T00:00:04.000+08:00| NaN|
+|2020-01-01T00:00:05.000+08:00| 5|
+-----------------------------+---------------+
```
-用于查询的SQL语句：
+
+用于查询的 SQL 语句：
```sql
-select completeness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select acf(s1) from root.test.d1 where time <= 2020-01-01 00:00:05
```
输出序列：
```
-+-----------------------------+-----------------------------+
-| Time|completeness(root.test.d1.s1)|
-+-----------------------------+-----------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.875|
-+-----------------------------+-----------------------------+
++-----------------------------+--------------------+
+| Time|acf(root.test.d1.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.001+08:00| 1.0|
+|1970-01-01T08:00:00.002+08:00| 0.0|
+|1970-01-01T08:00:00.003+08:00| 3.6|
+|1970-01-01T08:00:00.004+08:00| 0.0|
+|1970-01-01T08:00:00.005+08:00| 7.0|
+|1970-01-01T08:00:00.006+08:00| 0.0|
+|1970-01-01T08:00:00.007+08:00| 3.6|
+|1970-01-01T08:00:00.008+08:00| 0.0|
+|1970-01-01T08:00:00.009+08:00| 1.0|
++-----------------------------+--------------------+
```
-#### 示例：指定窗口大小
+### Distinct
-在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算完整性。
+#### 函数简介
+
+本函数可以返回输入序列中出现的所有不同的元素。
+
+**函数名：** DISTINCT
+
+**输入序列：** 仅支持单个输入序列，类型可以是任意的
+
+**输出序列：** 输出单个序列，类型与输入相同。
+
+**提示：**
+
++ 输出序列的时间戳是无意义的。输出顺序是任意的。
++ 缺失值和空值将被忽略，但`NaN`不会被忽略。
++ 字符串区分大小写
+
+
+#### 使用示例
+
+输入序列：
-输入序列:
```
+-----------------------------+---------------+
-| Time|root.test.d1.s1|
+| Time|root.test.d2.s2|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
+|2020-01-01T08:00:00.001+08:00| Hello|
+|2020-01-01T08:00:00.002+08:00| hello|
+|2020-01-01T08:00:00.003+08:00| Hello|
+|2020-01-01T08:00:00.004+08:00| World|
+|2020-01-01T08:00:00.005+08:00| World|
+-----------------------------+---------------+
```
用于查询的 SQL 语句：
```sql
-select completeness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select distinct(s2) from root.test.d2
```
输出序列：
```
-+-----------------------------+--------------------------------------------+
-| Time|completeness(root.test.d1.s1, "window"="15")|
-+-----------------------------+--------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.875|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+--------------------------------------------+
++-----------------------------+-------------------------+
+| Time|distinct(root.test.d2.s2)|
++-----------------------------+-------------------------+
+|1970-01-01T08:00:00.001+08:00| Hello|
+|1970-01-01T08:00:00.002+08:00| hello|
+|1970-01-01T08:00:00.003+08:00| World|
++-----------------------------+-------------------------+
```
-### 一致性(Consistency)
+### Histogram
#### 函数简介
-本函数用于计算时间序列的一致性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的一致性，并输出窗口第一个数据点的时间戳和窗口的时效性。
-**函数名：** CONSISTENCY
+本函数用于计算单列数值型数据的分布直方图。
-**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+**函数名：** HISTOGRAM
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
**参数：**
-+ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
++ `min`：表示所求数据范围的下限，默认值为 -Double.MAX_VALUE。
++ `max`：表示所求数据范围的上限，默认值为 Double.MAX_VALUE，`start`的值必须小于或等于`end`。
++ `count`: 表示直方图分桶的数量，默认值为 1，其值必须为正整数。
-**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+**输出序列：** 直方图分桶的值，其中第 i 个桶（从 1 开始计数）表示的数据范围下界为$min+ (i-1)\cdot\frac{max-min}{count}$，数据范围上界为$min+ i \cdot \frac{max-min}{count}$。
-**提示：** 只有当窗口内的数据点数目超过10时，才会进行一致性计算。否则，该窗口将被忽略，不做任何输出。
-#### 示例：参数缺省
+**提示：**
-在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算一致性。
++ 如果某个数据点的数值小于`min`，它会被放入第 1 个桶；如果某个数据点的数值大于`max`，它会被放入最后 1 个桶。
++ 数据中的空值、缺失值和`NaN`将会被忽略。
+
+#### 使用示例
输入序列：
+
```
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:00.000+08:00| 1.0|
+|2020-01-01T00:00:01.000+08:00| 2.0|
+|2020-01-01T00:00:02.000+08:00| 3.0|
+|2020-01-01T00:00:03.000+08:00| 4.0|
+|2020-01-01T00:00:04.000+08:00| 5.0|
+|2020-01-01T00:00:05.000+08:00| 6.0|
+|2020-01-01T00:00:06.000+08:00| 7.0|
+|2020-01-01T00:00:07.000+08:00| 8.0|
+|2020-01-01T00:00:08.000+08:00| 9.0|
+|2020-01-01T00:00:09.000+08:00| 10.0|
+|2020-01-01T00:00:10.000+08:00| 11.0|
+|2020-01-01T00:00:11.000+08:00| 12.0|
+|2020-01-01T00:00:12.000+08:00| 13.0|
+|2020-01-01T00:00:13.000+08:00| 14.0|
+|2020-01-01T00:00:14.000+08:00| 15.0|
+|2020-01-01T00:00:15.000+08:00| 16.0|
+|2020-01-01T00:00:16.000+08:00| 17.0|
+|2020-01-01T00:00:17.000+08:00| 18.0|
+|2020-01-01T00:00:18.000+08:00| 19.0|
+|2020-01-01T00:00:19.000+08:00| 20.0|
+-----------------------------+---------------+
```
用于查询的SQL语句：
```sql
-select consistency(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select histogram(s1,"min"="1","max"="20","count"="10") from root.test.d1
```
输出序列：
```
-+-----------------------------+----------------------------+
-| Time|consistency(root.test.d1.s1)|
-+-----------------------------+----------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-+-----------------------------+----------------------------+
++-----------------------------+---------------------------------------------------------------+
+| Time|histogram(root.test.d1.s1, "min"="1", "max"="20", "count"="10")|
++-----------------------------+---------------------------------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 2|
+|1970-01-01T08:00:00.001+08:00| 2|
+|1970-01-01T08:00:00.002+08:00| 2|
+|1970-01-01T08:00:00.003+08:00| 2|
+|1970-01-01T08:00:00.004+08:00| 2|
+|1970-01-01T08:00:00.005+08:00| 2|
+|1970-01-01T08:00:00.006+08:00| 2|
+|1970-01-01T08:00:00.007+08:00| 2|
+|1970-01-01T08:00:00.008+08:00| 2|
+|1970-01-01T08:00:00.009+08:00| 2|
++-----------------------------+---------------------------------------------------------------+
```
-#### 示例：指定窗口大小
+### Integral
-在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算一致性。
+#### 函数简介
+
+本函数用于计算时间序列的数值积分，即以时间为横坐标、数值为纵坐标绘制的折线图中折线以下的面积。
+
+**函数名：** INTEGRAL
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `unit`：积分求解所用的时间轴单位，取值为 "1S", "1s", "1m", "1H", "1d"（区分大小写），分别表示以毫秒、秒、分钟、小时、天为单位计算积分。
+ 缺省情况下取 "1s"，以秒为单位。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE，序列仅包含一个时间戳为 0、值为积分结果的数据点。
+
+**提示：**
+
++ 积分值等于折线图中每相邻两个数据点和时间轴形成的直角梯形的面积之和，不同时间单位下相当于横轴进行不同倍数放缩，得到的积分值可直接按放缩倍数转换。
+
++ 数据中`NaN`将会被忽略。折线将以临近两个有值数据点为准。
+
+#### 使用示例
+
+##### 参数缺省
+
+缺省情况下积分以1s为时间单位。
+
+输入序列：
-输入序列:
```
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
+|2020-01-01T00:00:01.000+08:00| 1|
+|2020-01-01T00:00:02.000+08:00| 2|
+|2020-01-01T00:00:03.000+08:00| 5|
+|2020-01-01T00:00:04.000+08:00| 6|
+|2020-01-01T00:00:05.000+08:00| 7|
+|2020-01-01T00:00:08.000+08:00| 8|
+|2020-01-01T00:00:09.000+08:00| NaN|
+|2020-01-01T00:00:10.000+08:00| 10|
+-----------------------------+---------------+
```
-用于查询的SQL语句：
+
+用于查询的 SQL 语句：
```sql
-select consistency(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select integral(s1) from root.test.d1 where time <= 2020-01-01 00:00:10
```
输出序列：
```
-+-----------------------------+-------------------------------------------+
-| Time|consistency(root.test.d1.s1, "window"="15")|
-+-----------------------------+-------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+-------------------------------------------+
++-----------------------------+-------------------------+
+| Time|integral(root.test.d1.s1)|
++-----------------------------+-------------------------+
+|1970-01-01T08:00:00.000+08:00| 57.5|
++-----------------------------+-------------------------+
```
-### 时效性(Timeliness)
+其计算公式为：
+$$\frac{1}{2}[(1+2)\times 1 + (2+5) \times 1 + (5+6) \times 1 + (6+7) \times 1 + (7+8) \times 3 + (8+10) \times 2] = 57.5$$
+
+
+#### 指定时间单位
+
+指定以分钟为时间单位。
+
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select integral(s1, "unit"="1m") from root.test.d1 where time <= 2020-01-01 00:00:10
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------+
+| Time|integral(root.test.d1.s1)|
++-----------------------------+-------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.958|
++-----------------------------+-------------------------+
+```
+
+其计算公式为：
+$$\frac{1}{2\times 60}[(1+2) \times 1 + (2+3) \times 1 + (5+6) \times 1 + (6+7) \times 1 + (7+8) \times 3 + (8+10) \times 2] = 0.958$$
+
+### IntegralAvg
#### 函数简介
-本函数用于计算时间序列的时效性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的时效性，并输出窗口第一个数据点的时间戳和窗口的时效性。
-**函数名：** TIMELINESS
+本函数用于计算时间序列的函数均值，即在相同时间单位下的数值积分除以序列总的时间跨度。更多关于数值积分计算的信息请参考`Integral`函数。
-**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+**函数名：** INTEGRALAVG
-**参数：**
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
-+ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
+**输出序列：** 输出单个序列，类型为 DOUBLE，序列仅包含一个时间戳为 0、值为时间加权平均结果的数据点。
-**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+**提示：**
-**提示：** 只有当窗口内的数据点数目超过10时，才会进行时效性计算。否则，该窗口将被忽略，不做任何输出。
++ 时间加权的平均值等于在任意时间单位`unit`下计算的数值积分（即折线图中每相邻两个数据点和时间轴形成的直角梯形的面积之和），
+ 除以相同时间单位下输入序列的时间跨度，其值与具体采用的时间单位无关，默认与 IoTDB 时间单位一致。
-#### 示例：参数缺省
++ 数据中的`NaN`将会被忽略。折线将以临近两个有值数据点为准。
-在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算时效性。
++ 输入序列为空时，函数输出结果为 0；仅有一个数据点时，输出结果为该点数值。
+
+#### 使用示例
输入序列：
+
```
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:01.000+08:00| 1|
+|2020-01-01T00:00:02.000+08:00| 2|
+|2020-01-01T00:00:03.000+08:00| 5|
+|2020-01-01T00:00:04.000+08:00| 6|
+|2020-01-01T00:00:05.000+08:00| 7|
+|2020-01-01T00:00:08.000+08:00| 8|
+|2020-01-01T00:00:09.000+08:00| NaN|
+|2020-01-01T00:00:10.000+08:00| 10|
+-----------------------------+---------------+
```
-用于查询的SQL语句：
+
+用于查询的 SQL 语句：
```sql
-select timeliness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select integralavg(s1) from root.test.d1 where time <= 2020-01-01 00:00:10
```
输出序列：
```
-+-----------------------------+---------------------------+
-| Time|timeliness(root.test.d1.s1)|
-+-----------------------------+---------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-+-----------------------------+---------------------------+
++-----------------------------+----------------------------+
+| Time|integralavg(root.test.d1.s1)|
++-----------------------------+----------------------------+
+|1970-01-01T08:00:00.000+08:00| 5.75|
++-----------------------------+----------------------------+
```
-#### 示例：指定窗口大小
+其计算公式为：
+$$\frac{1}{2}[(1+2)\times 1 + (2+5) \times 1 + (5+6) \times 1 + (6+7) \times 1 + (7+8) \times 3 + (8+10) \times 2] / 10 = 5.75$$
-在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算时效性。
+### Mad
-输入序列:
-```
-+-----------------------------+---------------+
-| Time|root.test.d1.s1|
-+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
+#### 函数简介
+
+本函数用于计算单列数值型数据的精确或近似绝对中位差，绝对中位差为所有数值与其中位数绝对偏移量的中位数。
+
+如有数据集$\{1,3,3,5,5,6,7,8,9\}$，其中位数为5，所有数值与中位数的偏移量的绝对值为$\{0,0,1,2,2,2,3,4,4\}$，其中位数为2，故而原数据集的绝对中位差为2。
+
+**函数名：** MAD
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `error`：近似绝对中位差的基于数值的误差百分比，取值范围为 [0,1)，默认值为 0。如当`error`=0.01 时，记精确绝对中位差为a，近似绝对中位差为b，不等式 $0.99a \le b \le 1.01a$ 成立。当`error`=0 时，计算结果为精确绝对中位差。
+
+
+**输出序列：** 输出单个序列，类型为DOUBLE，序列仅包含一个时间戳为 0、值为绝对中位差的数据点。
+
+**提示：** 数据中的空值、缺失值和`NaN`将会被忽略。
+
+#### 使用示例
+
+##### 精确查询
+
+当`error`参数缺省或为0时，本函数计算精确绝对中位差。
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|2021-03-17T10:32:17.054+08:00| 0.5319929|
+|2021-03-17T10:32:18.054+08:00| 0.9304316|
+|2021-03-17T10:32:19.054+08:00| -1.4800133|
+|2021-03-17T10:32:20.054+08:00| 0.6114087|
+|2021-03-17T10:32:21.054+08:00| 2.5163336|
+|2021-03-17T10:32:22.054+08:00| -1.0845392|
+|2021-03-17T10:32:23.054+08:00| 1.0562582|
+|2021-03-17T10:32:24.054+08:00| 1.3867859|
+|2021-03-17T10:32:25.054+08:00| -0.45429882|
+|2021-03-17T10:32:26.054+08:00| 1.0353678|
+|2021-03-17T10:32:27.054+08:00| 0.7307929|
+|2021-03-17T10:32:28.054+08:00| 2.3167255|
+|2021-03-17T10:32:29.054+08:00| 2.342443|
+|2021-03-17T10:32:30.054+08:00| 1.5809103|
+|2021-03-17T10:32:31.054+08:00| 1.4829416|
+|2021-03-17T10:32:32.054+08:00| 1.5800357|
+|2021-03-17T10:32:33.054+08:00| 0.7124368|
+|2021-03-17T10:32:34.054+08:00| -0.78597564|
+|2021-03-17T10:32:35.054+08:00| 1.2058644|
+|2021-03-17T10:32:36.054+08:00| 1.4215064|
+|2021-03-17T10:32:37.054+08:00| 1.2808295|
+|2021-03-17T10:32:38.054+08:00| -0.6173715|
+|2021-03-17T10:32:39.054+08:00| 0.06644377|
+|2021-03-17T10:32:40.054+08:00| 2.349338|
+|2021-03-17T10:32:41.054+08:00| 1.7335888|
+|2021-03-17T10:32:42.054+08:00| 1.5872132|
+............
+Total line number = 10000
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select mad(s0) from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+------------------+
+| Time| mad(root.test.s0)|
++-----------------------------+------------------+
+|1970-01-01T08:00:00.000+08:00|0.6806197166442871|
++-----------------------------+------------------+
+```
+
+##### 近似查询
+
+当`error`参数取值不为 0 时，本函数计算近似绝对中位差。
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select mad(s0, "error"="0.01") from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+---------------------------------+
+| Time|mad(root.test.s0, "error"="0.01")|
++-----------------------------+---------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.6806616245859518|
++-----------------------------+---------------------------------+
+```
+
+### Median
+
+#### 函数简介
+
+本函数用于计算单列数值型数据的精确或近似中位数。中位数是顺序排列的一组数据中居于中间位置的数；当序列有偶数个时，中位数为中间二者的平均数。
+
+**函数名：** MEDIAN
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `error`：近似中位数的基于排名的误差百分比，取值范围 [0,1)，默认值为 0。如当`error`=0.01 时，计算出的中位数的真实排名百分比在 0.49~0.51 之间。当`error`=0 时，计算结果为精确中位数。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE，序列仅包含一个时间戳为 0、值为中位数的数据点。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|2021-03-17T10:32:17.054+08:00| 0.5319929|
+|2021-03-17T10:32:18.054+08:00| 0.9304316|
+|2021-03-17T10:32:19.054+08:00| -1.4800133|
+|2021-03-17T10:32:20.054+08:00| 0.6114087|
+|2021-03-17T10:32:21.054+08:00| 2.5163336|
+|2021-03-17T10:32:22.054+08:00| -1.0845392|
+|2021-03-17T10:32:23.054+08:00| 1.0562582|
+|2021-03-17T10:32:24.054+08:00| 1.3867859|
+|2021-03-17T10:32:25.054+08:00| -0.45429882|
+|2021-03-17T10:32:26.054+08:00| 1.0353678|
+|2021-03-17T10:32:27.054+08:00| 0.7307929|
+|2021-03-17T10:32:28.054+08:00| 2.3167255|
+|2021-03-17T10:32:29.054+08:00| 2.342443|
+|2021-03-17T10:32:30.054+08:00| 1.5809103|
+|2021-03-17T10:32:31.054+08:00| 1.4829416|
+|2021-03-17T10:32:32.054+08:00| 1.5800357|
+|2021-03-17T10:32:33.054+08:00| 0.7124368|
+|2021-03-17T10:32:34.054+08:00| -0.78597564|
+|2021-03-17T10:32:35.054+08:00| 1.2058644|
+|2021-03-17T10:32:36.054+08:00| 1.4215064|
+|2021-03-17T10:32:37.054+08:00| 1.2808295|
+|2021-03-17T10:32:38.054+08:00| -0.6173715|
+|2021-03-17T10:32:39.054+08:00| 0.06644377|
+|2021-03-17T10:32:40.054+08:00| 2.349338|
+|2021-03-17T10:32:41.054+08:00| 1.7335888|
+|2021-03-17T10:32:42.054+08:00| 1.5872132|
+............
+Total line number = 10000
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select median(s0, "error"="0.01") from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------+
+| Time|median(root.test.s0, "error"="0.01")|
++-----------------------------+------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.021884560585022|
++-----------------------------+------------------------------------+
+```
+
+### MinMax
+
+#### 函数简介
+
+本函数将输入序列使用 min-max 方法进行标准化。最小值归一至 0，最大值归一至 1.
