$integral (aggregation)

定義

$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:

• sortBy field values in the $setWindowFields stage for the integration intervals.

• 入力 フィールド 式 result values in $integral for the y axis values.

$integralは$setWindowFieldsステージでのみ使用可能です。

$integral構文:

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

$integralは次のフィールドを持つドキュメントを取得します。

動作

If you omit a ウィンドウ, a default window with unbounded upper and lower limits is used.

例

Create a powerConsumption collection that contains electrical power usage in kilowatts measured by meter devices at 30 second intervals:

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:

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

この例では、次のことが行われます。

• partitionBy: "$powerMeterID" partitions the documents in the collection by powerMeterID.

• sortBy: { timeStamp: 1 } は、各パーティション内のドキュメントを timeStamp を基準に昇順（1）にソートするため、最も古い timeStamp が最初になります。

• output sets the kilowatts integral value in a new field called powerMeterKilowattHours using $integral that is run in a 範囲 window.

  • The 入力 expression is set to "$kilowatts", which is used for the y axis values in the integral calculation.

  • The $integral 単位 is set to "hour" for the timeStamp field, which means $integral returns the kilowatt-hours energy consumption.

  • The ウィンドウ contains documents between an unbounded lower limit and the current document in the output. 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.

In this example output, the energy consumption measured by meters 1 and 2 are shown in the powerMeterKilowattHours field:

{ "_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 }