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$reduce (aggregation)

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Definition

$reduce

New in version 3.4.

Applies an expression to each element in an array and combines them into a single value.

$reduce has the following syntax:

{
    $reduce: {
        input: <array>,
        initialValue: <expression>,
        in: <expression>
    }
}
Field Type Description
input array

Can be any valid expression that resolves to an array. For more information on expressions, see Expressions.

If the argument resolves to a value of null or refers to a missing field, $reduce returns null.

If the argument does not resolve to an array or null nor refers to a missing field, $reduce returns an error.
initialValue expression The initial cumulative value set before in is applied to the first element of the input array.
in expression

A valid expression that $reduce applies to each element in the input array in left-to-right order. Wrap the input value with $reverseArray to yield the equivalent of applying the combining expression from right-to-left.

During evaluation of the in expression, two variables will be available:

  • value is the variable that represents the cumulative value of the expression.
  • this is the variable that refers to the element being processed.

If input resolves to an empty array, $reduce returns initialValue.

Example Results 
 {
    $reduce: {
       input: ["a", "b", "c"],
       initialValue: "",
       in: { $concat : ["$$value", "$$this"] }
     }
 }
"abc" 
{
   $reduce: {
      input: [ 1, 2, 3, 4 ],
      initialValue: { sum: 5, product: 2 },
      in: {
         sum: { $add : ["$$value.sum", "$$this"] },
         product: { $multiply: [ "$$value.product", "$$this" ] }
      }
   }
}
{ "sum" : 15, "product" : 48 } 
{
   $reduce: {
      input: [ [ 3, 4 ], [ 5, 6 ] ],
      initialValue: [ 1, 2 ],
      in: { $concatArrays : ["$$value", "$$this"] }
   }
}
[ 1, 2, 3, 4, 5, 6 ]

Examples

Multiplication

Probability

A collection named events contains the events of a probability experiment. Each experiment can have multiple events, such as rolling a die several times or drawing several cards (without replacement) in succession to achieve a desired result. In order to obtain the overall probability of the experiment, we will need to multiply the probability of each event in the experiment.

{_id:1, "type":"die", "experimentId":"r5", "description":"Roll a 5", "eventNum":1, "probability":0.16666666666667}
{_id:2, "type":"card", "experimentId":"d3rc", "description":"Draw 3 red cards", "eventNum":1, "probability":0.5}
{_id:3, "type":"card", "experimentId":"d3rc", "description":"Draw 3 red cards", "eventNum":2, "probability":0.49019607843137}
{_id:4, "type":"card", "experimentId":"d3rc", "description":"Draw 3 red cards", "eventNum":3, "probability":0.48}
{_id:5, "type":"die", "experimentId":"r16", "description":"Roll a 1 then a 6", "eventNum":1, "probability":0.16666666666667}
{_id:6, "type":"die", "experimentId":"r16", "description":"Roll a 1 then a 6", "eventNum":2, "probability":0.16666666666667}
{_id:7, "type":"card", "experimentId":"dak", "description":"Draw an ace, then a king", "eventNum":1, "probability":0.07692307692308}
{_id:8, "type":"card", "experimentId":"dak", "description":"Draw an ace, then a king", "eventNum":2, "probability":0.07843137254902}

Steps:

  1. Use $group to group by the experimentId and use $push to create an array with the probability of each event.
  2. Use $reduce with $multiply to multiply and combine the elements of probabilityArr into a single value and project it.
db.probability.aggregate(
  [
    {
      $group: {
        _id: "$experimentId",
        "probabilityArr": { $push: "$probability" }
      }
    },
    {
      $project: {
        "description": 1,
        "results": {
          $reduce: {
            input: "$probabilityArr",
            initialValue: 1,
            in: { $multiply: [ "$$value", "$$this" ] }
          }
        }
      }
    }
  ]
)

The operation returns the following:

{ "_id" : "dak", "results" : 0.00603318250377101 }
{ "_id" : "r5", "results" : 0.16666666666667 }
{ "_id" : "r16", "results" : 0.027777777777778886 }
{ "_id" : "d3rc", "results" : 0.11764705882352879 }

Discounted Merchandise

A collection named clothes contains the following documents:

{ "_id" : 1, "productId" : "ts1", "description" : "T-Shirt", "color" : "black", "size" : "M", "price" : 20, "discounts" : [ 0.5, 0.1 ] }
{ "_id" : 2, "productId" : "j1", "description" : "Jeans", "color" : "blue", "size" : "36", "price" : 40, "discounts" : [ 0.25, 0.15, 0.05 ] }
{ "_id" : 3, "productId" : "s1", "description" : "Shorts", "color" : "beige", "size" : "32", "price" : 30, "discounts" : [ 0.15, 0.05 ] }
{ "_id" : 4, "productId" : "ts2", "description" : "Cool T-Shirt", "color" : "White", "size" : "L", "price" : 25, "discounts" : [ 0.3 ] }
{ "_id" : 5, "productId" : "j2", "description" : "Designer Jeans", "color" : "blue", "size" : "30", "price" : 80, "discounts" : [ 0.1, 0.25 ] }

Each document contains a discounts array containing the currently available percent-off coupons for each item. If each discount can be applied to the product once, we can calculate the lowest price by using $reduce to apply the following formula for each element in the discounts array: (1 - discount) * price.

db.clothes.aggregate(
  [
    {
      $project: {
        "discountedPrice": {
          $reduce: {
            input: "$discounts",
            initialValue: "$price",
            in: { $multiply: [ "$$value", { $subtract: [ 1, "$$this" ] } ] }
          }
        }
      }
    }
  ]
)

The operation returns the following: