$derivative (Window Function)

Definition

$derivative

Returns the average rate of change within the specified window, which is calculated using the:

• First and last documents in the $setWindowFields stage window.
• Numerator, which is set to the result of subtracting the numeric expression value for the first document from the expression value for the last document.
• Denominator, which is set to the result of subtracting the sortBy field value for the first document from the sortBy field value for the last document.

$derivative is only available in the $setWindowFields stage. You must specify a window in the $setWindowFields stage when using $derivative.

$derivative syntax:

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

Behavior

You must specify a window in the $setWindowFields stage when using $derivative.

Example

Create a deliveryFleet collection that contains odometer readings for delivery trucks recorded at 30 second intervals:

db.deliveryFleet.insertMany( [
   { truckID: "1", timeStamp: new Date( "2020-05-18T14:10:30Z" ), miles: 1295.1 },
   { truckID: "1", timeStamp: new Date( "2020-05-18T14:11:00Z" ), miles: 1295.63 },
   { truckID: "1", timeStamp: new Date( "2020-05-18T14:11:30Z" ), miles: 1296.25 },
   { truckID: "1", timeStamp: new Date( "2020-05-18T14:12:00Z" ), miles: 1296.76 },
   { truckID: "2", timeStamp: new Date( "2020-05-18T14:10:30Z" ), miles: 10234.1 },
   { truckID: "2", timeStamp: new Date( "2020-05-18T14:11:00Z" ), miles: 10234.33 },
   { truckID: "2", timeStamp: new Date( "2020-05-18T14:11:30Z" ), miles: 10234.73 },
   { truckID: "2", timeStamp: new Date( "2020-05-18T14:12:00Z" ), miles: 10235.13 }
] )

This example uses $derivative in the $setWindowFields stage to obtain the average speed in miles per hour for each truck, and the $match stage to filter the results to trucks whose speed exceeded 50 miles per hour:

db.deliveryFleet.aggregate( [
   {
      $setWindowFields: {
         partitionBy: "$truckID",
         sortBy: { timeStamp: 1 },
         output: {
            truckAverageSpeed: {
               $derivative: {
                  input: "$miles",
                  unit: "hour"
               },
               window: {
                  range: [ -30, 0 ],
                  unit: "second"
               }
            }
         }
      }
   },
   {
      $match: {
         truckAverageSpeed: {
            $gt: 50
         }
      }
   }
] )

In the example:

• The $setWindowFields stage obtains the average speed in miles per hour for each truck:

  • partitionBy: "$truckID" partitions the documents in the collection by truckID.
  • sortBy: { timeStamp: 1 } sorts the documents in each partition by timeStamp in ascending order (1), so the earliest odometer reading is first.

  • output sets the miles derivative value in a new field called truckAverageSpeed using $derivative that is run in a range window.

    • The input expression is set to "$miles", which is used in the numerator for the derivative calculation.
    • The $derivative unit is set to "hour" for the timeStamp field, which is used in the denominator for the derivative calculation.
    • The window contains the range between a lower limit of -30 seconds (the previous 30 seconds from the current document in the output) and 0 seconds (matches the current document's timeStamp value in the output). This means $derivative returns the average speed for each truck in miles per hour in the 30 second window.
• The $match stage uses the greater than operator $gt to filter the results to trucks whose speed exceeded 50 miles per hour.

In the following example output, the speed for truck 1 is shown in the truckAverageSpeed field. The speed for truck 2 is not shown because truck 2 did not exceed 50 miles per hour.

{ "_id" : ObjectId("60cb8a7e833dfeadc8e6285c"), "truckID" : "1",
  "timeStamp" : ISODate("2020-05-18T14:11:00Z"), "miles" : 1295.63,
  "truckAverageSpeed" : 63.60000000002401 }
{ "_id" : ObjectId("60cb8a7e833dfeadc8e6285d"), "truckID" : "1",
  "timeStamp" : ISODate("2020-05-18T14:11:30Z"), "miles" : 1296.25,
  "truckAverageSpeed" : 74.3999999999869 }
{ "_id" : ObjectId("60cb8a7e833dfeadc8e6285e"), "truckID" : "1",
  "timeStamp" : ISODate("2020-05-18T14:12:00Z"), "miles" : 1296.76,
  "truckAverageSpeed" : 61.199999999998916 }