+
+**函数名：** MINMAX
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `compute`：若设置为"batch"，则将数据全部读入后转换；若设置为 "stream"，则需用户提供最大值及最小值进行流式计算转换。默认为 "batch"。
++ `min`：使用流式计算时的最小值。
++ `max`：使用流式计算时的最大值。
+
+**输出序列**：输出单个序列，类型为 DOUBLE。
+
+#### 使用示例
+
+##### 全数据计算
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select minmax(s1) from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------+
+| Time|minmax(root.test.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.100+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.200+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.300+08:00| 0.25|
+|1970-01-01T08:00:00.400+08:00| 0.08333333333333333|
+|1970-01-01T08:00:00.500+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.600+08:00| 0.16666666666666666|
+|1970-01-01T08:00:00.700+08:00| 0.0|
+|1970-01-01T08:00:00.800+08:00| 0.3333333333333333|
+|1970-01-01T08:00:00.900+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.000+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.100+08:00| 0.25|
+|1970-01-01T08:00:01.200+08:00| 0.08333333333333333|
+|1970-01-01T08:00:01.300+08:00| 0.08333333333333333|
+|1970-01-01T08:00:01.400+08:00| 0.25|
+|1970-01-01T08:00:01.500+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.600+08:00| 0.16666666666666666|
+|1970-01-01T08:00:01.700+08:00| 1.0|
+|1970-01-01T08:00:01.800+08:00| 0.3333333333333333|
+|1970-01-01T08:00:01.900+08:00| 0.0|
+|1970-01-01T08:00:02.000+08:00| 0.16666666666666666|
++-----------------------------+--------------------+
+```
+
+### Mode
+
+#### 函数简介
+
+本函数用于计算时间序列的众数，即出现次数最多的元素。
+
+**函数名：** MODE
+
+**输入序列：** 仅支持单个输入序列，类型可以是任意的。
+
+**输出序列：** 输出单个序列，类型与输入相同，序列仅包含一个时间戳为众数第一次出现的时间戳、值为众数的数据点。
+
+**提示：**
+
++ 如果有多个出现次数最多的元素，将会输出任意一个。
++ 数据中的空值和缺失值将会被忽略，但`NaN`不会被忽略。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s2|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.001+08:00| Hello|
+|1970-01-01T08:00:00.002+08:00| hello|
+|1970-01-01T08:00:00.003+08:00| Hello|
+|1970-01-01T08:00:00.004+08:00| World|
+|1970-01-01T08:00:00.005+08:00| World|
+|1970-01-01T08:00:01.600+08:00| World|
+|1970-01-15T09:37:34.451+08:00| Hello|
+|1970-01-15T09:37:34.452+08:00| hello|
+|1970-01-15T09:37:34.453+08:00| Hello|
+|1970-01-15T09:37:34.454+08:00| World|
+|1970-01-15T09:37:34.455+08:00| World|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select mode(s2) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+---------------------+
+| Time|mode(root.test.d2.s2)|
++-----------------------------+---------------------+
+|1970-01-01T08:00:00.004+08:00| World|
++-----------------------------+---------------------+
+```
+
+### MvAvg
+
+#### 函数简介
+
+本函数计算序列的移动平均。
+
+**函数名：** MVAVG
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `window`：移动窗口的长度。默认值为 10.
+
+**输出序列**：输出单个序列，类型为 DOUBLE。
+
+#### 使用示例
+
+##### 指定窗口长度
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select mvavg(s1, "window"="3") from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+---------------------------------+
+| Time|mvavg(root.test.s1, "window"="3")|
++-----------------------------+---------------------------------+
+|1970-01-01T08:00:00.300+08:00| 0.3333333333333333|
+|1970-01-01T08:00:00.400+08:00| 0.0|
+|1970-01-01T08:00:00.500+08:00| -0.3333333333333333|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -0.6666666666666666|
+|1970-01-01T08:00:00.800+08:00| 0.0|
+|1970-01-01T08:00:00.900+08:00| 0.6666666666666666|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 0.3333333333333333|
+|1970-01-01T08:00:01.200+08:00| 0.0|
+|1970-01-01T08:00:01.300+08:00| -0.6666666666666666|
+|1970-01-01T08:00:01.400+08:00| 0.0|
+|1970-01-01T08:00:01.500+08:00| 0.3333333333333333|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 3.3333333333333335|
+|1970-01-01T08:00:01.800+08:00| 4.0|
+|1970-01-01T08:00:01.900+08:00| 0.0|
+|1970-01-01T08:00:02.000+08:00| -0.6666666666666666|
++-----------------------------+---------------------------------+
+```
+
+### PACF
+
+#### 函数简介
+
+本函数通过求解 Yule-Walker 方程，计算序列的偏自相关系数。对于特殊的输入序列，方程可能没有解，此时输出`NaN`。
+
+**函数名：** PACF
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `lag`：最大滞后阶数。默认值为$\min(10\log_{10}n,n-1)$，$n$表示数据点个数。
+
+**输出序列**：输出单个序列，类型为 DOUBLE。
+
+#### 使用示例
+
+##### 指定滞后阶数
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|2019-12-27T00:00:00.000+08:00| 5.0|
+|2019-12-27T00:05:00.000+08:00| 5.0|
+|2019-12-27T00:10:00.000+08:00| 5.0|
+|2019-12-27T00:15:00.000+08:00| 5.0|
+|2019-12-27T00:20:00.000+08:00| 6.0|
+|2019-12-27T00:25:00.000+08:00| 5.0|
+|2019-12-27T00:30:00.000+08:00| 6.0|
+|2019-12-27T00:35:00.000+08:00| 6.0|
+|2019-12-27T00:40:00.000+08:00| 6.0|
+|2019-12-27T00:45:00.000+08:00| 6.0|
+|2019-12-27T00:50:00.000+08:00| 6.0|
+|2019-12-27T00:55:00.000+08:00| 5.982609|
+|2019-12-27T01:00:00.000+08:00| 5.9652176|
+|2019-12-27T01:05:00.000+08:00| 5.947826|
+|2019-12-27T01:10:00.000+08:00| 5.9304347|
+|2019-12-27T01:15:00.000+08:00| 5.9130435|
+|2019-12-27T01:20:00.000+08:00| 5.8956523|
+|2019-12-27T01:25:00.000+08:00| 5.878261|
+|2019-12-27T01:30:00.000+08:00| 5.8608694|
+|2019-12-27T01:35:00.000+08:00| 5.843478|
+............
+Total line number = 18066
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select pacf(s1, "lag"="5") from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------------+
+| Time|pacf(root.test.s1, "lag"="5")|
++-----------------------------+-----------------------------+
+|2019-12-27T00:00:00.000+08:00| 1.0|
+|2019-12-27T00:05:00.000+08:00| 0.3528915091942786|
+|2019-12-27T00:10:00.000+08:00| 0.1761346122516304|
+|2019-12-27T00:15:00.000+08:00| 0.1492391973294682|
+|2019-12-27T00:20:00.000+08:00| 0.03560059645868398|
+|2019-12-27T00:25:00.000+08:00| 0.0366222998995286|
++-----------------------------+-----------------------------+
+```
+
+### Percentile
+
+#### 函数简介
+
+本函数用于计算单列数值型数据的精确或近似分位数。
+
+**函数名：** PERCENTILE
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `rank`：所求分位数在所有数据中的排名百分比，取值范围为 (0,1]，默认值为 0.5。如当设为 0.5时则计算中位数。
++ `error`：近似分位数的基于排名的误差百分比，取值范围为 [0,1)，默认值为0。如`rank`=0.5 且`error`=0.01，则计算出的分位数的真实排名百分比在 0.49~0.51之间。当`error`=0 时，计算结果为精确分位数。
+
+**输出序列：** 输出单个序列，类型与输入序列相同。当`error`=0时，序列仅包含一个时间戳为分位数第一次出现的时间戳、值为分位数的数据点；否则，输出值的时间戳为0。
+
+**提示：** 数据中的空值、缺失值和`NaN`将会被忽略。
+
+#### 使用示例
+
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|2021-03-17T10:32:17.054+08:00| 0.5319929|
+|2021-03-17T10:32:18.054+08:00| 0.9304316|
+|2021-03-17T10:32:19.054+08:00| -1.4800133|
+|2021-03-17T10:32:20.054+08:00| 0.6114087|
+|2021-03-17T10:32:21.054+08:00| 2.5163336|
+|2021-03-17T10:32:22.054+08:00| -1.0845392|
+|2021-03-17T10:32:23.054+08:00| 1.0562582|
+|2021-03-17T10:32:24.054+08:00| 1.3867859|
+|2021-03-17T10:32:25.054+08:00| -0.45429882|
+|2021-03-17T10:32:26.054+08:00| 1.0353678|
+|2021-03-17T10:32:27.054+08:00| 0.7307929|
+|2021-03-17T10:32:28.054+08:00| 2.3167255|
+|2021-03-17T10:32:29.054+08:00| 2.342443|
+|2021-03-17T10:32:30.054+08:00| 1.5809103|
+|2021-03-17T10:32:31.054+08:00| 1.4829416|
+|2021-03-17T10:32:32.054+08:00| 1.5800357|
+|2021-03-17T10:32:33.054+08:00| 0.7124368|
+|2021-03-17T10:32:34.054+08:00| -0.78597564|
+|2021-03-17T10:32:35.054+08:00| 1.2058644|
+|2021-03-17T10:32:36.054+08:00| 1.4215064|
+|2021-03-17T10:32:37.054+08:00| 1.2808295|
+|2021-03-17T10:32:38.054+08:00| -0.6173715|
+|2021-03-17T10:32:39.054+08:00| 0.06644377|
+|2021-03-17T10:32:40.054+08:00| 2.349338|
+|2021-03-17T10:32:41.054+08:00| 1.7335888|
+|2021-03-17T10:32:42.054+08:00| 1.5872132|
+............
+Total line number = 10000
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select percentile(s0, "rank"="0.2", "error"="0.01") from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|percentile(root.test.s0, "rank"="0.2", "error"="0.01")|
++-----------------------------+------------------------------------------------------+
+|2021-03-17T10:35:02.054+08:00| 0.1801469624042511|
++-----------------------------+------------------------------------------------------+
+```
+
+### Period
+
+#### 函数简介
+
+本函数用于计算单列数值型数据的周期。
+
+**函数名：** PERIOD
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**输出序列：** 输出单个序列，类型为 INT32，序列仅包含一个时间戳为 0、值为周期的数据点。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d3.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.001+08:00| 1.0|
+|1970-01-01T08:00:00.002+08:00| 2.0|
+|1970-01-01T08:00:00.003+08:00| 3.0|
+|1970-01-01T08:00:00.004+08:00| 1.0|
+|1970-01-01T08:00:00.005+08:00| 2.0|
+|1970-01-01T08:00:00.006+08:00| 3.0|
+|1970-01-01T08:00:00.007+08:00| 1.0|
+|1970-01-01T08:00:00.008+08:00| 2.0|
+|1970-01-01T08:00:00.009+08:00| 3.0|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select period(s1) from root.test.d3
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------+
+| Time|period(root.test.d3.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| 3|
++-----------------------------+-----------------------+
+```
+
+### QLB
+
+#### 函数简介
+
+本函数对输入序列计算$Q_{LB} $统计量，并计算对应的p值。p值越小表明序列越有可能为非平稳序列。
+
+**函数名：** QLB
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `lag`：计算时用到的最大延迟阶数，取值应为 1 至 n-2 之间的整数，n 为序列采样总数。默认取 n-2。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。该序列是$Q_{LB} $统计量对应的 p 值，时间标签代表偏移阶数。
+
+**提示：** $Q_{LB} $统计量由自相关系数求得，如需得到统计量而非 p 值，可以使用 ACF 函数。
+
+#### 使用示例
+
+##### 使用默认参数
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T00:00:00.100+08:00| 1.22|
+|1970-01-01T00:00:00.200+08:00| -2.78|
+|1970-01-01T00:00:00.300+08:00| 1.53|
+|1970-01-01T00:00:00.400+08:00| 0.70|
+|1970-01-01T00:00:00.500+08:00| 0.75|
+|1970-01-01T00:00:00.600+08:00| -0.72|
+|1970-01-01T00:00:00.700+08:00| -0.22|
+|1970-01-01T00:00:00.800+08:00| 0.28|
+|1970-01-01T00:00:00.900+08:00| 0.57|
+|1970-01-01T00:00:01.000+08:00| -0.22|
+|1970-01-01T00:00:01.100+08:00| -0.72|
+|1970-01-01T00:00:01.200+08:00| 1.34|
+|1970-01-01T00:00:01.300+08:00| -0.25|
+|1970-01-01T00:00:01.400+08:00| 0.17|
+|1970-01-01T00:00:01.500+08:00| 2.51|
+|1970-01-01T00:00:01.600+08:00| 1.42|
+|1970-01-01T00:00:01.700+08:00| -1.34|
+|1970-01-01T00:00:01.800+08:00| -0.01|
+|1970-01-01T00:00:01.900+08:00| -0.49|
+|1970-01-01T00:00:02.000+08:00| 1.63|
++-----------------------------+---------------+
+```
+
+
+用于查询的 SQL 语句：
+
+```sql
+select QLB(s1) from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------+
+| Time|QLB(root.test.d1.s1)|
++-----------------------------+--------------------+
+|1970-01-01T00:00:00.001+08:00| 0.2168702295315677|
+|1970-01-01T00:00:00.002+08:00| 0.3068948509261751|
+|1970-01-01T00:00:00.003+08:00| 0.4217859150918444|
+|1970-01-01T00:00:00.004+08:00| 0.5114539874276656|
+|1970-01-01T00:00:00.005+08:00| 0.6560619525616759|
+|1970-01-01T00:00:00.006+08:00| 0.7722398654053280|
+|1970-01-01T00:00:00.007+08:00| 0.8532491661465290|
+|1970-01-01T00:00:00.008+08:00| 0.9028575017542528|
+|1970-01-01T00:00:00.009+08:00| 0.9434989988192729|
+|1970-01-01T00:00:00.010+08:00| 0.8950280161464689|
+|1970-01-01T00:00:00.011+08:00| 0.7701048398839656|
+|1970-01-01T00:00:00.012+08:00| 0.7845536060001281|
+|1970-01-01T00:00:00.013+08:00| 0.5943030981705825|
+|1970-01-01T00:00:00.014+08:00| 0.4618413512531093|
+|1970-01-01T00:00:00.015+08:00| 0.2645948244673964|
+|1970-01-01T00:00:00.016+08:00| 0.3167530476666645|
+|1970-01-01T00:00:00.017+08:00| 0.2330010780351453|
+|1970-01-01T00:00:00.018+08:00| 0.0666611237622325|
++-----------------------------+--------------------+
+```
+
+### Resample
+
+#### 函数简介
+
+本函数对输入序列按照指定的频率进行重采样，包括上采样和下采样。目前，本函数支持的上采样方法包括`NaN`填充法 (NaN)、前值填充法 (FFill)、后值填充法 (BFill) 以及线性插值法 (Linear)；本函数支持的下采样方法为分组聚合，聚合方法包括最大值 (Max)、最小值 (Min)、首值 (First)、末值 (Last)、平均值 (Mean)和中位数 (Median)。
+
+**函数名：** RESAMPLE
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `every`：重采样频率，是一个有单位的正数。目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。该参数不允许缺省。
++ `interp`：上采样的插值方法，取值为 'NaN'、'FFill'、'BFill' 或 'Linear'。在缺省情况下，使用`NaN`填充法。
++ `aggr`：下采样的聚合方法，取值为 'Max'、'Min'、'First'、'Last'、'Mean' 或 'Median'。在缺省情况下，使用平均数聚合。
++ `start`：重采样的起始时间（包含），是一个格式为 'yyyy-MM-dd HH:mm:ss' 的时间字符串。在缺省情况下，使用第一个有效数据点的时间戳。
++ `end`：重采样的结束时间（不包含），是一个格式为 'yyyy-MM-dd HH:mm:ss' 的时间字符串。在缺省情况下，使用最后一个有效数据点的时间戳。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。该序列按照重采样频率严格等间隔分布。
+
+**提示：** 数据中的`NaN`将会被忽略。
+
+#### 使用示例
+
+##### 上采样
+
+当重采样频率高于数据原始频率时，将会进行上采样。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2021-03-06T16:00:00.000+08:00| 3.09|
+|2021-03-06T16:15:00.000+08:00| 3.53|
+|2021-03-06T16:30:00.000+08:00| 3.5|
+|2021-03-06T16:45:00.000+08:00| 3.51|
+|2021-03-06T17:00:00.000+08:00| 3.41|
++-----------------------------+---------------+
+```
+
+
+用于查询的 SQL 语句：
+
+```sql
+select resample(s1,'every'='5m','interp'='linear') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------------------------------------------+
+| Time|resample(root.test.d1.s1, "every"="5m", "interp"="linear")|
++-----------------------------+----------------------------------------------------------+
+|2021-03-06T16:00:00.000+08:00| 3.0899999141693115|
+|2021-03-06T16:05:00.000+08:00| 3.2366665999094644|
+|2021-03-06T16:10:00.000+08:00| 3.3833332856496177|
+|2021-03-06T16:15:00.000+08:00| 3.5299999713897705|
+|2021-03-06T16:20:00.000+08:00| 3.5199999809265137|
+|2021-03-06T16:25:00.000+08:00| 3.509999990463257|
+|2021-03-06T16:30:00.000+08:00| 3.5|
+|2021-03-06T16:35:00.000+08:00| 3.503333330154419|
+|2021-03-06T16:40:00.000+08:00| 3.506666660308838|
+|2021-03-06T16:45:00.000+08:00| 3.509999990463257|
+|2021-03-06T16:50:00.000+08:00| 3.4766666889190674|
+|2021-03-06T16:55:00.000+08:00| 3.443333387374878|
+|2021-03-06T17:00:00.000+08:00| 3.4100000858306885|
++-----------------------------+----------------------------------------------------------+
+```
+
+##### 下采样
+
+当重采样频率低于数据原始频率时，将会进行下采样。
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select resample(s1,'every'='30m','aggr'='first') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------------------------------------------+
+| Time|resample(root.test.d1.s1, "every"="30m", "aggr"="first")|
++-----------------------------+--------------------------------------------------------+
+|2021-03-06T16:00:00.000+08:00| 3.0899999141693115|
+|2021-03-06T16:30:00.000+08:00| 3.5|
+|2021-03-06T17:00:00.000+08:00| 3.4100000858306885|
++-----------------------------+--------------------------------------------------------+
+```
+
+
+##### 指定重采样时间段
+
+可以使用`start`和`end`两个参数指定重采样的时间段，超出实际时间范围的部分会被插值填补。
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select resample(s1,'every'='30m','start'='2021-03-06 15:00:00') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------------------------------------------------------+
+| Time|resample(root.test.d1.s1, "every"="30m", "start"="2021-03-06 15:00:00")|
++-----------------------------+-----------------------------------------------------------------------+
+|2021-03-06T15:00:00.000+08:00| NaN|
+|2021-03-06T15:30:00.000+08:00| NaN|
+|2021-03-06T16:00:00.000+08:00| 3.309999942779541|
+|2021-03-06T16:30:00.000+08:00| 3.5049999952316284|
+|2021-03-06T17:00:00.000+08:00| 3.4100000858306885|
++-----------------------------+-----------------------------------------------------------------------+
+```
+
+### Sample
+
+#### 函数简介
+
+本函数对输入序列进行采样，即从输入序列中选取指定数量的数据点并输出。目前，本函数支持两种采样方法：**蓄水池采样法 (reservoir sampling)** 对数据进行随机采样，所有数据点被采样的概率相同；**等距采样法 (isometric sampling)** 按照相等的索引间隔对数据进行采样。
+
+**函数名：** SAMPLE
+
+**输入序列：** 仅支持单个输入序列，类型可以是任意的。
+
+**参数：**
+
++ `method`：采样方法，取值为 'reservoir' 或' isometric'。在缺省情况下，采用蓄水池采样法。
++ `k`：采样数，它是一个正整数，在缺省情况下为 1。
+
+**输出序列：** 输出单个序列，类型与输入序列相同。该序列的长度为采样数，序列中的每一个数据点都来自于输入序列。
+
+**提示：** 如果采样数大于序列长度，那么输入序列中所有的数据点都会被输出。
+
+#### 使用示例
+
+
+##### 蓄水池采样
+
+当`method`参数为 'reservoir' 或缺省时，采用蓄水池采样法对输入序列进行采样。由于该采样方法具有随机性，下面展示的输出序列只是一种可能的结果。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:01.000+08:00| 1.0|
+|2020-01-01T00:00:02.000+08:00| 2.0|
+|2020-01-01T00:00:03.000+08:00| 3.0|
+|2020-01-01T00:00:04.000+08:00| 4.0|
+|2020-01-01T00:00:05.000+08:00| 5.0|
+|2020-01-01T00:00:06.000+08:00| 6.0|
+|2020-01-01T00:00:07.000+08:00| 7.0|
+|2020-01-01T00:00:08.000+08:00| 8.0|
+|2020-01-01T00:00:09.000+08:00| 9.0|
+|2020-01-01T00:00:10.000+08:00| 10.0|
++-----------------------------+---------------+
+```
+
+
+用于查询的 SQL 语句：
+
+```sql
+select sample(s1,'method'='reservoir','k'='5') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|sample(root.test.d1.s1, "method"="reservoir", "k"="5")|
++-----------------------------+------------------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 2.0|
+|2020-01-01T00:00:03.000+08:00| 3.0|
+|2020-01-01T00:00:05.000+08:00| 5.0|
+|2020-01-01T00:00:08.000+08:00| 8.0|
+|2020-01-01T00:00:10.000+08:00| 10.0|
++-----------------------------+------------------------------------------------------+
+```
+
+
+##### 等距采样
+
+当`method`参数为 'isometric' 时，采用等距采样法对输入序列进行采样。
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select sample(s1,'method'='isometric','k'='5') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|sample(root.test.d1.s1, "method"="isometric", "k"="5")|
++-----------------------------+------------------------------------------------------+
+|2020-01-01T00:00:01.000+08:00| 1.0|
+|2020-01-01T00:00:03.000+08:00| 3.0|
+|2020-01-01T00:00:05.000+08:00| 5.0|
+|2020-01-01T00:00:07.000+08:00| 7.0|
+|2020-01-01T00:00:09.000+08:00| 9.0|
++-----------------------------+------------------------------------------------------+
+```
+
+### Segment
+
+#### 函数简介
+
+本函数按照数据的线性变化趋势将数据划分为多个子序列，返回分段直线拟合后的子序列首值或所有拟合值。
+
+**函数名：** SEGMENT
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `output`："all" 输出所有拟合值；"first" 输出子序列起点拟合值。默认为 "first"。
+
++ `error`：判定存在线性趋势的误差允许阈值。误差的定义为子序列进行线性拟合的误差的绝对值的均值。默认为 0.1.
