Java 类名:com.alibaba.alink.operator.stream.outlier.IForestOutlier4GroupedDataStreamOp
Python 类名:IForestOutlier4GroupedDataStreamOp

功能介绍

iForest 可以识别数据中异常点,在异常检测领域有比较好的效果。算法使用 sub-sampling 方法,降低了算法的计算复杂度。

文献或出处

  1. Isolation Forest

    参数说明

    | 名称 | 中文名称 | 描述 | 类型 | 是否必须? | 取值范围 | 默认值 | | —- | —- | —- | —- | —- | —- | —- |

| inputMTableCol | Not available! | Not available! | String | ✓ | | |

| outputMTableCol | Not available! | Not available! | String | ✓ | | |

| predictionCol | 预测结果列名 | 预测结果列名 | String | ✓ | | |

| featureCols | 特征列名数组 | 特征列名数组,默认全选 | String[] | | 所选列类型为 [BIGDECIMAL, BIGINTEGER, BYTE, DOUBLE, FLOAT, INTEGER, LONG, SHORT] | null |

| maxOutlierNumPerGroup | 每组最大异常点数目 | 每组最大异常点数目 | Integer | | | |

| maxOutlierRatio | 最大异常点比例 | 算法检测异常点的最大比例 | Double | | | |

| numTrees | 模型中树的棵数 | 模型中树的棵数 | Integer | | | 100 |

| outlierThreshold | 异常评分阈值 | 只有评分大于该阈值才会被认为是异常点 | Double | | | |

| predictionDetailCol | 预测详细信息列名 | 预测详细信息列名 | String | | | |

| subsamplingSize | 每棵树的样本采样行数 | 每棵树的样本采样行数,默认 256 ,最小 2 ,最大 100000 . | Integer | | [1, 100000] | 256 |

| tensorCol | tensor列 | tensor列 | String | | 所选列类型为 [BOOL_TENSOR, BYTE_TENSOR, DOUBLE_TENSOR, FLOAT_TENSOR, INT_TENSOR, LONG_TENSOR, STRING, STRING_TENSOR, TENSOR, UBYTE_TENSOR] | null |

| vectorCol | 向量列名 | 向量列对应的列名,默认值是null | String | | 所选列类型为 [DENSE_VECTOR, SPARSE_VECTOR, STRING, VECTOR] | null |

| numThreads | 组件多线程线程个数 | 组件多线程线程个数 | Integer | | | 1 |

代码示例

Python 代码

  1. import time
  2. import datetime
  3. import numpy as np
  4. import pandas as pd
  5. data = pd.DataFrame([
  6. [1, datetime.datetime.fromtimestamp(1), 10.0, 0],
  7. [1, datetime.datetime.fromtimestamp(2), 11.0, 0],
  8. [1, datetime.datetime.fromtimestamp(3), 12.0, 0],
  9. [1, datetime.datetime.fromtimestamp(4), 13.0, 0],
  10. [1, datetime.datetime.fromtimestamp(5), 14.0, 0],
  11. [1, datetime.datetime.fromtimestamp(6), 15.0, 0],
  12. [1, datetime.datetime.fromtimestamp(7), 16.0, 0],
  13. [1, datetime.datetime.fromtimestamp(8), 17.0, 0],
  14. [1, datetime.datetime.fromtimestamp(9), 18.0, 0],
  15. [1, datetime.datetime.fromtimestamp(10), 19.0, 0]
  16. ])
  17. dataOp = dataframeToOperator(
  18. data, schemaStr='id int, ts timestamp, val double, label int', op_type='stream')
  19. dataOp.link(
  20. OverCountWindowStreamOp()
  21. .setGroupCols(["id"])
  22. .setTimeCol("ts")
  23. .setPrecedingRows(5)
  24. .setClause("MTABLE_AGG(ts, val) as series_data")
  25. .setReservedCols(["id", "label"])
  26. ).link(
  27. IForestOutlier4GroupedDataStreamOp()
  28. .setInputMTableCol("series_data")
  29. .setFeatureCols(["val"])
  30. .setOutputMTableCol("output_series")
  31. .setPredictionCol("pred")
  32. ).link(
  33. FlattenMTableStreamOp()
  34. .setSelectedCol("output_series")
  35. .setSchemaStr("ts TIMESTAMP, val DOUBLE, pred BOOLEAN")
  36. ).print()
  37. StreamOperator.execute()

Java 代码

  1. import org.apache.flink.types.Row;
  2. import com.alibaba.alink.operator.stream.StreamOperator;
  3. import com.alibaba.alink.operator.stream.dataproc.FlattenMTableStreamOp;
  4. import com.alibaba.alink.operator.stream.feature.OverCountWindowStreamOp;
  5. import com.alibaba.alink.operator.stream.outlier.IForestOutlier4GroupedDataStreamOp;
  6. import com.alibaba.alink.operator.stream.source.MemSourceStreamOp;
  7. import org.junit.Test;
  8. import java.sql.Timestamp;
  9. import java.util.Arrays;
  10. import java.util.List;
  11. public class IForestOutlier4GroupedDataStreamOpTest {
  12. @Test
  13. public void test() throws Exception {
  14. List <Row> mTableData = Arrays.asList(
  15. Row.of(1, new Timestamp(1), 10.0, 0),
  16. Row.of(1, new Timestamp(2), 11.0, 0),
  17. Row.of(1, new Timestamp(3), 12.0, 0),
  18. Row.of(1, new Timestamp(4), 13.0, 0),
  19. Row.of(1, new Timestamp(5), 14.0, 0),
  20. Row.of(1, new Timestamp(6), 15.0, 0),
  21. Row.of(1, new Timestamp(7), 16.0, 0),
  22. Row.of(1, new Timestamp(8), 17.0, 0),
  23. Row.of(1, new Timestamp(9), 18.0, 0),
  24. Row.of(1, new Timestamp(10), 19.0, 0)
  25. );
  26. MemSourceStreamOp dataOp = new MemSourceStreamOp(mTableData,
  27. new String[] {"id", "ts", "val", "label"});
  28. dataOp.link(
  29. new OverCountWindowStreamOp()
  30. .setGroupCols("id")
  31. .setTimeCol("ts")
  32. .setPrecedingRows(10)
  33. .setClause("MTABLE_AGG(ts, val) as series_data")
  34. .setReservedCols("id", "label")
  35. ).link(
  36. new IForestOutlier4GroupedDataStreamOp()
  37. .setInputMTableCol("series_data")
  38. .setFeatureCols("val")
  39. .setOutputMTableCol("output_series")
  40. .setPredictionCol("pred")
  41. ).link(
  42. new FlattenMTableStreamOp()
  43. .setSelectedCol("output_series")
  44. .setSchemaStr("ts TIMESTAMP, val DOUBLE, pred BOOLEAN")
  45. ).print();
  46. StreamOperator.execute();
  47. }
  48. }

运行结果

| id | label | series_data | output_series | ts | val | pred | | —- | —- | —- | —- | —- | —- | —- |

| 1 | 0 | MTable(1,2)(ts,val) | MTable(1,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1 | 0 | MTable(2,2)(ts,val) | MTable(2,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1 | 0 | MTable(2,2)(ts,val) | MTable(2,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1 | 0 | MTable(3,2)(ts,val) | MTable(3,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1 | 0 | MTable(3,2)(ts,val) | MTable(3,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1 | 0 | MTable(3,2)(ts,val) | MTable(3,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1 | 0 | MTable(4,2)(ts,val) | MTable(4,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1 | 0 | MTable(4,2)(ts,val) | MTable(4,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1 | 0 | MTable(4,2)(ts,val) | MTable(4,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1 | 0 | MTable(4,2)(ts,val) | MTable(4,3)(ts,val,pred) | 1970-01-01 08:00:00.004 | 13.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1 | 0 | MTable(5,2)(ts,val) | MTable(5,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(5,2)(ts,val) | MTable(5,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(5,2)(ts,val) | MTable(5,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(5,2)(ts,val) | MTable(5,3)(ts,val,pred) | 1970-01-01 08:00:00.004 | 13.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(5,2)(ts,val) | MTable(5,3)(ts,val,pred) | 1970-01-01 08:00:00.005 | 14.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(6,2)(ts,val) | MTable(6,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(6,2)(ts,val) | MTable(6,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(6,2)(ts,val) | MTable(6,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(6,2)(ts,val) | MTable(6,3)(ts,val,pred) | 1970-01-01 08:00:00.004 | 13.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(6,2)(ts,val) | MTable(6,3)(ts,val,pred) | 1970-01-01 08:00:00.005 | 14.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(6,2)(ts,val) | MTable(6,3)(ts,val,pred) | 1970-01-01 08:00:00.006 | 15.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(7,2)(ts,val) | MTable(7,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(7,2)(ts,val) | MTable(7,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(7,2)(ts,val) | MTable(7,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(7,2)(ts,val) | MTable(7,3)(ts,val,pred) | 1970-01-01 08:00:00.004 | 13.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(7,2)(ts,val) | MTable(7,3)(ts,val,pred) | 1970-01-01 08:00:00.005 | 14.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(7,2)(ts,val) | MTable(7,3)(ts,val,pred) | 1970-01-01 08:00:00.006 | 15.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(7,2)(ts,val) | MTable(7,3)(ts,val,pred) | 1970-01-01 08:00:00.007 | 16.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.004 | 13.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.005 | 14.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.006 | 15.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.007 | 16.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(8,2)(ts,val) | MTable(8,3)(ts,val,pred) | 1970-01-01 08:00:00.008 | 17.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.004 | 13.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.005 | 14.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.006 | 15.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.007 | 16.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.008 | 17.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(9,2)(ts,val) | MTable(9,3)(ts,val,pred) | 1970-01-01 08:00:00.009 | 18.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.001 | 10.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.002 | 11.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.003 | 12.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.004 | 13.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.005 | 14.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.006 | 15.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.007 | 16.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.008 | 17.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.009 | 18.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |

| 1 | 0 | MTable(10,2)(ts,val) | MTable(10,3)(ts,val,pred) | 1970-01-01 08:00:00.01 | 19.0000 | false |

| 1970-01-01 08:00:00.001 | 10.0000 | 1970-01-01 08:00:00.001 | 10.0000 | false | | |

| 1970-01-01 08:00:00.002 | 11.0000 | 1970-01-01 08:00:00.002 | 11.0000 | false | | |

| 1970-01-01 08:00:00.003 | 12.0000 | 1970-01-01 08:00:00.003 | 12.0000 | false | | |

| 1970-01-01 08:00:00.004 | 13.0000 | 1970-01-01 08:00:00.004 | 13.0000 | false | | |

| 1970-01-01 08:00:00.005 | 14.0000 | 1970-01-01 08:00:00.005 | 14.0000 | false | | |