$max (aggregation)

Null or Missing Values

If some, but not all, documents for the $max operation have either a null value for the field or are missing the field, the $max operator only considers the non-null and the non-missing values for the field.

If all documents for the $max operation have null value for the field or are missing the field, the $max operator returns null for the maximum value.

Array Operand

In the $group and $setWindowFields stages, if the expression resolves to an array, $max does not traverse the array and compares the array as a whole.

In the other supported stages:

• With a single expression as its operand, if the expression resolves to an array, $max traverses into the array to operate on the numerical elements of the array to return a single value.

• With a list of expressions as its operand, if any of the expressions resolves to an array, $max does not traverse into the array but instead treats the array as a non-numerical value.

Use in $group Stage

Consider a sales collection with the following documents:

{ "_id" : 1, "item" : "abc", "price" : 10, "quantity" : 2, "date" : ISODate("2014-01-01T08:00:00Z") }
{ "_id" : 2, "item" : "jkl", "price" : 20, "quantity" : 1, "date" : ISODate("2014-02-03T09:00:00Z") }
{ "_id" : 3, "item" : "xyz", "price" : 5, "quantity" : 5, "date" : ISODate("2014-02-03T09:05:00Z") }
{ "_id" : 4, "item" : "abc", "price" : 10, "quantity" : 10, "date" : ISODate("2014-02-15T08:00:00Z") }
{ "_id" : 5, "item" : "xyz", "price" : 5, "quantity" : 10, "date" : ISODate("2014-02-15T09:05:00Z") }

Grouping the documents by the item field, the following operation uses the $max accumulator to compute the maximum total amount and maximum quantity for each group of documents.

db.sales.aggregate(
   [
     {
       $group:
         {
           _id: "$item",
           maxTotalAmount: { $max: { $multiply: [ "$price", "$quantity" ] } },
           maxQuantity: { $max: "$quantity" }
         }
     }
   ]
)

The operation returns the following results:

{ "_id" : "xyz", "maxTotalAmount" : 50, "maxQuantity" : 10 }
{ "_id" : "jkl", "maxTotalAmount" : 20, "maxQuantity" : 1 }
{ "_id" : "abc", "maxTotalAmount" : 100, "maxQuantity" : 10 }

Use in $project Stage

A collection students contains the following documents:

{ "_id": 1, "quizzes": [ 10, 6, 7 ], "labs": [ 5, 8 ], "final": 80, "midterm": 75 }
{ "_id": 2, "quizzes": [ 9, 10 ], "labs": [ 8, 8 ], "final": 95, "midterm": 80 }
{ "_id": 3, "quizzes": [ 4, 5, 5 ], "labs": [ 6, 5 ], "final": 78, "midterm": 70 }

The following example uses the $max in the $project stage to calculate the maximum quiz scores, the maximum lab scores, and the maximum of the final and the midterm:

db.students.aggregate([
   { $project: { quizMax: { $max: "$quizzes"}, labMax: { $max: "$labs" }, examMax: { $max: [ "$final", "$midterm" ] } } }
])

The operation results in the following documents:

{ "_id" : 1, "quizMax" : 10, "labMax" : 8, "examMax" : 80 }
{ "_id" : 2, "quizMax" : 10, "labMax" : 8, "examMax" : 95 }
{ "_id" : 3, "quizMax" : 5, "labMax" : 6, "examMax" : 78 }

Use in $setWindowFields Stage

Create a cakeSales collection that contains cake sales in the states of California (CA) and Washington (WA):

db.cakeSales.insertMany( [
   { _id: 0, type: "chocolate", orderDate: new Date("2020-05-18T14:10:30Z"),
     state: "CA", price: 13, quantity: 120 },
   { _id: 1, type: "chocolate", orderDate: new Date("2021-03-20T11:30:05Z"),
     state: "WA", price: 14, quantity: 140 },
   { _id: 2, type: "vanilla", orderDate: new Date("2021-01-11T06:31:15Z"),
     state: "CA", price: 12, quantity: 145 },
   { _id: 3, type: "vanilla", orderDate: new Date("2020-02-08T13:13:23Z"),
     state: "WA", price: 13, quantity: 104 },
   { _id: 4, type: "strawberry", orderDate: new Date("2019-05-18T16:09:01Z"),
     state: "CA", price: 41, quantity: 162 },
   { _id: 5, type: "strawberry", orderDate: new Date("2019-01-08T06:12:03Z"),
     state: "WA", price: 43, quantity: 134 }
] )

This example uses $max in the $setWindowFields stage to output the maximum quantity of cake sales for each state:

db.cakeSales.aggregate( [
   {
      $setWindowFields: {
         partitionBy: "$state",
         sortBy: { orderDate: 1 },
         output: {
            maximumQuantityForState: {
               $max: "$quantity",
               window: {
                  documents: [ "unbounded", "current" ]
               }
            }
         }
      }
   }
] )

In the example:

• partitionBy: "$state" partitions the documents in the collection by state. There are partitions for CA and WA.

• sortBy: { orderDate: 1 } sorts the documents in each partition by orderDate in ascending order (1), so the earliest orderDate is first.

• output sets the maximumQuantityForState field to the maximum quantity value using $max that is run in a documents window.

  The window contains documents between an unbounded lower limit and the current document in the output. This means $max returns the maximum quantity for the documents between the beginning of the partition and the current document.

In this output, the maximum quantity for CA and WA is shown in the maximumQuantityForState field:

{ "_id" : 4, "type" : "strawberry", "orderDate" : ISODate("2019-05-18T16:09:01Z"),
  "state" : "CA", "price" : 41, "quantity" : 162, "maximumQuantityForState" : 162 }
{ "_id" : 0, "type" : "chocolate", "orderDate" : ISODate("2020-05-18T14:10:30Z"),
  "state" : "CA", "price" : 13, "quantity" : 120, "maximumQuantityForState" : 162 }
{ "_id" : 2, "type" : "vanilla", "orderDate" : ISODate("2021-01-11T06:31:15Z"),
  "state" : "CA", "price" : 12, "quantity" : 145, "maximumQuantityForState" : 162 }
{ "_id" : 5, "type" : "strawberry", "orderDate" : ISODate("2019-01-08T06:12:03Z"),
  "state" : "WA", "price" : 43, "quantity" : 134, "maximumQuantityForState" : 134 }
{ "_id" : 3, "type" : "vanilla", "orderDate" : ISODate("2020-02-08T13:13:23Z"),
  "state" : "WA", "price" : 13, "quantity" : 104, "maximumQuantityForState" : 134 }
{ "_id" : 1, "type" : "chocolate", "orderDate" : ISODate("2021-03-20T11:30:05Z"),
  "state" : "WA", "price" : 14, "quantity" : 140, "maximumQuantityForState" : 140 }