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。
+
+**提示：** 函数默认所有数据等时间间隔分布。函数读取所有数据，若原始数据过多，请先进行降采样处理。拟合采用自底向上方法，子序列的尾值可能会被认作子序列首值输出。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 5.0|
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 1.0|
+|1970-01-01T08:00:00.300+08:00| 2.0|
+|1970-01-01T08:00:00.400+08:00| 3.0|
+|1970-01-01T08:00:00.500+08:00| 4.0|
+|1970-01-01T08:00:00.600+08:00| 5.0|
+|1970-01-01T08:00:00.700+08:00| 6.0|
+|1970-01-01T08:00:00.800+08:00| 7.0|
+|1970-01-01T08:00:00.900+08:00| 8.0|
+|1970-01-01T08:00:01.000+08:00| 9.0|
+|1970-01-01T08:00:01.100+08:00| 9.1|
+|1970-01-01T08:00:01.200+08:00| 9.2|
+|1970-01-01T08:00:01.300+08:00| 9.3|
+|1970-01-01T08:00:01.400+08:00| 9.4|
+|1970-01-01T08:00:01.500+08:00| 9.5|
+|1970-01-01T08:00:01.600+08:00| 9.6|
+|1970-01-01T08:00:01.700+08:00| 9.7|
+|1970-01-01T08:00:01.800+08:00| 9.8|
+|1970-01-01T08:00:01.900+08:00| 9.9|
+|1970-01-01T08:00:02.000+08:00| 10.0|
+|1970-01-01T08:00:02.100+08:00| 8.0|
+|1970-01-01T08:00:02.200+08:00| 6.0|
+|1970-01-01T08:00:02.300+08:00| 4.0|
+|1970-01-01T08:00:02.400+08:00| 2.0|
+|1970-01-01T08:00:02.500+08:00| 0.0|
+|1970-01-01T08:00:02.600+08:00| -2.0|
+|1970-01-01T08:00:02.700+08:00| -4.0|
+|1970-01-01T08:00:02.800+08:00| -6.0|
+|1970-01-01T08:00:02.900+08:00| -8.0|
+|1970-01-01T08:00:03.000+08:00| -10.0|
+|1970-01-01T08:00:03.100+08:00| 10.0|
+|1970-01-01T08:00:03.200+08:00| 10.0|
+|1970-01-01T08:00:03.300+08:00| 10.0|
+|1970-01-01T08:00:03.400+08:00| 10.0|
+|1970-01-01T08:00:03.500+08:00| 10.0|
+|1970-01-01T08:00:03.600+08:00| 10.0|
+|1970-01-01T08:00:03.700+08:00| 10.0|
+|1970-01-01T08:00:03.800+08:00| 10.0|
+|1970-01-01T08:00:03.900+08:00| 10.0|
++-----------------------------+------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select segment(s1,"error"="0.1") from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------+
+| Time|segment(root.test.s1, "error"="0.1")|
++-----------------------------+------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 5.0|
+|1970-01-01T08:00:00.200+08:00| 1.0|
+|1970-01-01T08:00:01.000+08:00| 9.0|
+|1970-01-01T08:00:02.000+08:00| 10.0|
+|1970-01-01T08:00:03.000+08:00| -10.0|
+|1970-01-01T08:00:03.200+08:00| 10.0|
++-----------------------------+------------------------------------+
+```
+
+### Skew
+
+#### 函数简介
+
+本函数用于计算单列数值型数据的总体偏度
+
+**函数名：** SKEW
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**输出序列：** 输出单个序列，类型为 DOUBLE，序列仅包含一个时间戳为 0、值为总体偏度的数据点。
+
+**提示：** 数据中的空值、缺失值和`NaN`将会被忽略。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0|
+|2020-01-01T00:00:01.000+08:00| 2.0|
+|2020-01-01T00:00:02.000+08:00| 3.0|
+|2020-01-01T00:00:03.000+08:00| 4.0|
+|2020-01-01T00:00:04.000+08:00| 5.0|
+|2020-01-01T00:00:05.000+08:00| 6.0|
+|2020-01-01T00:00:06.000+08:00| 7.0|
+|2020-01-01T00:00:07.000+08:00| 8.0|
+|2020-01-01T00:00:08.000+08:00| 9.0|
+|2020-01-01T00:00:09.000+08:00| 10.0|
+|2020-01-01T00:00:10.000+08:00| 10.0|
+|2020-01-01T00:00:11.000+08:00| 10.0|
+|2020-01-01T00:00:12.000+08:00| 10.0|
+|2020-01-01T00:00:13.000+08:00| 10.0|
+|2020-01-01T00:00:14.000+08:00| 10.0|
+|2020-01-01T00:00:15.000+08:00| 10.0|
+|2020-01-01T00:00:16.000+08:00| 10.0|
+|2020-01-01T00:00:17.000+08:00| 10.0|
+|2020-01-01T00:00:18.000+08:00| 10.0|
+|2020-01-01T00:00:19.000+08:00| 10.0|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select skew(s1) from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------+
+| Time| skew(root.test.d1.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| -0.9998427402292644|
++-----------------------------+-----------------------+
+```
+
+### Spline
+
+#### 函数简介
+
+本函数提供对原始序列进行三次样条曲线拟合后的插值重采样。
+
+**函数名：** SPLINE
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `points`：重采样个数。
+
+**输出序列**：输出单个序列，类型为 DOUBLE。
+
+**提示**：输出序列保留输入序列的首尾值，等时间间隔采样。仅当输入点个数不少于 4 个时才计算插值。
+
+#### 使用示例
+
+##### 指定插值个数
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.2|
+|1970-01-01T08:00:00.500+08:00| 1.7|
+|1970-01-01T08:00:00.700+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 2.1|
+|1970-01-01T08:00:01.100+08:00| 2.0|
+|1970-01-01T08:00:01.200+08:00| 1.8|
+|1970-01-01T08:00:01.300+08:00| 1.2|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 1.6|
++-----------------------------+------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select spline(s1, "points"="151") from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------+
+| Time|spline(root.test.s1, "points"="151")|
++-----------------------------+------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.010+08:00| 0.04870000251134237|
+|1970-01-01T08:00:00.020+08:00| 0.09680000495910646|
+|1970-01-01T08:00:00.030+08:00| 0.14430000734329226|
+|1970-01-01T08:00:00.040+08:00| 0.19120000966389972|
+|1970-01-01T08:00:00.050+08:00| 0.23750001192092896|
+|1970-01-01T08:00:00.060+08:00| 0.2832000141143799|
+|1970-01-01T08:00:00.070+08:00| 0.32830001624425253|
+|1970-01-01T08:00:00.080+08:00| 0.3728000183105469|
+|1970-01-01T08:00:00.090+08:00| 0.416700020313263|
+|1970-01-01T08:00:00.100+08:00| 0.4600000222524008|
+|1970-01-01T08:00:00.110+08:00| 0.5027000241279602|
+|1970-01-01T08:00:00.120+08:00| 0.5448000259399414|
+|1970-01-01T08:00:00.130+08:00| 0.5863000276883443|
+|1970-01-01T08:00:00.140+08:00| 0.627200029373169|
+|1970-01-01T08:00:00.150+08:00| 0.6675000309944153|
+|1970-01-01T08:00:00.160+08:00| 0.7072000325520833|
+|1970-01-01T08:00:00.170+08:00| 0.7463000340461731|
+|1970-01-01T08:00:00.180+08:00| 0.7848000354766846|
+|1970-01-01T08:00:00.190+08:00| 0.8227000368436178|
+|1970-01-01T08:00:00.200+08:00| 0.8600000381469728|
+|1970-01-01T08:00:00.210+08:00| 0.8967000393867494|
+|1970-01-01T08:00:00.220+08:00| 0.9328000405629477|
+|1970-01-01T08:00:00.230+08:00| 0.9683000416755676|
+|1970-01-01T08:00:00.240+08:00| 1.0032000427246095|
+|1970-01-01T08:00:00.250+08:00| 1.037500043710073|
+|1970-01-01T08:00:00.260+08:00| 1.071200044631958|
+|1970-01-01T08:00:00.270+08:00| 1.1043000454902647|
+|1970-01-01T08:00:00.280+08:00| 1.1368000462849934|
+|1970-01-01T08:00:00.290+08:00| 1.1687000470161437|
+|1970-01-01T08:00:00.300+08:00| 1.2000000476837158|
+|1970-01-01T08:00:00.310+08:00| 1.2307000483103594|
+|1970-01-01T08:00:00.320+08:00| 1.2608000489139557|
+|1970-01-01T08:00:00.330+08:00| 1.2903000494873524|
+|1970-01-01T08:00:00.340+08:00| 1.3192000500233967|
+|1970-01-01T08:00:00.350+08:00| 1.3475000505149364|
+|1970-01-01T08:00:00.360+08:00| 1.3752000509548186|
+|1970-01-01T08:00:00.370+08:00| 1.402300051335891|
+|1970-01-01T08:00:00.380+08:00| 1.4288000516510009|
+|1970-01-01T08:00:00.390+08:00| 1.4547000518929958|
+|1970-01-01T08:00:00.400+08:00| 1.480000052054723|
+|1970-01-01T08:00:00.410+08:00| 1.5047000521290301|
+|1970-01-01T08:00:00.420+08:00| 1.5288000521087646|
+|1970-01-01T08:00:00.430+08:00| 1.5523000519867738|
+|1970-01-01T08:00:00.440+08:00| 1.575200051755905|
+|1970-01-01T08:00:00.450+08:00| 1.597500051409006|
+|1970-01-01T08:00:00.460+08:00| 1.619200050938924|
+|1970-01-01T08:00:00.470+08:00| 1.6403000503385066|
+|1970-01-01T08:00:00.480+08:00| 1.660800049600601|
+|1970-01-01T08:00:00.490+08:00| 1.680700048718055|
+|1970-01-01T08:00:00.500+08:00| 1.7000000476837158|
+|1970-01-01T08:00:00.510+08:00| 1.7188475466453037|
+|1970-01-01T08:00:00.520+08:00| 1.7373800457262996|
+|1970-01-01T08:00:00.530+08:00| 1.7555825448831923|
+|1970-01-01T08:00:00.540+08:00| 1.7734400440724702|
+|1970-01-01T08:00:00.550+08:00| 1.790937543250622|
+|1970-01-01T08:00:00.560+08:00| 1.8080600423741364|
+|1970-01-01T08:00:00.570+08:00| 1.8247925413995016|
+|1970-01-01T08:00:00.580+08:00| 1.8411200402832066|
+|1970-01-01T08:00:00.590+08:00| 1.8570275389817397|
+|1970-01-01T08:00:00.600+08:00| 1.8725000374515897|
+|1970-01-01T08:00:00.610+08:00| 1.8875225356492449|
+|1970-01-01T08:00:00.620+08:00| 1.902080033531194|
+|1970-01-01T08:00:00.630+08:00| 1.9161575310539258|
+|1970-01-01T08:00:00.640+08:00| 1.9297400281739288|
+|1970-01-01T08:00:00.650+08:00| 1.9428125248476913|
+|1970-01-01T08:00:00.660+08:00| 1.9553600210317021|
+|1970-01-01T08:00:00.670+08:00| 1.96736751668245|
+|1970-01-01T08:00:00.680+08:00| 1.9788200117564232|
+|1970-01-01T08:00:00.690+08:00| 1.9897025062101101|
+|1970-01-01T08:00:00.700+08:00| 2.0|
+|1970-01-01T08:00:00.710+08:00| 2.0097024933913334|
+|1970-01-01T08:00:00.720+08:00| 2.0188199867081615|
+|1970-01-01T08:00:00.730+08:00| 2.027367479995188|
+|1970-01-01T08:00:00.740+08:00| 2.0353599732971155|
+|1970-01-01T08:00:00.750+08:00| 2.0428124666586482|
+|1970-01-01T08:00:00.760+08:00| 2.049739960124489|
+|1970-01-01T08:00:00.770+08:00| 2.056157453739342|
+|1970-01-01T08:00:00.780+08:00| 2.06207994754791|
+|1970-01-01T08:00:00.790+08:00| 2.067522441594897|
+|1970-01-01T08:00:00.800+08:00| 2.072499935925006|
+|1970-01-01T08:00:00.810+08:00| 2.07702743058294|
+|1970-01-01T08:00:00.820+08:00| 2.081119925613404|
+|1970-01-01T08:00:00.830+08:00| 2.0847924210611|
+|1970-01-01T08:00:00.840+08:00| 2.0880599169707317|
+|1970-01-01T08:00:00.850+08:00| 2.0909374133870027|
+|1970-01-01T08:00:00.860+08:00| 2.0934399103546166|
+|1970-01-01T08:00:00.870+08:00| 2.0955824079182768|
+|1970-01-01T08:00:00.880+08:00| 2.0973799061226863|
+|1970-01-01T08:00:00.890+08:00| 2.098847405012549|
+|1970-01-01T08:00:00.900+08:00| 2.0999999046325684|
+|1970-01-01T08:00:00.910+08:00| 2.1005574051201332|
+|1970-01-01T08:00:00.920+08:00| 2.1002599065303778|
+|1970-01-01T08:00:00.930+08:00| 2.0991524087846245|
+|1970-01-01T08:00:00.940+08:00| 2.0972799118041947|
+|1970-01-01T08:00:00.950+08:00| 2.0946874155104105|
+|1970-01-01T08:00:00.960+08:00| 2.0914199198245944|
+|1970-01-01T08:00:00.970+08:00| 2.0875224246680673|
+|1970-01-01T08:00:00.980+08:00| 2.083039929962151|
+|1970-01-01T08:00:00.990+08:00| 2.0780174356281687|
+|1970-01-01T08:00:01.000+08:00| 2.0724999415874406|
+|1970-01-01T08:00:01.010+08:00| 2.06653244776129|
+|1970-01-01T08:00:01.020+08:00| 2.060159954071038|
+|1970-01-01T08:00:01.030+08:00| 2.053427460438006|
+|1970-01-01T08:00:01.040+08:00| 2.046379966783517|
+|1970-01-01T08:00:01.050+08:00| 2.0390624730288924|
+|1970-01-01T08:00:01.060+08:00| 2.031519979095454|
+|1970-01-01T08:00:01.070+08:00| 2.0237974849045237|
+|1970-01-01T08:00:01.080+08:00| 2.015939990377423|
+|1970-01-01T08:00:01.090+08:00| 2.0079924954354746|
+|1970-01-01T08:00:01.100+08:00| 2.0|
+|1970-01-01T08:00:01.110+08:00| 1.9907018211101906|
+|1970-01-01T08:00:01.120+08:00| 1.9788509124245144|
+|1970-01-01T08:00:01.130+08:00| 1.9645127287932083|
+|1970-01-01T08:00:01.140+08:00| 1.9477527250665083|
+|1970-01-01T08:00:01.150+08:00| 1.9286363560946513|
+|1970-01-01T08:00:01.160+08:00| 1.9072290767278735|
+|1970-01-01T08:00:01.170+08:00| 1.8835963418164114|
+|1970-01-01T08:00:01.180+08:00| 1.8578036062105014|
+|1970-01-01T08:00:01.190+08:00| 1.8299163247603802|
+|1970-01-01T08:00:01.200+08:00| 1.7999999523162842|
+|1970-01-01T08:00:01.210+08:00| 1.7623635841923329|
+|1970-01-01T08:00:01.220+08:00| 1.7129696477516976|
+|1970-01-01T08:00:01.230+08:00| 1.6543635959181928|
+|1970-01-01T08:00:01.240+08:00| 1.5890908816156328|
+|1970-01-01T08:00:01.250+08:00| 1.5196969577678319|
+|1970-01-01T08:00:01.260+08:00| 1.4487272772986044|
+|1970-01-01T08:00:01.270+08:00| 1.3787272931317647|
+|1970-01-01T08:00:01.280+08:00| 1.3122424581911272|
+|1970-01-01T08:00:01.290+08:00| 1.251818225400506|
+|1970-01-01T08:00:01.300+08:00| 1.2000000476837158|
+|1970-01-01T08:00:01.310+08:00| 1.1548000470995912|
+|1970-01-01T08:00:01.320+08:00| 1.1130667107899999|
+|1970-01-01T08:00:01.330+08:00| 1.0756000393033045|
+|1970-01-01T08:00:01.340+08:00| 1.043200033187868|
+|1970-01-01T08:00:01.350+08:00| 1.016666692992053|
+|1970-01-01T08:00:01.360+08:00| 0.9968000192642223|
+|1970-01-01T08:00:01.370+08:00| 0.9844000125527389|
+|1970-01-01T08:00:01.380+08:00| 0.9802666734059655|
+|1970-01-01T08:00:01.390+08:00| 0.9852000023722649|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.410+08:00| 1.023999999165535|
+|1970-01-01T08:00:01.420+08:00| 1.0559999990463256|
+|1970-01-01T08:00:01.430+08:00| 1.0959999996423722|
+|1970-01-01T08:00:01.440+08:00| 1.1440000009536744|
+|1970-01-01T08:00:01.450+08:00| 1.2000000029802322|
+|1970-01-01T08:00:01.460+08:00| 1.264000005722046|
+|1970-01-01T08:00:01.470+08:00| 1.3360000091791153|
+|1970-01-01T08:00:01.480+08:00| 1.4160000133514405|
+|1970-01-01T08:00:01.490+08:00| 1.5040000182390214|
