$integral（积分） (expression operator)（表达式运算符）

Definition定义

$integral

Returns the approximation of the area under a curve, which is calculated using the trapezoidal rule where each set of adjacent documents form a trapezoid using the:返回曲线下面积的近似值，该值使用梯形规则计算，其中每组相邻文档使用以下公式形成梯形：

• sortBy field values in the $setWindowFields stage for the integration intervals.$setWindowFields阶段中用于积分间隔的sortBy字段值。
• input field expression result values in $integral for the y axis values.y轴值的$integral中的input字段表达式结果值。

$integral is only available in the $setWindowFields stage.$integral仅在$setWindowFields阶段可用。

$integral syntax:语法：

{
   $integral: {
      input: <expression>,
      unit: <time unit>
   }
}

$integral takes a document with these fields:获取包含以下字段的文档：

Behavior行为

If you omit a window, a default window with unbounded upper and lower limits is used.如果省略window，则使用具有无上限和下限的默认窗口。

Example示例

Create a powerConsumption collection that contains electrical power usage in kilowatts measured by meter devices at 30 second intervals:创建一个powerConsumption（功耗）集合，其中包含电表设备以30秒为间隔测量的用电量（单位：千瓦）：

db.powerConsumption.insertMany( [
   { powerMeterID: "1", timeStamp: new Date( "2020-05-18T14:10:30Z" ),
     kilowatts: 2.95 },
   { powerMeterID: "1", timeStamp: new Date( "2020-05-18T14:11:00Z" ),
     kilowatts: 2.7 },
   { powerMeterID: "1", timeStamp: new Date( "2020-05-18T14:11:30Z" ),
     kilowatts: 2.6 },
   { powerMeterID: "1", timeStamp: new Date( "2020-05-18T14:12:00Z" ),
     kilowatts: 2.98 },
   { powerMeterID: "2", timeStamp: new Date( "2020-05-18T14:10:30Z" ),
     kilowatts: 2.5 },
   { powerMeterID: "2", timeStamp: new Date( "2020-05-18T14:11:00Z" ),
     kilowatts: 2.25 },
   { powerMeterID: "2", timeStamp: new Date( "2020-05-18T14:11:30Z" ),
     kilowatts: 2.75 },
   { powerMeterID: "2", timeStamp: new Date( "2020-05-18T14:12:00Z" ),
     kilowatts: 2.82 }
] )

This example uses $integral in the $setWindowFields stage to output the energy consumption in kilowatt-hours measured by each meter device:此示例在$setWindowFields阶段使用$integral输出每个仪表设备测量的能耗（千瓦时）：

db.powerConsumption.aggregate( [
   {
      $setWindowFields: {
         partitionBy: "$powerMeterID",
         sortBy: { timeStamp: 1 },
         output: {
            powerMeterKilowattHours: {
               $integral: {
                  input: "$kilowatts",
                  unit: "hour"
               },
               window: {
                  range: [ "unbounded", "current" ],
                  unit: "hour"
               }
            }
         }
      }
   }
] )

In the example:在示例中：

• partitionBy: "$powerMeterID" partitions the documents in the collection by powerMeterID.通过powerMeterID对集合中的文档进行分区。
• sortBy: { timeStamp: 1 } sorts the documents in each partition by timeStamp in ascending order (1), so the earliest timeStamp is first.按timeStamp升序（1）对每个分区中的文档进行排序，因此最早的timeStamp位居前列。

• output sets the kilowatts integral value in a new field called powerMeterKilowattHours using $integral that is run in a range window.output在一个名为powerMeterKilowattHours的新字段中设置kilowatts积分值，该字段使用在范围窗口中运行的$integral。

  • The input expression is set to "$kilowatts", which is used for the y axis values in the integral calculation.input表达式设置为"$kilowatts"（千瓦），用于积分计算中的y轴值。
  • The $integral unit is set to "hour" for the timeStamp field, which means $integral returns the kilowatt-hours energy consumption.timeStamp字段的$integral单位设置为"hour"，这意味着$integral返回千瓦时的能耗。
  • The window contains documents between an unbounded lower limit and the current document in the output. 该window包含的文档位于unbounded下限和输出中的current文档之间。This means $integral returns the total kilowatt-hours energy consumption for the documents from the beginning of the partition, which is the first data point in the partition for each power meter, to the timestamp of the current document in the output.这意味着$integral返回文档从分区开始（即每个电表分区中的第一个数据点）到输出中当前文档的时间戳的总千瓦时能耗。

In this example output, the energy consumption measured by meters 1 and 2 are shown in the powerMeterKilowattHours field:在这个示例输出中，电表1和2测量的能耗显示在powerMeterKilowattHours字段中：

{ "_id" : ObjectId("60cbdc3f833dfeadc8e62863"), "powerMeterID" : "1",
  "timeStamp" : ISODate("2020-05-18T14:10:30Z"), "kilowatts" : 2.95,
  "powerMeterKilowattHours" : 0 }
{ "_id" : ObjectId("60cbdc3f833dfeadc8e62864"), "powerMeterID" : "1",
  "timeStamp" : ISODate("2020-05-18T14:11:00Z"), "kilowatts" : 2.7,
  "powerMeterKilowattHours" : 0.023541666666666666 }
{ "_id" : ObjectId("60cbdc3f833dfeadc8e62865"), "powerMeterID" : "1",
  "timeStamp" : ISODate("2020-05-18T14:11:30Z"), "kilowatts" : 2.6,
  "powerMeterKilowattHours" : 0.045625 }
{ "_id" : ObjectId("60cbdc3f833dfeadc8e62866"), "powerMeterID" : "1",
  "timeStamp" : ISODate("2020-05-18T14:12:00Z"), "kilowatts" : 2.98,
  "powerMeterKilowattHours" : 0.068875 }
{ "_id" : ObjectId("60cbdc3f833dfeadc8e62867"), "powerMeterID" : "2",
  "timeStamp" : ISODate("2020-05-18T14:10:30Z"), "kilowatts" : 2.5,
  "powerMeterKilowattHours" : 0 }
{ "_id" : ObjectId("60cbdc3f833dfeadc8e62868"), "powerMeterID" : "2",
  "timeStamp" : ISODate("2020-05-18T14:11:00Z"), "kilowatts" : 2.25,
  "powerMeterKilowattHours" : 0.019791666666666666 }
{ "_id" : ObjectId("60cbdc3f833dfeadc8e62869"), "powerMeterID" : "2",
  "timeStamp" : ISODate("2020-05-18T14:11:30Z"), "kilowatts" : 2.75,
  "powerMeterKilowattHours" : 0.040625 }
{ "_id" : ObjectId("60cbdc3f833dfeadc8e6286a"), "powerMeterID" : "2",
  "timeStamp" : ISODate("2020-05-18T14:12:00Z"), "kilowatts" : 2.82,
  "powerMeterKilowattHours" : 0.06383333333333334 }