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Aggregation Operators

$reduce (aggregation)

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  • Definition
  • Examples

Definition

$reduce

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 Expression Operators.

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.

db.events.insertMany( [
   { _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:

db.clothes.insertMany( [
   { _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:

{ _id : ObjectId("57c893067054e6e47674ce01"), discountedPrice : 9 }
{ _id : ObjectId("57c9932b7054e6e47674ce12"), discountedPrice : 24.224999999999998 }
{ _id : ObjectId("57c993457054e6e47674ce13"), discountedPrice : 24.224999999999998 }
{ _id : ObjectId("57c993687054e6e47674ce14"), discountedPrice : 17.5 }
{ _id : ObjectId("57c993837054e6e47674ce15"), discountedPrice : 54 }

String Concatenation

A collection named people contains the following documents:

db.people.insertMany( [
   { _id : 1, name : "Melissa", hobbies : [ "softball", "drawing", "reading" ] },
   { _id : 2, name : "Brad", hobbies : [ "gaming", "skateboarding" ] },
   { _id : 3, name : "Scott", hobbies : [ "basketball", "music", "fishing" ] },
   { _id : 4, name : "Tracey", hobbies : [ "acting", "yoga" ] },
   { _id : 5, name : "Josh", hobbies : [ "programming" ] },
   { _id : 6, name : "Claire" }
] )

The following example reduces the hobbies array of strings into a single string bio:

db.people.aggregate(
   [
     // Filter to return only non-empty arrays
     { $match: { "hobbies": { $gt: [ ] } } },
     {
       $project: {
         name: 1,
         bio: {
           $reduce: {
             input: "$hobbies",
             initialValue: "My hobbies include:",
             in: {
               $concat: [
                 "$$value",
                 {
                   $cond: {
                     if: { $eq: [ "$$value", "My hobbies include:" ] },
                     then: " ",
                     else: ", "
                   }
                 },
                 "$$this"
               ]
             }
           }
         }
       }
     }
   ]
)

The operation returns the following:

{ _id : 1, name : "Melissa", bio : "My hobbies include: softball, drawing, reading" }
{ _id : 2, name : "Brad", bio : "My hobbies include: gaming, skateboarding" }
{ _id : 3, name : "Scott", bio : "My hobbies include: basketball, music, fishing" }
{ _id : 4, name : "Tracey", bio : "My hobbies include: acting, yoga" }
{ _id : 5, name : "Josh", bio : "My hobbies include: programming" }

Array Concatenation

A collection named matrices contains the following documents:

db.matrices.insertMany( [
   { _id : 1, arr : [ [ 24, 55, 79 ], [ 14, 78, 35 ], [ 84, 90, 3 ], [ 50, 89, 70 ] ] },
   { _id : 2, arr : [ [ 39, 32, 43, 7 ], [ 62, 17, 80, 64 ], [ 17, 88, 11, 73 ] ] },
   { _id : 3, arr : [ [ 42 ], [ 26, 59 ], [ 17 ], [ 72, 19, 35 ] ] },
   { _id : 4 }
] )

Computing a Single Reduction

The following example collapses the two dimensional arrays into a single array collapsed:

db.arrayconcat.aggregate(
  [
    {
      $project: {
        collapsed: {
          $reduce: {
            input: "$arr",
            initialValue: [ ],
            in: { $concatArrays: [ "$$value", "$$this" ] }
          }
        }
      }
    }
  ]
)

The operation returns the following:

{ _id : 1, collapsed : [ 24, 55, 79, 14, 78, 35, 84, 90, 3, 50, 89, 70 ] }
{ _id : 2, collapsed : [ 39, 32, 43, 7, 62, 17, 80, 64, 17, 88, 11, 73 ] }
{ _id : 3, collapsed : [ 42, 26, 59, 17, 72, 19, 35 ] }
{ _id : 4, collapsed : null }

Computing a Multiple Reductions

The following example performs the same two dimensional array collapse as the example above, but also creates a new array containing only the first element of each array.

db.arrayconcat.aggregate(
  [
    {
      $project: {
        results: {
          $reduce: {
            input: "$arr",
            initialValue: [ ],
            in: {
              collapsed: {
                $concatArrays: [ "$$value.collapsed", "$$this" ]
              },
              firstValues: {
                $concatArrays: [ "$$value.firstValues", { $slice: [ "$$this", 1 ] } ]
              }
            }
          }
        }
      }
    }
  ]
)

The operation returns the following:

{ _id : 1, results : { collapsed : [ 24, 55, 79, 14, 78, 35, 84, 90, 3, 50, 89, 70 ], firstValues : [ 24, 14, 84, 50 ] } }
{ _id : 2, results : { collapsed : [ 39, 32, 43, 7, 62, 17, 80, 64, 17, 88, 11, 73 ], firstValues : [ 39, 62, 17 ] } }
{ _id : 3, results : { collapsed : [ 42, 26, 59, 17, 72, 19, 35 ], firstValues : [ 42, 26, 17, 72 ] } }
{ _id : 4, results : null }

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