+|1970-01-01T08:00:01.500+08:00| 1.600000023841858|
++-----------------------------+------------------------------------+
+```
+
+### Spread
+
+#### 函数简介
+
+本函数用于计算时间序列的极差，即最大值减去最小值的结果。
+
+**函数名：** SPREAD
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**输出序列：** 输出单个序列，类型与输入相同，序列仅包含一个时间戳为 0 、值为极差的数据点。
+
+**提示：** 数据中的空值、缺失值和`NaN`将会被忽略。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select spread(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------+
+| Time|spread(root.test.d1.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| 26.0|
++-----------------------------+-----------------------+
+```
+
+### Stddev
+
+#### 函数简介
+
+本函数用于计算单列数值型数据的总体标准差。
+
+**函数名：** STDDEV
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。序列仅包含一个时间戳为 0、值为总体标准差的数据点。
+
+**提示：** 数据中的空值、缺失值和`NaN`将会被忽略。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0|
+|2020-01-01T00:00:01.000+08:00| 2.0|
+|2020-01-01T00:00:02.000+08:00| 3.0|
+|2020-01-01T00:00:03.000+08:00| 4.0|
+|2020-01-01T00:00:04.000+08:00| 5.0|
+|2020-01-01T00:00:05.000+08:00| 6.0|
+|2020-01-01T00:00:06.000+08:00| 7.0|
+|2020-01-01T00:00:07.000+08:00| 8.0|
+|2020-01-01T00:00:08.000+08:00| 9.0|
+|2020-01-01T00:00:09.000+08:00| 10.0|
+|2020-01-01T00:00:10.000+08:00| 11.0|
+|2020-01-01T00:00:11.000+08:00| 12.0|
+|2020-01-01T00:00:12.000+08:00| 13.0|
+|2020-01-01T00:00:13.000+08:00| 14.0|
+|2020-01-01T00:00:14.000+08:00| 15.0|
+|2020-01-01T00:00:15.000+08:00| 16.0|
+|2020-01-01T00:00:16.000+08:00| 17.0|
+|2020-01-01T00:00:17.000+08:00| 18.0|
+|2020-01-01T00:00:18.000+08:00| 19.0|
+|2020-01-01T00:00:19.000+08:00| 20.0|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select stddev(s1) from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------+
+| Time|stddev(root.test.d1.s1)|
++-----------------------------+-----------------------+
+|1970-01-01T08:00:00.000+08:00| 5.7662812973353965|
++-----------------------------+-----------------------+
+```
+
+### ZScore
+
+#### 函数简介
+
+本函数将输入序列使用z-score方法进行归一化。
+
+**函数名：** ZSCORE
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `compute`：若设置为 "batch"，则将数据全部读入后转换；若设置为 "stream"，则需用户提供均值及方差进行流式计算转换。默认为 "batch"。
++ `avg`：使用流式计算时的均值。
++ `sd`：使用流式计算时的标准差。
+
+**输出序列**：输出单个序列，类型为 DOUBLE。
+
+#### 使用示例
+
+##### 全数据计算
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select zscore(s1) from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------+
+| Time|zscore(root.test.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.100+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.200+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.300+08:00| 0.20672455764868078|
+|1970-01-01T08:00:00.400+08:00| -0.6201736729460423|
+|1970-01-01T08:00:00.500+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.600+08:00|-0.20672455764868078|
+|1970-01-01T08:00:00.700+08:00| -1.033622788243404|
+|1970-01-01T08:00:00.800+08:00| 0.6201736729460423|
+|1970-01-01T08:00:00.900+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.000+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.100+08:00| 0.20672455764868078|
+|1970-01-01T08:00:01.200+08:00| -0.6201736729460423|
+|1970-01-01T08:00:01.300+08:00| -0.6201736729460423|
+|1970-01-01T08:00:01.400+08:00| 0.20672455764868078|
+|1970-01-01T08:00:01.500+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.600+08:00|-0.20672455764868078|
+|1970-01-01T08:00:01.700+08:00| 3.9277665953249348|
+|1970-01-01T08:00:01.800+08:00| 0.6201736729460423|
+|1970-01-01T08:00:01.900+08:00| -1.033622788243404|
+|1970-01-01T08:00:02.000+08:00|-0.20672455764868078|
++-----------------------------+--------------------+
+```
+
+
+
+## 数据质量
+
+### Completeness
+
+#### 函数简介
+
+本函数用于计算时间序列的完整性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的完整性，并输出窗口第一个数据点的时间戳和窗口的完整性。
+
+**函数名：** COMPLETENESS
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
++ `downtime`：完整性计算是否考虑停机异常。它的取值为 'true' 或 'false'，默认值为 'true'. 在考虑停机异常时，长时间的数据缺失将被视作停机，不对完整性产生影响。
+
+**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+
+**提示：** 只有当窗口内的数据点数目超过10时，才会进行完整性计算。否则，该窗口将被忽略，不做任何输出。
+
+
+#### 使用示例
+
+##### 参数缺省
+
+在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算完整性。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select completeness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------------+
+| Time|completeness(root.test.d1.s1)|
++-----------------------------+-----------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.875|
++-----------------------------+-----------------------------+
+```
+
+##### 指定窗口大小
+
+在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算完整性。
+
+输入序列:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select completeness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------------------------------+
+| Time|completeness(root.test.d1.s1, "window"="15")|
++-----------------------------+--------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.875|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+--------------------------------------------+
+```
+
+### Consistency
+
+#### 函数简介
+
+本函数用于计算时间序列的一致性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的一致性，并输出窗口第一个数据点的时间戳和窗口的时效性。
+
+**函数名：** CONSISTENCY
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
+
+**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+
+**提示：** 只有当窗口内的数据点数目超过10时，才会进行一致性计算。否则，该窗口将被忽略，不做任何输出。
+
+
+#### 使用示例
+
+##### 参数缺省
+
+在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算一致性。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select consistency(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------------+
+| Time|consistency(root.test.d1.s1)|
++-----------------------------+----------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
++-----------------------------+----------------------------+
+```
+
+##### 指定窗口大小
+
+在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算一致性。
+
+输入序列:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select consistency(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------------------------+
+| Time|consistency(root.test.d1.s1, "window"="15")|
++-----------------------------+-------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+-------------------------------------------+
+```
+
+### Timeliness
+
+#### 函数简介
+
+本函数用于计算时间序列的时效性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的时效性，并输出窗口第一个数据点的时间戳和窗口的时效性。
+
+**函数名：** TIMELINESS
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
+
+**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+
+**提示：** 只有当窗口内的数据点数目超过10时，才会进行时效性计算。否则，该窗口将被忽略，不做任何输出。
+
+
+#### 使用示例
+
+##### 参数缺省
+
+在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算时效性。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select timeliness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+输出序列：
+
+```
++-----------------------------+---------------------------+
+| Time|timeliness(root.test.d1.s1)|
++-----------------------------+---------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
++-----------------------------+---------------------------+
+```
+
+##### 指定窗口大小
+
+在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算时效性。
+
+输入序列:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select timeliness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------+
+| Time|timeliness(root.test.d1.s1, "window"="15")|
++-----------------------------+------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+------------------------------------------+
+```
+
+### Validity
+
+#### 函数简介
+
+本函数用于计算时间序列的有效性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的有效性，并输出窗口第一个数据点的时间戳和窗口的有效性。
+
+
+**函数名：** VALIDITY
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
+
+**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+
+**提示：** 只有当窗口内的数据点数目超过10时，才会进行有效性计算。否则，该窗口将被忽略，不做任何输出。
+
+
+#### 使用示例
+
+##### 参数缺省
+
+在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算有效性。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select validity(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------+
+| Time|validity(root.test.d1.s1)|
++-----------------------------+-------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
++-----------------------------+-------------------------+
+```
+
+##### 指定窗口大小
+
+在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算有效性。
+
+输入序列:
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
+|2020-01-01T00:00:32.000+08:00| 130.0|
+|2020-01-01T00:00:34.000+08:00| 132.0|
+|2020-01-01T00:00:36.000+08:00| 134.0|
+|2020-01-01T00:00:38.000+08:00| 136.0|
+|2020-01-01T00:00:40.000+08:00| 138.0|
+|2020-01-01T00:00:42.000+08:00| 140.0|
+|2020-01-01T00:00:44.000+08:00| 142.0|
+|2020-01-01T00:00:46.000+08:00| 144.0|
+|2020-01-01T00:00:48.000+08:00| 146.0|
+|2020-01-01T00:00:50.000+08:00| 148.0|
+|2020-01-01T00:00:52.000+08:00| 150.0|
+|2020-01-01T00:00:54.000+08:00| 152.0|
+|2020-01-01T00:00:56.000+08:00| 154.0|
+|2020-01-01T00:00:58.000+08:00| 156.0|
+|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select validity(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------------------------+
+| Time|validity(root.test.d1.s1, "window"="15")|
++-----------------------------+----------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
+|2020-01-01T00:00:32.000+08:00| 1.0|
++-----------------------------+----------------------------------------+
+```
+
+
+
+## 数据修复
+
+### TimestampRepair
+
+#### 函数简介
+
+本函数用于时间戳修复。根据给定的标准时间间隔，采用最小化修复代价的方法，通过对数据时间戳的微调，将原本时间戳间隔不稳定的数据修复为严格等间隔的数据。在未给定标准时间间隔的情况下，本函数将使用时间间隔的中位数 (median)、众数 (mode) 或聚类中心 (cluster) 来推算标准时间间隔。
+
+
+**函数名：** TIMESTAMPREPAIR
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `interval`: 标准时间间隔（单位是毫秒），是一个正整数。在缺省情况下，将根据指定的方法推算。
++ `method`：推算标准时间间隔的方法，取值为 'median', 'mode' 或 'cluster'，仅在`interval`缺省时有效。在缺省情况下，将使用中位数方法进行推算。
+
+**输出序列：** 输出单个序列，类型与输入序列相同。该序列是修复后的输入序列。
+
+#### 使用示例
+
+##### 指定标准时间间隔
+
+在给定`interval`参数的情况下，本函数将按照指定的标准时间间隔进行修复。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s1|
++-----------------------------+---------------+
+|2021-07-01T12:00:00.000+08:00| 1.0|
+|2021-07-01T12:00:10.000+08:00| 2.0|
+|2021-07-01T12:00:19.000+08:00| 3.0|
+|2021-07-01T12:00:30.000+08:00| 4.0|
+|2021-07-01T12:00:40.000+08:00| 5.0|
+|2021-07-01T12:00:50.000+08:00| 6.0|
+|2021-07-01T12:01:01.000+08:00| 7.0|
+|2021-07-01T12:01:11.000+08:00| 8.0|
+|2021-07-01T12:01:21.000+08:00| 9.0|
+|2021-07-01T12:01:31.000+08:00| 10.0|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select timestamprepair(s1,'interval'='10000') from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------------------------------------+
+| Time|timestamprepair(root.test.d2.s1, "interval"="10000")|
++-----------------------------+----------------------------------------------------+
+|2021-07-01T12:00:00.000+08:00| 1.0|
+|2021-07-01T12:00:10.000+08:00| 2.0|
+|2021-07-01T12:00:20.000+08:00| 3.0|
+|2021-07-01T12:00:30.000+08:00| 4.0|
+|2021-07-01T12:00:40.000+08:00| 5.0|
+|2021-07-01T12:00:50.000+08:00| 6.0|
+|2021-07-01T12:01:00.000+08:00| 7.0|
+|2021-07-01T12:01:10.000+08:00| 8.0|
+|2021-07-01T12:01:20.000+08:00| 9.0|
+|2021-07-01T12:01:30.000+08:00| 10.0|
++-----------------------------+----------------------------------------------------+
+```
+
+##### 自动推算标准时间间隔
+
+如果`interval`参数没有给定，本函数将按照推算的标准时间间隔进行修复。
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select timestamprepair(s1) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------------------+
+| Time|timestamprepair(root.test.d2.s1)|
++-----------------------------+--------------------------------+
+|2021-07-01T12:00:00.000+08:00| 1.0|
+|2021-07-01T12:00:10.000+08:00| 2.0|
+|2021-07-01T12:00:20.000+08:00| 3.0|
+|2021-07-01T12:00:30.000+08:00| 4.0|
+|2021-07-01T12:00:40.000+08:00| 5.0|
+|2021-07-01T12:00:50.000+08:00| 6.0|
+|2021-07-01T12:01:00.000+08:00| 7.0|
+|2021-07-01T12:01:10.000+08:00| 8.0|
+|2021-07-01T12:01:20.000+08:00| 9.0|
+|2021-07-01T12:01:30.000+08:00| 10.0|
++-----------------------------+--------------------------------+
+```
+
+### ValueFill
+
+#### 函数简介
+
+**函数名：** ValueFill
+
+**输入序列：** 单列时序数据，类型为INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `method`: {"mean", "previous", "linear", "likelihood", "AR", "MA", "SCREEN"}, 默认为 "linear"。其中，“mean” 指使用均值填补的方法； “previous" 指使用前值填补方法；“linear" 指使用线性插值填补方法；“likelihood” 为基于速度的正态分布的极大似然估计方法；“AR” 指自回归的填补方法；“MA” 指滑动平均的填补方法；"SCREEN" 指约束填补方法；缺省情况下使用 “linear”。
+
+**输出序列：** 填补后的单维序列。
+
+**备注：** AR 模型采用 AR(1)，时序列需满足自相关条件，否则将输出单个数据点 (0, 0.0).
