How to calculate the running total using aggregate

I'm developing a simple financial app for keeping track of incomes and outcomes.

For the sake of simplicity, let's suppose these are some of my documents:

{ "_id" : ObjectId("54adc0659413535e02fba115"), "description" : "test1", "amount" : 100, "dateEntry" : ISODate("2015-01-07T23:00:00Z") }
{ "_id" : ObjectId("54adc21a0d150c760270f99c"), "description" : "test2", "amount" : 50, "dateEntry" : ISODate("2015-01-06T23:00:00Z") }
{ "_id" : ObjectId("54b05da766341e4802b785c0"), "description" : "test3", "amount" : 11, "dateEntry" : ISODate("2015-01-09T23:00:00Z") }
{ "_id" : ObjectId("54b05db066341e4802b785c1"), "description" : "test4", "amount" : 2, "dateEntry" : ISODate("2015-01-09T23:00:00Z") }
{ "_id" : ObjectId("54b05dbb66341e4802b785c2"), "description" : "test5", "amount" : 12, "dateEntry" : ISODate("2015-01-09T23:00:00Z") }
{ "_id" : ObjectId("54b05f4ee0933a5c02398d55"), "description" : "test6", "amount" : 4, "dateEntry" : ISODate("2015-01-09T23:00:00Z") }

What I would like now is to draw a "balance" chart, based on such data:

[
   { day:'2015-01-06', amount:50}, 
   { day:'2015-01-07', amount:150}, 
   { day:'2015-01-09', amount:179},
...
]

In other words, I need to group all my transactions by day, and for each day I need to sum all of my previous transactions ( since the beginning of the world ).

I already know how to group by day:

$group: {
   _id: { 
      y: {$year:"$dateEntry"}, 
      m: {$month:"$dateEntry"}, 
      d: {$dayOfMonth:"$dateEntry"} 
   }, 
   sum: ???
}

But I don't know how to go back and sum all the amounts. Imagine I need to show a monthly balance report: should I run 31 queries, one for each day summing all transaction's amount except next days? Sure I can, but don't think that's the best solution.

Thanks in advance!

Actually more suited to mapReduce than the aggregation framework, at least in the initial problem solving. The aggregation framework has no concept of the value of a previous document, or the previous "grouped" value of a document so this is why it cannot do this.

On the other hand, mapReduce has a "global scope" that can be shared between stages and documents as they are processed. This will get you the "running total" for the current balance at end of day you require.

db.collection.mapReduce(
  function () {
    var date = new Date(this.dateEntry.valueOf() -
      ( this.dateEntry.valueOf() % ( 1000 * 60 * 60 * 24 ) )
    );

    emit( date, this.amount );
  },
  function(key,values) {
      return Array.sum( values );
  },
  { 
      "scope": { "total": 0 },
      "finalize": function(key,value) {
          total += value;
          return total;
      },
      "out": { "inline": 1 }
  }
)

That will sum by date grouping and then in the "finalize" section it makes a cumulative sum from each day.

   "results" : [
            {
                    "_id" : ISODate("2015-01-06T00:00:00Z"),
                    "value" : 50
            },
            {
                    "_id" : ISODate("2015-01-07T00:00:00Z"),
                    "value" : 150
            },
            {
                    "_id" : ISODate("2015-01-09T00:00:00Z"),
                    "value" : 179
            }
    ],

In the longer term you would be best of having a separate collection with an entry for each day an alter the balance using $inc in an update. Just also do an $inc upsert at the beginning of each day to create a new document carrying forward the balance from the previous day:

// increase balance
db.daily(
    { "dateEntry": currentDate },
    { "$inc": { "balance": amount } },
    { "upsert": true }
);

// decrease balance
db.daily(
    { "dateEntry": currentDate },
    { "$inc": { "balance": -amount } },
    { "upsert": true }
);

// Each day
var lastDay = db.daily.findOne({ "dateEntry": lastDate });
db.daily(
    { "dateEntry": currentDate },
    { "$inc": { "balance": lastDay.balance } },
    { "upsert": true }
);