+
+#### 使用示例
+
+##### 使用 linear 方法进行填补
+
+当`method`缺省或取值为 'linear' 时，本函数将使用线性插值方法进行填补。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| NaN|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| NaN|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| NaN|
+|2020-01-01T00:00:22.000+08:00| NaN|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select valuefill(s1) from root.test.d2
+```
+
+输出序列：
+
+
+
+```
++-----------------------------+-----------------------+
+| Time|valuefill(root.test.d2)|
++-----------------------------+-----------------------+
+|2020-01-01T00:00:02.000+08:00| NaN|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 108.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.7|
+|2020-01-01T00:00:22.000+08:00| 121.3|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+-----------------------+
+```
+
+##### 使用 previous 方法进行填补
+
+当`method`取值为 'previous' 时，本函数将使前值填补方法进行数值填补。
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select valuefill(s1,"method"="previous") from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------------------------+
+| Time|valuefill(root.test.d2,"method"="previous")|
++-----------------------------+-------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| NaN|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 110.5|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 116.0|
+|2020-01-01T00:00:22.000+08:00| 116.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+-------------------------------------------+
+```
+
+### ValueRepair
+
+#### 函数简介
+
+本函数用于对时间序列的数值进行修复。目前，本函数支持两种修复方法：**Screen** 是一种基于速度阈值的方法，在最小改动的前提下使得所有的速度符合阈值要求；**LsGreedy** 是一种基于速度变化似然的方法，将速度变化建模为高斯分布，并采用贪心算法极大化似然函数。
+
+**函数名：** VALUEREPAIR
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `method`：修复时采用的方法，取值为 'Screen' 或 'LsGreedy'. 在缺省情况下，使用 Screen 方法进行修复。
++ `minSpeed`：该参数仅在使用 Screen 方法时有效。当速度小于该值时会被视作数值异常点加以修复。在缺省情况下为中位数减去三倍绝对中位差。
++ `maxSpeed`：该参数仅在使用 Screen 方法时有效。当速度大于该值时会被视作数值异常点加以修复。在缺省情况下为中位数加上三倍绝对中位差。
++ `center`：该参数仅在使用 LsGreedy 方法时有效。对速度变化分布建立的高斯模型的中心。在缺省情况下为 0。
++ `sigma` ：该参数仅在使用 LsGreedy 方法时有效。对速度变化分布建立的高斯模型的标准差。在缺省情况下为绝对中位差。
+
+**输出序列：** 输出单个序列，类型与输入序列相同。该序列是修复后的输入序列。
+
+**提示：** 输入序列中的`NaN`在修复之前会先进行线性插值填补。
+
+#### 使用示例
+
+##### 使用 Screen 方法进行修复
+
+当`method`缺省或取值为 'Screen' 时，本函数将使用 Screen 方法进行数值修复。
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 126.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 100.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select valuerepair(s1) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------------+
+| Time|valuerepair(root.test.d2.s1)|
++-----------------------------+----------------------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 106.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+----------------------------+
+```
+
+##### 使用 LsGreedy 方法进行修复
+
+当`method`取值为 'LsGreedy' 时，本函数将使用 LsGreedy 方法进行数值修复。
+
+输入序列同上，用于查询的 SQL 语句如下：
+
+```sql
+select valuerepair(s1,'method'='LsGreedy') from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------------------------------+
+| Time|valuerepair(root.test.d2.s1, "method"="LsGreedy")|
++-----------------------------+-------------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:03.000+08:00| 101.0|
+|2020-01-01T00:00:04.000+08:00| 102.0|
+|2020-01-01T00:00:06.000+08:00| 104.0|
+|2020-01-01T00:00:08.000+08:00| 106.0|
+|2020-01-01T00:00:10.000+08:00| 108.0|
+|2020-01-01T00:00:14.000+08:00| 112.0|
+|2020-01-01T00:00:15.000+08:00| 113.0|
+|2020-01-01T00:00:16.000+08:00| 114.0|
+|2020-01-01T00:00:18.000+08:00| 116.0|
+|2020-01-01T00:00:20.000+08:00| 118.0|
+|2020-01-01T00:00:22.000+08:00| 120.0|
+|2020-01-01T00:00:26.000+08:00| 124.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
+|2020-01-01T00:00:30.000+08:00| 128.0|
++-----------------------------+-------------------------------------------------+
+```
+
+
+
+## 数据匹配
+
+### Cov
+
+#### 函数简介
+
+本函数用于计算两列数值型数据的总体协方差。
+
+**函数名：** COV
+
+**输入序列：** 仅支持两个输入序列，类型均为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。序列仅包含一个时间戳为 0、值为总体协方差的数据点。
+
+**提示：**
+
++ 如果某行数据中包含空值、缺失值或`NaN`，该行数据将会被忽略；
++ 如果数据中所有的行都被忽略，函数将会输出`NaN`。
+
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0| 101.0|
+|2020-01-01T00:00:03.000+08:00| 101.0| null|
+|2020-01-01T00:00:04.000+08:00| 102.0| 101.0|
+|2020-01-01T00:00:06.000+08:00| 104.0| 102.0|
+|2020-01-01T00:00:08.000+08:00| 126.0| 102.0|
+|2020-01-01T00:00:10.000+08:00| 108.0| 103.0|
+|2020-01-01T00:00:12.000+08:00| null| 103.0|
+|2020-01-01T00:00:14.000+08:00| 112.0| 104.0|
+|2020-01-01T00:00:15.000+08:00| 113.0| null|
+|2020-01-01T00:00:16.000+08:00| 114.0| 104.0|
+|2020-01-01T00:00:18.000+08:00| 116.0| 105.0|
+|2020-01-01T00:00:20.000+08:00| 118.0| 105.0|
+|2020-01-01T00:00:22.000+08:00| 100.0| 106.0|
+|2020-01-01T00:00:26.000+08:00| 124.0| 108.0|
+|2020-01-01T00:00:28.000+08:00| 126.0| 108.0|
+|2020-01-01T00:00:30.000+08:00| NaN| 108.0|
++-----------------------------+---------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select cov(s1,s2) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------------------+
+| Time|cov(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 12.291666666666666|
++-----------------------------+-------------------------------------+
+```
+
+### Dtw
+
+#### 函数简介
+
+本函数用于计算两列数值型数据的 DTW 距离。
+
+**函数名：** DTW
+
+**输入序列：** 仅支持两个输入序列，类型均为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。序列仅包含一个时间戳为 0、值为两个时间序列的 DTW 距离值。
+
+**提示：**
+
++ 如果某行数据中包含空值、缺失值或`NaN`，该行数据将会被忽略；
++ 如果数据中所有的行都被忽略，函数将会输出 0。
+
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.001+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.002+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.003+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.004+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.005+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.006+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.007+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.008+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.009+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.010+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.011+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.012+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.013+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.014+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.015+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.016+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.017+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.018+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.019+08:00| 1.0| 2.0|
+|1970-01-01T08:00:00.020+08:00| 1.0| 2.0|
++-----------------------------+---------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select dtw(s1,s2) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------------------+
+| Time|dtw(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 20.0|
++-----------------------------+-------------------------------------+
+```
+
+### Pearson
+
+#### 函数简介
+
+本函数用于计算两列数值型数据的皮尔森相关系数。
+
+**函数名：** PEARSON
+
+**输入序列：** 仅支持两个输入序列，类型均为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。序列仅包含一个时间戳为 0、值为皮尔森相关系数的数据点。
+
+**提示：**
+
++ 如果某行数据中包含空值、缺失值或`NaN`，该行数据将会被忽略；
++ 如果数据中所有的行都被忽略，函数将会输出`NaN`。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0| 101.0|
+|2020-01-01T00:00:03.000+08:00| 101.0| null|
+|2020-01-01T00:00:04.000+08:00| 102.0| 101.0|
+|2020-01-01T00:00:06.000+08:00| 104.0| 102.0|
+|2020-01-01T00:00:08.000+08:00| 126.0| 102.0|
+|2020-01-01T00:00:10.000+08:00| 108.0| 103.0|
+|2020-01-01T00:00:12.000+08:00| null| 103.0|
+|2020-01-01T00:00:14.000+08:00| 112.0| 104.0|
+|2020-01-01T00:00:15.000+08:00| 113.0| null|
+|2020-01-01T00:00:16.000+08:00| 114.0| 104.0|
+|2020-01-01T00:00:18.000+08:00| 116.0| 105.0|
+|2020-01-01T00:00:20.000+08:00| 118.0| 105.0|
+|2020-01-01T00:00:22.000+08:00| 100.0| 106.0|
+|2020-01-01T00:00:26.000+08:00| 124.0| 108.0|
+|2020-01-01T00:00:28.000+08:00| 126.0| 108.0|
+|2020-01-01T00:00:30.000+08:00| NaN| 108.0|
++-----------------------------+---------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select pearson(s1,s2) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------------------------+
+| Time|pearson(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+-----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.5630881927754872|
++-----------------------------+-----------------------------------------+
+```
+
+### PtnSym
+
+#### 函数简介
+
+本函数用于寻找序列中所有对称度小于阈值的对称子序列。对称度通过 DTW 计算，值越小代表序列对称性越高。
+
+**函数名：** PTNSYM
+
+**输入序列：** 仅支持一个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `window`：对称子序列的长度，是一个正整数，默认值为 10。
++ `threshold`：对称度阈值，是一个非负数，只有对称度小于等于该值的对称子序列才会被输出。在缺省情况下，所有的子序列都会被输出。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。序列中的每一个数据点对应于一个对称子序列，时间戳为子序列的起始时刻，值为对称度。
+
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s4|
++-----------------------------+---------------+
+|2021-01-01T12:00:00.000+08:00| 1.0|
+|2021-01-01T12:00:01.000+08:00| 2.0|
+|2021-01-01T12:00:02.000+08:00| 3.0|
+|2021-01-01T12:00:03.000+08:00| 2.0|
+|2021-01-01T12:00:04.000+08:00| 1.0|
+|2021-01-01T12:00:05.000+08:00| 1.0|
+|2021-01-01T12:00:06.000+08:00| 1.0|
+|2021-01-01T12:00:07.000+08:00| 1.0|
+|2021-01-01T12:00:08.000+08:00| 2.0|
+|2021-01-01T12:00:09.000+08:00| 3.0|
+|2021-01-01T12:00:10.000+08:00| 2.0|
+|2021-01-01T12:00:11.000+08:00| 1.0|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select ptnsym(s4, 'window'='5', 'threshold'='0') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|ptnsym(root.test.d1.s4, "window"="5", "threshold"="0")|
++-----------------------------+------------------------------------------------------+
+|2021-01-01T12:00:00.000+08:00| 0.0|
+|2021-01-01T12:00:07.000+08:00| 0.0|
++-----------------------------+------------------------------------------------------+
+```
+
+### XCorr
+
+#### 函数简介
+
+本函数用于计算两条时间序列的互相关函数值，
+对离散序列而言，互相关函数可以表示为
+$$CR(n) = \frac{1}{N} \sum_{m=1}^N S_1[m]S_2[m+n]$$
+常用于表征两条序列在不同对齐条件下的相似度。
+
+**函数名：** XCORR
+
+**输入序列：** 仅支持两个输入序列，类型均为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**输出序列：** 输出单个序列，类型为 DOUBLE。序列中共包含$2N-1$个数据点，
+其中正中心的值为两条序列按照预先对齐的结果计算的互相关系数（即等于以上公式的$CR(0)$），
+前半部分的值表示将后一条输入序列向前平移时计算的互相关系数，
+直至两条序列没有重合的数据点（不包含完全分离时的结果$CR(-N)=0.0$），
+后半部分类似。
+用公式可表示为（所有序列的索引从1开始计数）：
+$$OS[i] = CR(-N+i) = \frac{1}{N} \sum_{m=1}^{i} S_1[m]S_2[N-i+m],\ if\ i <= N$$
+$$OS[i] = CR(i-N) = \frac{1}{N} \sum_{m=1}^{2N-i} S_1[i-N+m]S_2[m],\ if\ i > N$$
+
+**提示：**
+
++ 两条序列中的`null` 和`NaN` 值会被忽略，在计算中表现为 0。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:01.000+08:00| null| 6|
+|2020-01-01T00:00:02.000+08:00| 2| 7|
+|2020-01-01T00:00:03.000+08:00| 3| NaN|
+|2020-01-01T00:00:04.000+08:00| 4| 9|
+|2020-01-01T00:00:05.000+08:00| 5| 10|
++-----------------------------+---------------+---------------+
+```
+
+
+用于查询的 SQL 语句：
+
+```sql
+select xcorr(s1, s2) from root.test.d1 where time <= 2020-01-01 00:00:05
+```
+
+输出序列：
+
+```
++-----------------------------+---------------------------------------+
+| Time|xcorr(root.test.d1.s1, root.test.d1.s2)|
++-----------------------------+---------------------------------------+
+|1970-01-01T08:00:00.001+08:00| 0.0|
+|1970-01-01T08:00:00.002+08:00| 4.0|
+|1970-01-01T08:00:00.003+08:00| 9.6|
+|1970-01-01T08:00:00.004+08:00| 13.4|
+|1970-01-01T08:00:00.005+08:00| 20.0|
+|1970-01-01T08:00:00.006+08:00| 15.6|
+|1970-01-01T08:00:00.007+08:00| 9.2|
+|1970-01-01T08:00:00.008+08:00| 11.8|
+|1970-01-01T08:00:00.009+08:00| 6.0|
++-----------------------------+---------------------------------------+
+```
+
+
+
+## 异常检测
+
+### IQR
+
+#### 函数简介
+
+本函数用于检验超出上下四分位数1.5倍IQR的数据分布异常。
+
+**函数名：** IQR
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `method`：若设置为 "batch"，则将数据全部读入后检测；若设置为 "stream"，则需用户提供上下四分位数进行流式检测。默认为 "batch"。
++ `q1`：使用流式计算时的下四分位数。
++ `q3`：使用流式计算时的上四分位数。
+
+**输出序列**：输出单个序列，类型为 DOUBLE。
+
+**说明**：$IQR=Q_3-Q_1$
+
+#### 使用示例
+
+##### 全数据计算
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s1|
++-----------------------------+------------+
+|1970-01-01T08:00:00.100+08:00| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0|
+|1970-01-01T08:00:00.300+08:00| 1.0|
+|1970-01-01T08:00:00.400+08:00| -1.0|
+|1970-01-01T08:00:00.500+08:00| 0.0|
+|1970-01-01T08:00:00.600+08:00| 0.0|
+|1970-01-01T08:00:00.700+08:00| -2.0|
+|1970-01-01T08:00:00.800+08:00| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 1.0|
+|1970-01-01T08:00:01.200+08:00| -1.0|
+|1970-01-01T08:00:01.300+08:00| -1.0|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 0.0|
+|1970-01-01T08:00:01.600+08:00| 0.0|
+|1970-01-01T08:00:01.700+08:00| 10.0|
+|1970-01-01T08:00:01.800+08:00| 2.0|
+|1970-01-01T08:00:01.900+08:00| -2.0|
+|1970-01-01T08:00:02.000+08:00| 0.0|
++-----------------------------+------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select iqr(s1) from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------+
+| Time|iqr(root.test.s1)|
++-----------------------------+-----------------+
+|1970-01-01T08:00:01.700+08:00| 10.0|
++-----------------------------+-----------------+
+```
+
+### KSigma
+
+#### 函数简介
+
+本函数利用动态 K-Sigma 算法进行异常检测。在一个窗口内，与平均值的差距超过k倍标准差的数据将被视作异常并输出。
+
+**函数名：** KSIGMA
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `k`：在动态 K-Sigma 算法中，分布异常的标准差倍数阈值，默认值为 3。
++ `window`：动态 K-Sigma 算法的滑动窗口大小，默认值为 10000。
+
+
+**输出序列：** 输出单个序列，类型与输入序列相同。
+
+**提示：** k 应大于 0，否则将不做输出。
+
+#### 使用示例
+
+##### 指定k
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 0.0|
+|2020-01-01T00:00:03.000+08:00| 50.0|
+|2020-01-01T00:00:04.000+08:00| 100.0|
+|2020-01-01T00:00:06.000+08:00| 150.0|
+|2020-01-01T00:00:08.000+08:00| 200.0|
+|2020-01-01T00:00:10.000+08:00| 200.0|
+|2020-01-01T00:00:14.000+08:00| 200.0|
+|2020-01-01T00:00:15.000+08:00| 200.0|
+|2020-01-01T00:00:16.000+08:00| 200.0|
+|2020-01-01T00:00:18.000+08:00| 200.0|
+|2020-01-01T00:00:20.000+08:00| 150.0|
+|2020-01-01T00:00:22.000+08:00| 100.0|
+|2020-01-01T00:00:26.000+08:00| 50.0|
+|2020-01-01T00:00:28.000+08:00| 0.0|
+|2020-01-01T00:00:30.000+08:00| NaN|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select ksigma(s1,"k"="1.0") from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+输出序列：
+
+```
++-----------------------------+---------------------------------+
+|Time |ksigma(root.test.d1.s1,"k"="3.0")|
++-----------------------------+---------------------------------+
+|2020-01-01T00:00:02.000+08:00| 0.0|
+|2020-01-01T00:00:03.000+08:00| 50.0|
+|2020-01-01T00:00:26.000+08:00| 50.0|
+|2020-01-01T00:00:28.000+08:00| 0.0|
++-----------------------------+---------------------------------+
+```
+
+### LOF
+
+#### 函数简介
+
+本函数使用局部离群点检测方法用于查找序列的密度异常。将根据提供的第k距离数及局部离群点因子(lof)阈值，判断输入数据是否为离群点，即异常，并输出各点的 LOF 值。
+
+**函数名：** LOF
+
+**输入序列：** 多个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `method`:使用的检测方法。默认为 default，以高维数据计算。设置为 series，将一维时间序列转换为高维数据计算。
++ `k`:使用第k距离计算局部离群点因子.默认为 3。
++ `window`:每次读取数据的窗口长度。默认为 10000.
++ `windowsize`:使用series方法时，转化高维数据的维数，即单个窗口的大小。默认为 5。
+
+**输出序列：** 输出单时间序列，类型为DOUBLE。
+
+**提示：** 不完整的数据行会被忽略，不参与计算，也不标记为离群点。
+
+
+#### 使用示例
+
+##### 默认参数
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.100+08:00| 0.0| 0.0|
+|1970-01-01T08:00:00.200+08:00| 0.0| 1.0|
+|1970-01-01T08:00:00.300+08:00| 1.0| 1.0|
+|1970-01-01T08:00:00.400+08:00| 1.0| 0.0|
+|1970-01-01T08:00:00.500+08:00| 0.0| -1.0|
+|1970-01-01T08:00:00.600+08:00| -1.0| -1.0|
+|1970-01-01T08:00:00.700+08:00| -1.0| 0.0|
+|1970-01-01T08:00:00.800+08:00| 2.0| 2.0|
+|1970-01-01T08:00:00.900+08:00| 0.0| null|
++-----------------------------+---------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select lof(s1,s2) from root.test.d1 where time<1000
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------------------+
+| Time|lof(root.test.d1.s1, root.test.d1.s2)|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.100+08:00| 3.8274824267668244|
+|1970-01-01T08:00:00.200+08:00| 3.0117631741126156|
+|1970-01-01T08:00:00.300+08:00| 2.838155437762879|
+|1970-01-01T08:00:00.400+08:00| 3.0117631741126156|
+|1970-01-01T08:00:00.500+08:00| 2.73518261244453|
+|1970-01-01T08:00:00.600+08:00| 2.371440975708148|
+|1970-01-01T08:00:00.700+08:00| 2.73518261244453|
+|1970-01-01T08:00:00.800+08:00| 1.7561416374270742|
++-----------------------------+-------------------------------------+
+```
+
+##### 诊断一维时间序列
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.100+08:00| 1.0|
+|1970-01-01T08:00:00.200+08:00| 2.0|
+|1970-01-01T08:00:00.300+08:00| 3.0|
+|1970-01-01T08:00:00.400+08:00| 4.0|
+|1970-01-01T08:00:00.500+08:00| 5.0|
+|1970-01-01T08:00:00.600+08:00| 6.0|
+|1970-01-01T08:00:00.700+08:00| 7.0|
+|1970-01-01T08:00:00.800+08:00| 8.0|
+|1970-01-01T08:00:00.900+08:00| 9.0|
+|1970-01-01T08:00:01.000+08:00| 10.0|
+|1970-01-01T08:00:01.100+08:00| 11.0|
+|1970-01-01T08:00:01.200+08:00| 12.0|
+|1970-01-01T08:00:01.300+08:00| 13.0|
+|1970-01-01T08:00:01.400+08:00| 14.0|
+|1970-01-01T08:00:01.500+08:00| 15.0|
+|1970-01-01T08:00:01.600+08:00| 16.0|
+|1970-01-01T08:00:01.700+08:00| 17.0|
+|1970-01-01T08:00:01.800+08:00| 18.0|
+|1970-01-01T08:00:01.900+08:00| 19.0|
+|1970-01-01T08:00:02.000+08:00| 20.0|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select lof(s1, "method"="series") from root.test.d1 where time<1000
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------+
+| Time|lof(root.test.d1.s1)|
++-----------------------------+--------------------+
+|1970-01-01T08:00:00.100+08:00| 3.77777777777778|
+|1970-01-01T08:00:00.200+08:00| 4.32727272727273|
+|1970-01-01T08:00:00.300+08:00| 4.85714285714286|
+|1970-01-01T08:00:00.400+08:00| 5.40909090909091|
+|1970-01-01T08:00:00.500+08:00| 5.94999999999999|
+|1970-01-01T08:00:00.600+08:00| 6.43243243243243|
+|1970-01-01T08:00:00.700+08:00| 6.79999999999999|
+|1970-01-01T08:00:00.800+08:00| 7.0|
+|1970-01-01T08:00:00.900+08:00| 7.0|
+|1970-01-01T08:00:01.000+08:00| 6.79999999999999|
+|1970-01-01T08:00:01.100+08:00| 6.43243243243243|
+|1970-01-01T08:00:01.200+08:00| 5.94999999999999|
+|1970-01-01T08:00:01.300+08:00| 5.40909090909091|
+|1970-01-01T08:00:01.400+08:00| 4.85714285714286|
+|1970-01-01T08:00:01.500+08:00| 4.32727272727273|
+|1970-01-01T08:00:01.600+08:00| 3.77777777777778|
++-----------------------------+--------------------+
+```
+
+### MissDetect
+
+#### 函数简介
+
+本函数用于检测数据中的缺失异常。在一些数据中，缺失数据会被线性插值填补，在数据中出现完美的线性片段，且这些片段往往长度较大。本函数通过在数据中发现这些完美线性片段来检测缺失异常。
+
+**函数名：** MISSDETECT
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE。
+
+**参数：**
+
++ `minlen`：被标记为异常的完美线性片段的最小长度，是一个大于等于 10 的整数，默认值为 10。
+
+**输出序列：** 输出单个序列，类型为 BOOLEAN，即该数据点是否为缺失异常。
+
+**提示：** 数据中的`NaN`将会被忽略。
+
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d2.s2|
++-----------------------------+---------------+
+|2021-07-01T12:00:00.000+08:00| 0.0|
+|2021-07-01T12:00:01.000+08:00| 1.0|
+|2021-07-01T12:00:02.000+08:00| 0.0|
+|2021-07-01T12:00:03.000+08:00| 1.0|
+|2021-07-01T12:00:04.000+08:00| 0.0|
+|2021-07-01T12:00:05.000+08:00| 0.0|
+|2021-07-01T12:00:06.000+08:00| 0.0|
+|2021-07-01T12:00:07.000+08:00| 0.0|
+|2021-07-01T12:00:08.000+08:00| 0.0|
+|2021-07-01T12:00:09.000+08:00| 0.0|
+|2021-07-01T12:00:10.000+08:00| 0.0|
+|2021-07-01T12:00:11.000+08:00| 0.0|
+|2021-07-01T12:00:12.000+08:00| 0.0|
+|2021-07-01T12:00:13.000+08:00| 0.0|
+|2021-07-01T12:00:14.000+08:00| 0.0|
+|2021-07-01T12:00:15.000+08:00| 0.0|
+|2021-07-01T12:00:16.000+08:00| 1.0|
+|2021-07-01T12:00:17.000+08:00| 0.0|
+|2021-07-01T12:00:18.000+08:00| 1.0|
+|2021-07-01T12:00:19.000+08:00| 0.0|
+|2021-07-01T12:00:20.000+08:00| 1.0|
++-----------------------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select missdetect(s2,'minlen'='10') from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------+
+| Time|missdetect(root.test.d2.s2, "minlen"="10")|
++-----------------------------+------------------------------------------+
+|2021-07-01T12:00:00.000+08:00| false|
+|2021-07-01T12:00:01.000+08:00| false|
+|2021-07-01T12:00:02.000+08:00| false|
+|2021-07-01T12:00:03.000+08:00| false|
+|2021-07-01T12:00:04.000+08:00| true|
+|2021-07-01T12:00:05.000+08:00| true|
+|2021-07-01T12:00:06.000+08:00| true|
+|2021-07-01T12:00:07.000+08:00| true|
+|2021-07-01T12:00:08.000+08:00| true|
+|2021-07-01T12:00:09.000+08:00| true|
+|2021-07-01T12:00:10.000+08:00| true|
+|2021-07-01T12:00:11.000+08:00| true|
+|2021-07-01T12:00:12.000+08:00| true|
+|2021-07-01T12:00:13.000+08:00| true|
+|2021-07-01T12:00:14.000+08:00| true|
+|2021-07-01T12:00:15.000+08:00| true|
+|2021-07-01T12:00:16.000+08:00| false|
+|2021-07-01T12:00:17.000+08:00| false|
+|2021-07-01T12:00:18.000+08:00| false|
+|2021-07-01T12:00:19.000+08:00| false|
+|2021-07-01T12:00:20.000+08:00| false|
++-----------------------------+------------------------------------------+
+```
+
+### Range
+
+#### 函数简介
+
+本函数用于查找时间序列的范围异常。将根据提供的上界与下界，判断输入数据是否越界，即异常，并输出所有异常点为新的时间序列。
+
+**函数名：** RANGE
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `lower_bound`:范围异常检测的下界。
++ `upper_bound`:范围异常检测的上界。
+
+**输出序列：** 输出单个序列，类型与输入序列相同。
+
+**提示：** 应满足`upper_bound`大于`lower_bound`，否则将不做输出。
+
+
+#### 使用示例
+
+##### 指定上界与下界
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
|2020-01-01T00:00:03.000+08:00| 101.0|
|2020-01-01T00:00:04.000+08:00| 102.0|
|2020-01-01T00:00:06.000+08:00| 104.0|
@@ -382,475 +3399,1122 @@ select timeliness(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
|2020-01-01T00:00:26.000+08:00| 124.0|
|2020-01-01T00:00:28.000+08:00| 126.0|
|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
++-----------------------------+---------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select range(s1,"lower_bound"="101.0","upper_bound"="125.0") from root.test.d1 where time <= 2020-01-01 00:00:30
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------------------------------+
+|Time |range(root.test.d1.s1,"lower_bound"="101.0","upper_bound"="125.0")|
++-----------------------------+------------------------------------------------------------------+
+|2020-01-01T00:00:02.000+08:00| 100.0|
+|2020-01-01T00:00:28.000+08:00| 126.0|
++-----------------------------+------------------------------------------------------------------+
+```
+
+### TwoSidedFilter
+
+#### 函数简介
+
+本函数基于双边窗口检测法对输入序列中的异常点进行过滤。
+
+**函数名：** TWOSIDEDFILTER
+
+**输出序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**输出序列：** 输出单个序列，类型与输入相同，是输入序列去除异常点后的结果。
+
+**参数：**
+
+- `len`：双边窗口检测法中的窗口大小，取值范围为正整数，默认值为 5.如当`len`=3 时，算法向前、向后各取长度为3的窗口，在窗口中计算异常度。
+- `threshold`：异常度的阈值，取值范围为(0,1)，默认值为 0.3。阈值越高，函数对于异常度的判定标准越严格。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 2002.0|
+|1970-01-01T08:00:01.000+08:00| 1946.0|
+|1970-01-01T08:00:02.000+08:00| 1958.0|
+|1970-01-01T08:00:03.000+08:00| 2012.0|
+|1970-01-01T08:00:04.000+08:00| 2051.0|
+|1970-01-01T08:00:05.000+08:00| 1898.0|
+|1970-01-01T08:00:06.000+08:00| 2014.0|
+|1970-01-01T08:00:07.000+08:00| 2052.0|
+|1970-01-01T08:00:08.000+08:00| 1935.0|
+|1970-01-01T08:00:09.000+08:00| 1901.0|
+|1970-01-01T08:00:10.000+08:00| 1972.0|
+|1970-01-01T08:00:11.000+08:00| 1969.0|
+|1970-01-01T08:00:12.000+08:00| 1984.0|
+|1970-01-01T08:00:13.000+08:00| 2018.0|
+|1970-01-01T08:00:37.000+08:00| 1484.0|
+|1970-01-01T08:00:38.000+08:00| 1055.0|
+|1970-01-01T08:00:39.000+08:00| 1050.0|
+|1970-01-01T08:01:05.000+08:00| 1023.0|
+|1970-01-01T08:01:06.000+08:00| 1056.0|
+|1970-01-01T08:01:07.000+08:00| 978.0|
+|1970-01-01T08:01:08.000+08:00| 1050.0|
+|1970-01-01T08:01:09.000+08:00| 1123.0|
+|1970-01-01T08:01:10.000+08:00| 1150.0|
+|1970-01-01T08:01:11.000+08:00| 1034.0|
+|1970-01-01T08:01:12.000+08:00| 950.0|
+|1970-01-01T08:01:13.000+08:00| 1059.0|
++-----------------------------+------------+
+```
+
+用于查询的 SQL 语句：
+
+```sql
+select TwoSidedFilter(s0, 'len'='5', 'threshold'='0.3') from root.test
+```
+
+输出序列：
+
+```
++-----------------------------+------------+
+| Time|root.test.s0|
++-----------------------------+------------+
+|1970-01-01T08:00:00.000+08:00| 2002.0|
+|1970-01-01T08:00:01.000+08:00| 1946.0|
+|1970-01-01T08:00:02.000+08:00| 1958.0|
+|1970-01-01T08:00:03.000+08:00| 2012.0|
+|1970-01-01T08:00:04.000+08:00| 2051.0|
+|1970-01-01T08:00:05.000+08:00| 1898.0|
+|1970-01-01T08:00:06.000+08:00| 2014.0|
+|1970-01-01T08:00:07.000+08:00| 2052.0|
+|1970-01-01T08:00:08.000+08:00| 1935.0|
+|1970-01-01T08:00:09.000+08:00| 1901.0|
+|1970-01-01T08:00:10.000+08:00| 1972.0|
+|1970-01-01T08:00:11.000+08:00| 1969.0|
+|1970-01-01T08:00:12.000+08:00| 1984.0|
+|1970-01-01T08:00:13.000+08:00| 2018.0|
+|1970-01-01T08:01:05.000+08:00| 1023.0|
+|1970-01-01T08:01:06.000+08:00| 1056.0|
+|1970-01-01T08:01:07.000+08:00| 978.0|
+|1970-01-01T08:01:08.000+08:00| 1050.0|
+|1970-01-01T08:01:09.000+08:00| 1123.0|
+|1970-01-01T08:01:10.000+08:00| 1150.0|
+|1970-01-01T08:01:11.000+08:00| 1034.0|
+|1970-01-01T08:01:12.000+08:00| 950.0|
+|1970-01-01T08:01:13.000+08:00| 1059.0|
++-----------------------------+------------+
+```
+
+
+
+## 频域处理
+
+### Conv
+
+#### 函数简介
+
+本函数对两个输入序列进行卷积，即多项式乘法。
+
+
+**函数名：** CONV
+
+**输入序列：** 仅支持两个输入序列，类型均为 INT32 / INT64 / FLOAT / DOUBLE
+
+**输出序列：** 输出单个序列，类型为DOUBLE，它是两个序列卷积的结果。序列的时间戳从0开始，仅用于表示顺序。
+
+**提示：** 输入序列中的`NaN`将被忽略。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s1|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 1.0| 7.0|
+|1970-01-01T08:00:00.001+08:00| 0.0| 2.0|
+|1970-01-01T08:00:00.002+08:00| 1.0| null|
++-----------------------------+---------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select conv(s1,s2) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------------------------+
+| Time|conv(root.test.d2.s1, root.test.d2.s2)|
++-----------------------------+--------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 7.0|
+|1970-01-01T08:00:00.001+08:00| 2.0|
+|1970-01-01T08:00:00.002+08:00| 7.0|
+|1970-01-01T08:00:00.003+08:00| 2.0|
++-----------------------------+--------------------------------------+
+```
+
+### Deconv
+
+#### 函数简介
+
+本函数对两个输入序列进行去卷积，即多项式除法运算。
+
+**函数名：** DECONV
+
+**输入序列：** 仅支持两个输入序列，类型均为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `result`：去卷积的结果，取值为'quotient'或'remainder'，分别对应于去卷积的商和余数。在缺省情况下，输出去卷积的商。
+
+**输出序列：** 输出单个序列，类型为DOUBLE。它是将第二个序列从第一个序列中去卷积（第一个序列除以第二个序列）的结果。序列的时间戳从0开始，仅用于表示顺序。
+
+**提示：** 输入序列中的`NaN`将被忽略。
+
+#### 使用示例
+
+##### 计算去卷积的商
+
+当`result`参数缺省或为'quotient'时，本函数计算去卷积的商。
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d2.s3|root.test.d2.s2|
++-----------------------------+---------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 8.0| 7.0|
+|1970-01-01T08:00:00.001+08:00| 2.0| 2.0|
+|1970-01-01T08:00:00.002+08:00| 7.0| null|
+|1970-01-01T08:00:00.003+08:00| 2.0| null|
++-----------------------------+---------------+---------------+
+```
+
+
+用于查询的SQL语句：
+
+```sql
+select deconv(s3,s2) from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------------------------+
+| Time|deconv(root.test.d2.s3, root.test.d2.s2)|
++-----------------------------+----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.0|
+|1970-01-01T08:00:00.001+08:00| 0.0|
+|1970-01-01T08:00:00.002+08:00| 1.0|
++-----------------------------+----------------------------------------+
+```
+
+##### 计算去卷积的余数
+
+当`result`参数为'remainder'时，本函数计算去卷积的余数。输入序列同上，用于查询的SQL语句如下：
+
+```sql
+select deconv(s3,s2,'result'='remainder') from root.test.d2
+```
+
+输出序列：
+
+```
++-----------------------------+--------------------------------------------------------------+
+| Time|deconv(root.test.d2.s3, root.test.d2.s2, "result"="remainder")|
++-----------------------------+--------------------------------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.0|
+|1970-01-01T08:00:00.001+08:00| 0.0|
+|1970-01-01T08:00:00.002+08:00| 0.0|
+|1970-01-01T08:00:00.003+08:00| 0.0|
++-----------------------------+--------------------------------------------------------------+
+```
+
+### DWT
+
+#### 函数简介
+
+本函数对输入序列进行一维离散小波变换。
+
+**函数名：** DWT
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `method`：小波滤波的类型，提供'Haar', 'DB4', 'DB6', 'DB8'，其中DB指代Daubechies。若不设置该参数，则用户需提供小波滤波的系数。不区分大小写。
++ `coef`：小波滤波的系数。若提供该参数，请使用英文逗号','分割各项，不添加空格或其它符号。
++ `layer`：进行变换的次数，最终输出的向量个数等同于$layer+1$.默认取1。
+
+**输出序列：** 输出单个序列，类型为DOUBLE，长度与输入相等。
+
+**提示：** 输入序列长度必须为2的整数次幂。
+
+#### 使用示例
+
+##### Haar变换
+
+
+输入序列：
+
+```
++-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.100+08:00| 0.2|
+|1970-01-01T08:00:00.200+08:00| 1.5|
+|1970-01-01T08:00:00.300+08:00| 1.2|
+|1970-01-01T08:00:00.400+08:00| 0.6|
+|1970-01-01T08:00:00.500+08:00| 1.7|
+|1970-01-01T08:00:00.600+08:00| 0.8|
+|1970-01-01T08:00:00.700+08:00| 2.0|
+|1970-01-01T08:00:00.800+08:00| 2.5|
+|1970-01-01T08:00:00.900+08:00| 2.1|
+|1970-01-01T08:00:01.000+08:00| 0.0|
+|1970-01-01T08:00:01.100+08:00| 2.0|
+|1970-01-01T08:00:01.200+08:00| 1.8|
+|1970-01-01T08:00:01.300+08:00| 1.2|
+|1970-01-01T08:00:01.400+08:00| 1.0|
+|1970-01-01T08:00:01.500+08:00| 1.6|
+-----------------------------+---------------+
```
用于查询的SQL语句：
```sql
-select timeliness(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select dwt(s1,"method"="haar") from root.test.d1
```
输出序列：
```
-+-----------------------------+------------------------------------------+
-| Time|timeliness(root.test.d1.s1, "window"="15")|
-+-----------------------------+------------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.9333333333333333|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+------------------------------------------+
++-----------------------------+-------------------------------------+
+| Time|dwt(root.test.d1.s1, "method"="haar")|
++-----------------------------+-------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.14142135834465192|
+|1970-01-01T08:00:00.100+08:00| 1.909188342921157|
+|1970-01-01T08:00:00.200+08:00| 1.6263456473052773|
+|1970-01-01T08:00:00.300+08:00| 1.9798989957517026|
+|1970-01-01T08:00:00.400+08:00| 3.252691126023161|
+|1970-01-01T08:00:00.500+08:00| 1.414213562373095|
+|1970-01-01T08:00:00.600+08:00| 2.1213203435596424|
+|1970-01-01T08:00:00.700+08:00| 1.8384776479437628|
+|1970-01-01T08:00:00.800+08:00| -0.14142135834465192|
+|1970-01-01T08:00:00.900+08:00| 0.21213200063848547|
+|1970-01-01T08:00:01.000+08:00| -0.7778174761639416|
+|1970-01-01T08:00:01.100+08:00| -0.8485281289944873|
+|1970-01-01T08:00:01.200+08:00| 0.2828427799095765|
+|1970-01-01T08:00:01.300+08:00| -1.414213562373095|
+|1970-01-01T08:00:01.400+08:00| 0.42426400127697095|
+|1970-01-01T08:00:01.500+08:00| -0.42426408557066786|
++-----------------------------+-------------------------------------+
```
-### Validity
+### FFT
#### 函数简介
-本函数用于计算时间序列的有效性。将输入序列划分为若干个连续且不重叠的窗口，分别计算每一个窗口的有效性，并输出窗口第一个数据点的时间戳和窗口的有效性。
+本函数对输入序列进行快速傅里叶变换。
-**函数名：** VALIDITY
+**函数名：** FFT
**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
**参数：**
-+ `window`：窗口大小，它是一个大于0的整数或者一个有单位的正数。前者代表每一个窗口包含的数据点数目，最后一个窗口的数据点数目可能会不足；后者代表窗口的时间跨度，目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。缺省情况下，全部输入数据都属于同一个窗口。
++ `method`：傅里叶变换的类型，取值为'uniform'或'nonuniform'，缺省情况下为'uniform'。当取值为'uniform'时，时间戳将被忽略，所有数据点都将被视作等距的，并应用等距快速傅里叶算法；当取值为'nonuniform'时，将根据时间戳应用非等距快速傅里叶算法（未实现）。
++ `result`：傅里叶变换的结果，取值为'real'、'imag'、'abs'或'angle'，分别对应于变换结果的实部、虚部、模和幅角。在缺省情况下，输出变换的模。
++ `compress`：压缩参数，取值范围(0,1]，是有损压缩时保留的能量比例。在缺省情况下，不进行压缩。
-**输出序列：** 输出单个序列，类型为DOUBLE，其中每一个数据点的值的范围都是 [0,1].
+**输出序列：** 输出单个序列，类型为DOUBLE，长度与输入相等。序列的时间戳从0开始，仅用于表示顺序。
-**提示：** 只有当窗口内的数据点数目超过10时，才会进行有效性计算。否则，该窗口将被忽略，不做任何输出。
+**提示：** 输入序列中的`NaN`将被忽略。
-#### 示例：参数缺省
+#### 使用示例
-在参数缺省的情况下，本函数将会把全部输入数据都作为同一个窗口计算有效性。
+##### 等距傅里叶变换
+
+当`type`参数缺省或为'uniform'时，本函数进行等距傅里叶变换。
输入序列：
+
```
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
+|1970-01-01T08:00:00.000+08:00| 2.902113|
+|1970-01-01T08:00:01.000+08:00| 1.1755705|
+|1970-01-01T08:00:02.000+08:00| -2.1755705|
+|1970-01-01T08:00:03.000+08:00| -1.9021131|
+|1970-01-01T08:00:04.000+08:00| 1.0|
+|1970-01-01T08:00:05.000+08:00| 1.9021131|
+|1970-01-01T08:00:06.000+08:00| 0.1755705|
+|1970-01-01T08:00:07.000+08:00| -1.1755705|
+|1970-01-01T08:00:08.000+08:00| -0.902113|
+|1970-01-01T08:00:09.000+08:00| 0.0|
+|1970-01-01T08:00:10.000+08:00| 0.902113|
+|1970-01-01T08:00:11.000+08:00| 1.1755705|
+|1970-01-01T08:00:12.000+08:00| -0.1755705|
+|1970-01-01T08:00:13.000+08:00| -1.9021131|
+|1970-01-01T08:00:14.000+08:00| -1.0|
+|1970-01-01T08:00:15.000+08:00| 1.9021131|
+|1970-01-01T08:00:16.000+08:00| 2.1755705|
+|1970-01-01T08:00:17.000+08:00| -1.1755705|
+|1970-01-01T08:00:18.000+08:00| -2.902113|
+|1970-01-01T08:00:19.000+08:00| 0.0|
+-----------------------------+---------------+
```
用于查询的SQL语句：
```sql
-select validity(s1) from root.test.d1 where time <= 2020-01-01 00:00:30
+select fft(s1) from root.test.d1
```
输出序列：
```
-+-----------------------------+-------------------------+
-| Time|validity(root.test.d1.s1)|
-+-----------------------------+-------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
-+-----------------------------+-------------------------+
++-----------------------------+----------------------+
+| Time| fft(root.test.d1.s1)|
++-----------------------------+----------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0|
+|1970-01-01T08:00:00.001+08:00| 1.2727111142703152E-8|
+|1970-01-01T08:00:00.002+08:00| 2.385520799101839E-7|
+|1970-01-01T08:00:00.003+08:00| 8.723291723972645E-8|
+|1970-01-01T08:00:00.004+08:00| 19.999999960195904|
+|1970-01-01T08:00:00.005+08:00| 9.999999850988388|
+|1970-01-01T08:00:00.006+08:00| 3.2260694930700566E-7|
+|1970-01-01T08:00:00.007+08:00| 8.723291605373329E-8|
+|1970-01-01T08:00:00.008+08:00| 1.108657103979944E-7|
+|1970-01-01T08:00:00.009+08:00| 1.2727110997246171E-8|
+|1970-01-01T08:00:00.010+08:00|1.9852334701272664E-23|
+|1970-01-01T08:00:00.011+08:00| 1.2727111194499847E-8|
+|1970-01-01T08:00:00.012+08:00| 1.108657103979944E-7|
+|1970-01-01T08:00:00.013+08:00| 8.723291785769131E-8|
+|1970-01-01T08:00:00.014+08:00| 3.226069493070057E-7|
+|1970-01-01T08:00:00.015+08:00| 9.999999850988388|
+|1970-01-01T08:00:00.016+08:00| 19.999999960195904|
+|1970-01-01T08:00:00.017+08:00| 8.723291747109068E-8|
+|1970-01-01T08:00:00.018+08:00| 2.3855207991018386E-7|
+|1970-01-01T08:00:00.019+08:00| 1.2727112069910878E-8|
++-----------------------------+----------------------+
```
-#### 示例：指定窗口大小
+注：输入序列服从$y=sin(2\pi t/4)+2sin(2\pi t/5)$，长度为20，因此在输出序列中$k=4$和$k=5$处有尖峰。
-在指定窗口大小的情况下，本函数会把输入数据划分为若干个窗口计算有效性。
+##### 等距傅里叶变换并压缩
+
+输入序列同上，用于查询的SQL语句如下：
+
+```sql
+select fft(s1, 'result'='real', 'compress'='0.99'), fft(s1, 'result'='imag','compress'='0.99') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------+----------------------+
+| Time| fft(root.test.d1.s1,| fft(root.test.d1.s1,|
+| | "result"="real",| "result"="imag",|
+| | "compress"="0.99")| "compress"="0.99")|
++-----------------------------+----------------------+----------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0| 0.0|
+|1970-01-01T08:00:00.001+08:00| -3.932894010461041E-9| 1.2104201863039066E-8|
+|1970-01-01T08:00:00.002+08:00|-1.4021739447490164E-7| 1.9299268669082926E-7|
+|1970-01-01T08:00:00.003+08:00| -7.057291240286645E-8| 5.127422242345858E-8|
+|1970-01-01T08:00:00.004+08:00| 19.021130288047125| -6.180339875198807|
+|1970-01-01T08:00:00.005+08:00| 9.999999850988388| 3.501852745067114E-16|
+|1970-01-01T08:00:00.019+08:00| -3.932894898639461E-9|-1.2104202549376264E-8|
++-----------------------------+----------------------+----------------------+
+```
+
+注：基于傅里叶变换结果的共轭性质，压缩结果只保留前一半；根据给定的压缩参数，从低频到高频保留数据点，直到保留的能量比例超过该值；保留最后一个数据点以表示序列长度。
+
+### HighPass
+
+#### 函数简介
+
+本函数对输入序列进行高通滤波，提取高于截止频率的分量。输入序列的时间戳将被忽略，所有数据点都将被视作等距的。
+
+**函数名：** HIGHPASS
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `wpass`：归一化后的截止频率，取值为(0,1)，不可缺省。
+
+**输出序列：** 输出单个序列，类型为DOUBLE，它是滤波后的序列，长度与时间戳均与输入一致。
+
+**提示：** 输入序列中的`NaN`将被忽略。
+
+#### 使用示例
+
+
+输入序列：
-输入序列:
```
+-----------------------------+---------------+
| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| 100.0|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 112.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.0|
-|2020-01-01T00:00:22.000+08:00| 120.0|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| NaN|
-|2020-01-01T00:00:32.000+08:00| 130.0|
-|2020-01-01T00:00:34.000+08:00| 132.0|
-|2020-01-01T00:00:36.000+08:00| 134.0|
-|2020-01-01T00:00:38.000+08:00| 136.0|
-|2020-01-01T00:00:40.000+08:00| 138.0|
-|2020-01-01T00:00:42.000+08:00| 140.0|
-|2020-01-01T00:00:44.000+08:00| 142.0|
-|2020-01-01T00:00:46.000+08:00| 144.0|
-|2020-01-01T00:00:48.000+08:00| 146.0|
-|2020-01-01T00:00:50.000+08:00| 148.0|
-|2020-01-01T00:00:52.000+08:00| 150.0|
-|2020-01-01T00:00:54.000+08:00| 152.0|
-|2020-01-01T00:00:56.000+08:00| 154.0|
-|2020-01-01T00:00:58.000+08:00| 156.0|
-|2020-01-01T00:01:00.000+08:00| 158.0|
+|1970-01-01T08:00:00.000+08:00| 2.902113|
+|1970-01-01T08:00:01.000+08:00| 1.1755705|
+|1970-01-01T08:00:02.000+08:00| -2.1755705|
+|1970-01-01T08:00:03.000+08:00| -1.9021131|
+|1970-01-01T08:00:04.000+08:00| 1.0|
+|1970-01-01T08:00:05.000+08:00| 1.9021131|
+|1970-01-01T08:00:06.000+08:00| 0.1755705|
+|1970-01-01T08:00:07.000+08:00| -1.1755705|
+|1970-01-01T08:00:08.000+08:00| -0.902113|
+|1970-01-01T08:00:09.000+08:00| 0.0|
+|1970-01-01T08:00:10.000+08:00| 0.902113|
+|1970-01-01T08:00:11.000+08:00| 1.1755705|
+|1970-01-01T08:00:12.000+08:00| -0.1755705|
+|1970-01-01T08:00:13.000+08:00| -1.9021131|
+|1970-01-01T08:00:14.000+08:00| -1.0|
+|1970-01-01T08:00:15.000+08:00| 1.9021131|
+|1970-01-01T08:00:16.000+08:00| 2.1755705|
+|1970-01-01T08:00:17.000+08:00| -1.1755705|
+|1970-01-01T08:00:18.000+08:00| -2.902113|
+|1970-01-01T08:00:19.000+08:00| 0.0|
++-----------------------------+---------------+
+```
+
+
+用于查询的SQL语句：
+
+```sql
+select highpass(s1,'wpass'='0.45') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+-----------------------------------------+
+| Time|highpass(root.test.d1.s1, "wpass"="0.45")|
++-----------------------------+-----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 0.9999999534830373|
+|1970-01-01T08:00:01.000+08:00| 1.7462829277628608E-8|
+|1970-01-01T08:00:02.000+08:00| -0.9999999593178128|
+|1970-01-01T08:00:03.000+08:00| -4.1115269056426626E-8|
+|1970-01-01T08:00:04.000+08:00| 0.9999999925494194|
+|1970-01-01T08:00:05.000+08:00| 3.328126513330016E-8|
+|1970-01-01T08:00:06.000+08:00| -1.0000000183304454|
+|1970-01-01T08:00:07.000+08:00| 6.260191433311374E-10|
+|1970-01-01T08:00:08.000+08:00| 1.0000000018134796|
+|1970-01-01T08:00:09.000+08:00| -3.097210911744423E-17|
+|1970-01-01T08:00:10.000+08:00| -1.0000000018134794|
+|1970-01-01T08:00:11.000+08:00| -6.260191627862097E-10|
+|1970-01-01T08:00:12.000+08:00| 1.0000000183304454|
+|1970-01-01T08:00:13.000+08:00| -3.328126501424346E-8|
+|1970-01-01T08:00:14.000+08:00| -0.9999999925494196|
+|1970-01-01T08:00:15.000+08:00| 4.111526915498874E-8|
+|1970-01-01T08:00:16.000+08:00| 0.9999999593178128|
+|1970-01-01T08:00:17.000+08:00| -1.7462829341296528E-8|
+|1970-01-01T08:00:18.000+08:00| -0.9999999534830369|
+|1970-01-01T08:00:19.000+08:00| -1.035237222742873E-16|
++-----------------------------+-----------------------------------------+
+```
+
+注：输入序列服从$y=sin(2\pi t/4)+2sin(2\pi t/5)$，长度为20，因此高通滤波之后的输出序列服从$y=sin(2\pi t/4)$。
+
+### IFFT
+
+#### 函数简介
+
+本函数将输入的两个序列作为实部和虚部视作一个复数，进行逆快速傅里叶变换，并输出结果的实部。输入数据的格式参见`FFT`函数的输出，并支持以`FFT`函数压缩后的输出作为本函数的输入。
+
+**函数名：** IFFT
+
+**输入序列：** 仅支持两个输入序列，类型均为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `start`：输出序列的起始时刻，是一个格式为'yyyy-MM-dd HH:mm:ss'的时间字符串。在缺省情况下，为'1970-01-01 08:00:00'。
++ `interval`：输出序列的时间间隔，是一个有单位的正数。目前支持五种单位，分别是'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。在缺省情况下，为1s。
+
+
+**输出序列：** 输出单个序列，类型为DOUBLE。该序列是一个等距时间序列，它的值是将两个输入序列依次作为实部和虚部进行逆快速傅里叶变换的结果。
+
+**提示：** 如果某行数据中包含空值或`NaN`，该行数据将会被忽略。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+----------------------+----------------------+
+| Time| root.test.d1.re| root.test.d1.im|
++-----------------------------+----------------------+----------------------+
+|1970-01-01T08:00:00.000+08:00| 0.0| 0.0|
+|1970-01-01T08:00:00.001+08:00| -3.932894010461041E-9| 1.2104201863039066E-8|
+|1970-01-01T08:00:00.002+08:00|-1.4021739447490164E-7| 1.9299268669082926E-7|
+|1970-01-01T08:00:00.003+08:00| -7.057291240286645E-8| 5.127422242345858E-8|
+|1970-01-01T08:00:00.004+08:00| 19.021130288047125| -6.180339875198807|
+|1970-01-01T08:00:00.005+08:00| 9.999999850988388| 3.501852745067114E-16|
+|1970-01-01T08:00:00.019+08:00| -3.932894898639461E-9|-1.2104202549376264E-8|
++-----------------------------+----------------------+----------------------+
+```
+
+
+用于查询的SQL语句：
+
+```sql
+select ifft(re, im, 'interval'='1m', 'start'='2021-01-01 00:00:00') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+-------------------------------------------------------+
+| Time|ifft(root.test.d1.re, root.test.d1.im, "interval"="1m",|
+| | "start"="2021-01-01 00:00:00")|
++-----------------------------+-------------------------------------------------------+
+|2021-01-01T00:00:00.000+08:00| 2.902112992431231|
+|2021-01-01T00:01:00.000+08:00| 1.1755704705132448|
+|2021-01-01T00:02:00.000+08:00| -2.175570513757101|
+|2021-01-01T00:03:00.000+08:00| -1.9021130389094498|
+|2021-01-01T00:04:00.000+08:00| 0.9999999925494194|
+|2021-01-01T00:05:00.000+08:00| 1.902113046743454|
+|2021-01-01T00:06:00.000+08:00| 0.17557053610884188|
+|2021-01-01T00:07:00.000+08:00| -1.1755704886020932|
+|2021-01-01T00:08:00.000+08:00| -0.9021130371347148|
+|2021-01-01T00:09:00.000+08:00| 3.552713678800501E-16|
+|2021-01-01T00:10:00.000+08:00| 0.9021130371347154|
+|2021-01-01T00:11:00.000+08:00| 1.1755704886020932|
+|2021-01-01T00:12:00.000+08:00| -0.17557053610884144|
+|2021-01-01T00:13:00.000+08:00| -1.902113046743454|
+|2021-01-01T00:14:00.000+08:00| -0.9999999925494196|
+|2021-01-01T00:15:00.000+08:00| 1.9021130389094498|
+|2021-01-01T00:16:00.000+08:00| 2.1755705137571004|
+|2021-01-01T00:17:00.000+08:00| -1.1755704705132448|
+|2021-01-01T00:18:00.000+08:00| -2.902112992431231|
+|2021-01-01T00:19:00.000+08:00| -3.552713678800501E-16|
++-----------------------------+-------------------------------------------------------+
+```
+
+### LowPass
+
+#### 函数简介
+
+本函数对输入序列进行低通滤波，提取低于截止频率的分量。输入序列的时间戳将被忽略，所有数据点都将被视作等距的。
+
+**函数名：** LOWPASS
+
+**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+
+**参数：**
+
++ `wpass`：归一化后的截止频率，取值为(0,1)，不可缺省。
+
+**输出序列：** 输出单个序列，类型为DOUBLE，它是滤波后的序列，长度与时间戳均与输入一致。
+
+**提示：** 输入序列中的`NaN`将被忽略。
+
+#### 使用示例
+
+输入序列：
+
+```
+-----------------------------+---------------+
+| Time|root.test.d1.s1|
++-----------------------------+---------------+
+|1970-01-01T08:00:00.000+08:00| 2.902113|
+|1970-01-01T08:00:01.000+08:00| 1.1755705|
+|1970-01-01T08:00:02.000+08:00| -2.1755705|
+|1970-01-01T08:00:03.000+08:00| -1.9021131|
+|1970-01-01T08:00:04.000+08:00| 1.0|
+|1970-01-01T08:00:05.000+08:00| 1.9021131|
+|1970-01-01T08:00:06.000+08:00| 0.1755705|
+|1970-01-01T08:00:07.000+08:00| -1.1755705|
+|1970-01-01T08:00:08.000+08:00| -0.902113|
+|1970-01-01T08:00:09.000+08:00| 0.0|
+|1970-01-01T08:00:10.000+08:00| 0.902113|
+|1970-01-01T08:00:11.000+08:00| 1.1755705|
+|1970-01-01T08:00:12.000+08:00| -0.1755705|
+|1970-01-01T08:00:13.000+08:00| -1.9021131|
+|1970-01-01T08:00:14.000+08:00| -1.0|
+|1970-01-01T08:00:15.000+08:00| 1.9021131|
+|1970-01-01T08:00:16.000+08:00| 2.1755705|
+|1970-01-01T08:00:17.000+08:00| -1.1755705|
+|1970-01-01T08:00:18.000+08:00| -2.902113|
+|1970-01-01T08:00:19.000+08:00| 0.0|
++-----------------------------+---------------+
+```
+
+
+用于查询的SQL语句：
+
+```sql
+select lowpass(s1,'wpass'='0.45') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+----------------------------------------+
+| Time|lowpass(root.test.d1.s1, "wpass"="0.45")|
++-----------------------------+----------------------------------------+
+|1970-01-01T08:00:00.000+08:00| 1.9021130073323922|
+|1970-01-01T08:00:01.000+08:00| 1.1755704705132448|
+|1970-01-01T08:00:02.000+08:00| -1.1755705286582614|
+|1970-01-01T08:00:03.000+08:00| -1.9021130389094498|
+|1970-01-01T08:00:04.000+08:00| 7.450580419288145E-9|
+|1970-01-01T08:00:05.000+08:00| 1.902113046743454|
+|1970-01-01T08:00:06.000+08:00| 1.1755705212076808|
+|1970-01-01T08:00:07.000+08:00| -1.1755704886020932|
+|1970-01-01T08:00:08.000+08:00| -1.9021130222335536|
+|1970-01-01T08:00:09.000+08:00| 3.552713678800501E-16|
+|1970-01-01T08:00:10.000+08:00| 1.9021130222335536|
+|1970-01-01T08:00:11.000+08:00| 1.1755704886020932|
+|1970-01-01T08:00:12.000+08:00| -1.1755705212076801|
+|1970-01-01T08:00:13.000+08:00| -1.902113046743454|
+|1970-01-01T08:00:14.000+08:00| -7.45058112983088E-9|
+|1970-01-01T08:00:15.000+08:00| 1.9021130389094498|
+|1970-01-01T08:00:16.000+08:00| 1.1755705286582616|
+|1970-01-01T08:00:17.000+08:00| -1.1755704705132448|
+|1970-01-01T08:00:18.000+08:00| -1.9021130073323924|
+|1970-01-01T08:00:19.000+08:00| -2.664535259100376E-16|
++-----------------------------+----------------------------------------+
+```
+
+注：输入序列服从$y=sin(2\pi t/4)+2sin(2\pi t/5)$，长度为20，因此低通滤波之后的输出序列服从$y=2sin(2\pi t/5)$。
+
+
+
+
+## 序列发现
+
+### ConsecutiveSequences
+
+#### 函数简介
+
+本函数用于在多维严格等间隔数据中发现局部最长连续子序列。
+
+严格等间隔数据是指数据的时间间隔是严格相等的，允许存在数据缺失（包括行缺失和值缺失），但不允许存在数据冗余和时间戳偏移。
+
+连续子序列是指严格按照标准时间间隔等距排布，不存在任何数据缺失的子序列。如果某个连续子序列不是任何连续子序列的真子序列，那么它是局部最长的。
+
+
+**函数名：** CONSECUTIVESEQUENCES
+
+**输入序列：** 支持多个输入序列，类型可以是任意的，但要满足严格等间隔的要求。
+
+**参数：**
+
++ `gap`：标准时间间隔，是一个有单位的正数。目前支持五种单位，分别是'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。在缺省情况下，函数会利用众数估计标准时间间隔。
+
+**输出序列：** 输出单个序列，类型为 INT32。输出序列中的每一个数据点对应一个局部最长连续子序列，时间戳为子序列的起始时刻，值为子序列包含的数据点个数。
+
+**提示：** 对于不符合要求的输入，本函数不对输出做任何保证。
+
+#### 使用示例
+
+##### 手动指定标准时间间隔
+
+本函数可以通过`gap`参数手动指定标准时间间隔。需要注意的是，错误的参数设置会导致输出产生严重错误。
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:05:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:10:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:20:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:25:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:30:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:35:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:40:00.000+08:00| 1.0| null|
+|2020-01-01T00:45:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:50:00.000+08:00| 1.0| 1.0|
++-----------------------------+---------------+---------------+
+```
+
+用于查询的SQL语句：
+
+```sql
+select consecutivesequences(s1,s2,'gap'='5m') from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------------------------------+
+| Time|consecutivesequences(root.test.d1.s1, root.test.d1.s2, "gap"="5m")|
++-----------------------------+------------------------------------------------------------------+
+|2020-01-01T00:00:00.000+08:00| 3|
+|2020-01-01T00:20:00.000+08:00| 4|
+|2020-01-01T00:45:00.000+08:00| 2|
++-----------------------------+------------------------------------------------------------------+
+```
+
+##### 自动估计标准时间间隔
+
+当`gap`参数缺省时，本函数可以利用众数估计标准时间间隔，得到同样的结果。因此，这种用法更受推荐。
+
+输入序列同上，用于查询的SQL语句如下：
+
+```sql
+select consecutivesequences(s1,s2) from root.test.d1
+```
+
+输出序列：
+
+```
++-----------------------------+------------------------------------------------------+
+| Time|consecutivesequences(root.test.d1.s1, root.test.d1.s2)|
++-----------------------------+------------------------------------------------------+
+|2020-01-01T00:00:00.000+08:00| 3|
+|2020-01-01T00:20:00.000+08:00| 4|
+|2020-01-01T00:45:00.000+08:00| 2|
++-----------------------------+------------------------------------------------------+
+```
+
+### ConsecutiveWindows
+
+#### 函数简介
+
+本函数用于在多维严格等间隔数据中发现指定长度的连续窗口。
+
+严格等间隔数据是指数据的时间间隔是严格相等的，允许存在数据缺失（包括行缺失和值缺失），但不允许存在数据冗余和时间戳偏移。
+
+连续窗口是指严格按照标准时间间隔等距排布，不存在任何数据缺失的子序列。
+
+
+**函数名：** CONSECUTIVEWINDOWS
+
+**输入序列：** 支持多个输入序列，类型可以是任意的，但要满足严格等间隔的要求。
+
+**参数：**
+
++ `gap`：标准时间间隔，是一个有单位的正数。目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。在缺省情况下，函数会利用众数估计标准时间间隔。
++ `length`：序列长度，是一个有单位的正数。目前支持五种单位，分别是 'ms'（毫秒）、's'（秒）、'm'（分钟）、'h'（小时）和'd'（天）。该参数不允许缺省。
+
+**输出序列：** 输出单个序列，类型为 INT32。输出序列中的每一个数据点对应一个指定长度连续子序列，时间戳为子序列的起始时刻，值为子序列包含的数据点个数。
+
+**提示：** 对于不符合要求的输入，本函数不对输出做任何保证。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+---------------+---------------+
+| Time|root.test.d1.s1|root.test.d1.s2|
++-----------------------------+---------------+---------------+
+|2020-01-01T00:00:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:05:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:10:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:20:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:25:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:30:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:35:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:40:00.000+08:00| 1.0| null|
+|2020-01-01T00:45:00.000+08:00| 1.0| 1.0|
+|2020-01-01T00:50:00.000+08:00| 1.0| 1.0|
++-----------------------------+---------------+---------------+
```
用于查询的SQL语句：
```sql
-select validity(s1,"window"="15") from root.test.d1 where time <= 2020-01-01 00:01:00
+select consecutivewindows(s1,s2,'length'='10m') from root.test.d1
```
输出序列：
```
-+-----------------------------+----------------------------------------+
-| Time|validity(root.test.d1.s1, "window"="15")|
-+-----------------------------+----------------------------------------+
-|2020-01-01T00:00:02.000+08:00| 0.8833333333333333|
-|2020-01-01T00:00:32.000+08:00| 1.0|
-+-----------------------------+----------------------------------------+
++-----------------------------+--------------------------------------------------------------------+
+| Time|consecutivewindows(root.test.d1.s1, root.test.d1.s2, "length"="10m")|
++-----------------------------+--------------------------------------------------------------------+
+|2020-01-01T00:00:00.000+08:00| 3|
+|2020-01-01T00:20:00.000+08:00| 3|
+|2020-01-01T00:25:00.000+08:00| 3|
++-----------------------------+--------------------------------------------------------------------+
```
-## 数据修复
-### 时间戳修复(TimestampRepair)
+## 字符串处理
-#### 函数简介
+### RegexMatch
-本函数用于时间戳修复。根据给定的标准时间间隔，采用最小化修复代价的方法，通过对数据时间戳的微调，将原本时间戳间隔不稳定的数据修复为严格等间隔的数据。在未给定标准时间间隔的情况下，本函数将使用时间间隔的中位数 (median)、众数 (mode) 或聚类中心 (cluster) 来推算标准时间间隔。
+#### 函数简介
+本函数用于正则表达式匹配文本中的具体内容并返回。
-**函数名：** TIMESTAMPREPAIR
+**函数名：** REGEXMATCH
-**输入序列：** 仅支持单个输入序列，类型为 INT32 / INT64 / FLOAT / DOUBLE
+**输入序列：** 仅支持单个输入序列，类型为 TEXT。
**参数：**
-+ `interval`: 标准时间间隔（单位是毫秒），是一个正整数。在缺省情况下，将根据指定的方法推算。
-+ `method`：推算标准时间间隔的方法，取值为 'median', 'mode' 或 'cluster'，仅在`interval`缺省时有效。在缺省情况下，将使用中位数方法进行推算。
++ `regex`: 匹配的正则表达式，支持所有 Java 正则表达式语法，比如`\d+\.\d+\.\d+\.\d+`将会匹配任意 IPv4 地址.
++ `group`: 输出的匹配组序号，根据 java.util.regex 规定，第 0 组为整个正则表达式，此后的组按照左括号出现的顺序依次编号。
+ 如`A(B(CD))`中共有三个组，第 0 组`A(B(CD))`，第 1 组`B(CD)`和第 2 组`CD`。
-**输出序列：** 输出单个序列，类型与输入序列相同。该序列是修复后的输入序列。
+**输出序列：** 输出单个序列，类型为 TEXT。
-#### 示例：指定标准时间间隔
+**提示：** 空值或无法匹配给定的正则表达式的数据点没有输出结果。
+
+#### 使用示例
-在给定`interval`参数的情况下，本函数将按照指定的标准时间间隔进行修复。
输入序列：
```
-+-----------------------------+---------------+
-| Time|root.test.d2.s1|
-+-----------------------------+---------------+
-|2021-07-01T12:00:00.000+08:00| 1.0|
-|2021-07-01T12:00:10.000+08:00| 2.0|
-|2021-07-01T12:00:19.000+08:00| 3.0|
-|2021-07-01T12:00:30.000+08:00| 4.0|
-|2021-07-01T12:00:40.000+08:00| 5.0|
-|2021-07-01T12:00:50.000+08:00| 6.0|
-|2021-07-01T12:01:01.000+08:00| 7.0|
-|2021-07-01T12:01:11.000+08:00| 8.0|
-|2021-07-01T12:01:21.000+08:00| 9.0|
-|2021-07-01T12:01:31.000+08:00| 10.0|
-+-----------------------------+---------------+
++-----------------------------+-------------------------------+
+| Time| root.test.d1.s1|
++-----------------------------+-------------------------------+
+|2021-01-01T00:00:01.000+08:00| [192.168.0.1] [SUCCESS]|
+|2021-01-01T00:00:02.000+08:00| [192.168.0.24] [SUCCESS]|
+|2021-01-01T00:00:03.000+08:00| [192.168.0.2] [FAIL]|
+|2021-01-01T00:00:04.000+08:00| [192.168.0.5] [SUCCESS]|
+|2021-01-01T00:00:05.000+08:00| [192.168.0.124] [SUCCESS]|
++-----------------------------+-------------------------------+
```
-用于查询的SQL语句：
+用于查询的 SQL 语句：
```sql
-select timestamprepair(s1,'interval'='10000') from root.test.d2
+select regexmatch(s1, "regex"="\d+\.\d+\.\d+\.\d+", "group"="0") from root.test.d1
```
输出序列：
```
-+-----------------------------+----------------------------------------------------+
-| Time|timestamprepair(root.test.d2.s1, "interval"="10000")|
-+-----------------------------+----------------------------------------------------+
-|2021-07-01T12:00:00.000+08:00| 1.0|
-|2021-07-01T12:00:10.000+08:00| 2.0|
-|2021-07-01T12:00:20.000+08:00| 3.0|
-|2021-07-01T12:00:30.000+08:00| 4.0|
-|2021-07-01T12:00:40.000+08:00| 5.0|
-|2021-07-01T12:00:50.000+08:00| 6.0|
-|2021-07-01T12:01:00.000+08:00| 7.0|
-|2021-07-01T12:01:10.000+08:00| 8.0|
-|2021-07-01T12:01:20.000+08:00| 9.0|
-|2021-07-01T12:01:30.000+08:00| 10.0|
-+-----------------------------+----------------------------------------------------+
++-----------------------------+----------------------------------------------------------------------+
+| Time|regexmatch(root.test.d1.s1, "regex"="\d+\.\d+\.\d+\.\d+", "group"="0")|
++-----------------------------+----------------------------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| 192.168.0.1|
+|2021-01-01T00:00:02.000+08:00| 192.168.0.24|
+|2021-01-01T00:00:03.000+08:00| 192.168.0.2|
+|2021-01-01T00:00:04.000+08:00| 192.168.0.5|
+|2021-01-01T00:00:05.000+08:00| 192.168.0.124|
++-----------------------------+----------------------------------------------------------------------+
```
-#### 示例：自动推算标准时间间隔
+### RegexReplace
-如果`interval`参数没有给定，本函数将按照推算的标准时间间隔进行修复。
+#### 函数简介
-输入序列同上，用于查询的 SQL 语句如下：
+本函数用于将文本中符合正则表达式的匹配结果替换为指定的字符串。
+
+**函数名：** REGEXREPLACE
+
+**输入序列：** 仅支持单个输入序列，类型为 TEXT。
+
+**参数：**
+
++ `regex`: 需要替换的正则表达式，支持所有 Java 正则表达式语法。
++ `replace`: 替换后的字符串，支持 Java 正则表达式中的后向引用，
+ 形如'$1'指代了正则表达式`regex`中的第一个分组，并会在替换时自动填充匹配到的子串。
++ `limit`: 替换次数，大于等于 -1 的整数，默认为 -1 表示所有匹配的子串都会被替换。
++ `offset`: 需要跳过的匹配次数，即前`offset`次匹配到的字符子串并不会被替换，默认为 0。
++ `reverse`: 是否需要反向计数，默认为 false 即按照从左向右的次序。
+
+**输出序列：** 输出单个序列，类型为 TEXT。
+
+#### 使用示例
+
+输入序列：
+
+```
++-----------------------------+-------------------------------+
+| Time| root.test.d1.s1|
++-----------------------------+-------------------------------+
+|2021-01-01T00:00:01.000+08:00| [192.168.0.1] [SUCCESS]|
+|2021-01-01T00:00:02.000+08:00| [192.168.0.24] [SUCCESS]|
+|2021-01-01T00:00:03.000+08:00| [192.168.0.2] [FAIL]|
+|2021-01-01T00:00:04.000+08:00| [192.168.0.5] [SUCCESS]|
+|2021-01-01T00:00:05.000+08:00| [192.168.0.124] [SUCCESS]|
++-----------------------------+-------------------------------+
+```
+
+用于查询的 SQL 语句：
```sql
-select timestamprepair(s1) from root.test.d2
+select regexreplace(s1, "regex"="192\.168\.0\.(\d+)", "replace"="cluster-$1", "limit"="1") from root.test.d1
```
输出序列：
```
-+-----------------------------+--------------------------------+
-| Time|timestamprepair(root.test.d2.s1)|
-+-----------------------------+--------------------------------+
-|2021-07-01T12:00:00.000+08:00| 1.0|
-|2021-07-01T12:00:10.000+08:00| 2.0|
-|2021-07-01T12:00:20.000+08:00| 3.0|
-|2021-07-01T12:00:30.000+08:00| 4.0|
-|2021-07-01T12:00:40.000+08:00| 5.0|
-|2021-07-01T12:00:50.000+08:00| 6.0|
-|2021-07-01T12:01:00.000+08:00| 7.0|
-|2021-07-01T12:01:10.000+08:00| 8.0|
-|2021-07-01T12:01:20.000+08:00| 9.0|
-|2021-07-01T12:01:30.000+08:00| 10.0|
-+-----------------------------+--------------------------------+
++-----------------------------+-----------------------------------------------------------+
+| Time|regexreplace(root.test.d1.s1, "regex"="192\.168\.0\.(\d+)",|
+| | "replace"="cluster-$1", "limit"="1")|
++-----------------------------+-----------------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| [cluster-1] [SUCCESS]|
+|2021-01-01T00:00:02.000+08:00| [cluster-24] [SUCCESS]|
+|2021-01-01T00:00:03.000+08:00| [cluster-2] [FAIL]|
+|2021-01-01T00:00:04.000+08:00| [cluster-5] [SUCCESS]|
+|2021-01-01T00:00:05.000+08:00| [cluster-124] [SUCCESS]|
++-----------------------------+-----------------------------------------------------------+
```
-### ValueFill
+### RegexSplit
#### 函数简介
-**函数名：** ValueFill
+本函数用于使用给定的正则表达式切分文本，并返回指定的项。
-**输入序列：** 单列时序数据，类型为INT32 / INT64 / FLOAT / DOUBLE
+**函数名：** REGEXSPLIT
+
+**输入序列：** 仅支持单个输入序列，类型为 TEXT。
**参数：**
-+ `method`: {"mean", "previous", "linear", "likelihood", "AR", "MA", "SCREEN"}, 默认为 "linear"。其中，“mean” 指使用均值填补的方法； “previous" 指使用前值填补方法；“linear" 指使用线性插值填补方法；“likelihood” 为基于速度的正态分布的极大似然估计方法；“AR” 指自回归的填补方法；“MA” 指滑动平均的填补方法；"SCREEN" 指约束填补方法；缺省情况下使用 “linear”。
++ `regex`: 用于分割文本的正则表达式，支持所有 Java 正则表达式语法，比如`['"]`将会匹配任意的英文引号`'`和`"`。
++ `index`: 输出结果在切分后数组中的序号，需要是大于等于 -1 的整数，默认值为 -1 表示返回切分后数组的长度，其它非负整数即表示返回数组中对应位置的切分结果（数组的秩从 0 开始计数）。
-**输出序列：** 填补后的单维序列。
+**输出序列：** 输出单个序列，在`index`为 -1 时输出数据类型为 INT32，否则为 TEXT。
-**备注：** AR 模型采用 AR(1)，时序列需满足自相关条件，否则将输出单个数据点 (0, 0.0).
+**提示：** 如果`index`超出了切分后结果数组的秩范围，例如使用`,`切分`0,1,2`时输入`index`为 3，则该数据点没有输出结果。
+
+#### 使用示例
-### 示例：使用 linear 方法进行填补
-当`method`缺省或取值为 'linear' 时，本函数将使用线性插值方法进行填补。
输入序列：
```
+-----------------------------+---------------+
-| Time|root.test.d2.s1|
+| Time|root.test.d1.s1|
+-----------------------------+---------------+
-|2020-01-01T00:00:02.000+08:00| NaN|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| NaN|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| NaN|
-|2020-01-01T00:00:22.000+08:00| NaN|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| 128.0|
+|2021-01-01T00:00:01.000+08:00| A,B,A+,B-|
+|2021-01-01T00:00:02.000+08:00| A,A+,A,B+|
+|2021-01-01T00:00:03.000+08:00| B+,B,B|
+|2021-01-01T00:00:04.000+08:00| A+,A,A+,A|
+|2021-01-01T00:00:05.000+08:00| A,B-,B,B|
+-----------------------------+---------------+
```
用于查询的 SQL 语句：
```sql
-select valuefill(s1) from root.test.d2
+select regexsplit(s1, "regex"=",", "index"="-1") from root.test.d1
```
输出序列：
-
-
```
-+-----------------------------+-----------------------+
-| Time|valuefill(root.test.d2)|
-+-----------------------------+-----------------------+
-|2020-01-01T00:00:02.000+08:00| NaN|
-|2020-01-01T00:00:03.000+08:00| 101.0|
-|2020-01-01T00:00:04.000+08:00| 102.0|
-|2020-01-01T00:00:06.000+08:00| 104.0|
-|2020-01-01T00:00:08.000+08:00| 126.0|
-|2020-01-01T00:00:10.000+08:00| 108.0|
-|2020-01-01T00:00:14.000+08:00| 108.0|
-|2020-01-01T00:00:15.000+08:00| 113.0|
-|2020-01-01T00:00:16.000+08:00| 114.0|
-|2020-01-01T00:00:18.000+08:00| 116.0|
-|2020-01-01T00:00:20.000+08:00| 118.7|
-|2020-01-01T00:00:22.000+08:00| 121.3|
-|2020-01-01T00:00:26.000+08:00| 124.0|
-|2020-01-01T00:00:28.000+08:00| 126.0|
-|2020-01-01T00:00:30.000+08:00| 128.0|
-+-----------------------------+-----------------------+
++-----------------------------+------------------------------------------------------+
+| Time|regexsplit(root.test.d1.s1, "regex"=",", "index"="-1")|
++-----------------------------+------------------------------------------------------+
+|2021-01-01T00:00:01.000+08:00| 4|
+|2021-01-01T00:00:02.000+08:00| 4|
+|2021-01-01T00:00:03.000+08:00| 3|
+|2021-01-01T00:00:04.000+08:00| 4|
+|2021-01-01T00:00:05.000+08:00| 4|
++-----------------------------+------------------------------------------------------+
```
-#### 示例：使用 previous 方法进行填补
-
-当`method`取值为 'previous' 时，本函数将使前值填补方法进行数值填补。
-
-输入序列同上，用于查询的 SQL 语句如下：
+另一个查询的 SQL 语句：
```sql
-select valuefill(s1,"method"="previous") from root.test.d2
+select regexsplit(s1, "regex"=",", "index"="3") from root.test.d1
```
... 8154 lines suppressed ...