multiplication and group by in mongodb - mongodb

Question

I have a collection as follow in mongodb :
{
"_id" : ObjectId("54901212f315dce7077204af"),
"Date" : ISODate("2014-10-20T04:00:00.000Z"),
"Type" : "Twitter",
"Entities" : [
{
"ID" : 2,
"Name" : "test1",
"Sentiment" : {
"Value" : 20,
"Neutral" : 1
},
{
"ID" : 1,
"Name" : "test1",
"Sentiment" : {
"Value" : 1,
"Neutral" : 1
}
},
{
"ID" : 3,
"Name" : "test1",
"Sentiment" : {
"Value" : 2,
"Neutral" : 1
}
]
}
and I have couple of them , for example in date 2014-10-20 you might find 5 tweets each of which have different value for sentiment, now what I want to do is to group by date and then get the sum of sentiment value for each date multiply it by the number of collections for each date, for example if we have 2 collections in 2014-10-20 with sentiment values of 20,1,2 like the collection showed above and just 5 for another collection then the value for 2014-10-20 is (20+1+2+5)3(because this tweet is repeated for 3 entites) 2(because we have 2 tweets document in this date)=168 , if I do not consider frequency of collections my code works well as follow :
DBObject unwind = new BasicDBObject("$unwind", "$Entities"); // "$unwind" converts object with array into many duplicate objects, each with one from array
collectionG = db.getCollection("GraphDataCollection");
DBObject groupFields = new BasicDBObject( "_id", "$Date");
groupFields.put("value", new BasicDBObject( "$sum", "$Entities.Sentiment.Value"));
DBObject groupBy = new BasicDBObject("$group", groupFields );
DBObject sort = new BasicDBObject("$sort", new BasicDBObject("Date", 1));
stages.add(unwind);
stages.add(groupBy);
DBObject project = new BasicDBObject("_id",0);
project.put("Date","$_id");
project.put("value",1);
stages.add(new BasicDBObject("$project",project));
stages.add(sort);
AggregationOutput output = collectionG.aggregate(stages);
Now the result for for example 2014-10-20 returns 28 but I want 168
can anyone help me ?
Update : the last version of the code that I used is as follow:
DBCollection collectionG;
collectionG = db.getCollection("GraphDataCollection");
List<DBObject> stages = new ArrayList<DBObject>();
ArrayList<DBObject> andArray = null;
DBObject groupFields = new BasicDBObject( "_id", "$_id");
groupFields.put("value", new BasicDBObject( "$sum", "$Entities.Sentiment.Value"));
groupFields.put("date", new BasicDBObject( "$first", "$Date"));
DBObject groupBy = new BasicDBObject("$group", groupFields );
stages.add(groupBy);
DBObject groupByDate = new BasicDBObject( "_id", "$date");
groupByDate.put("value",new BasicDBObject("$sum","$value"));
groupByDate.put("count",new BasicDBObject("$sum",1));
DBObject dtGrp = new BasicDBObject("$group", groupByDate );
stages.add(dtGrp);
DBObject project = new BasicDBObject("_id",1);
project.put("value",new BasicDBObject("$multiply",
new Object[]{"$value","$count"}));
stages.add(new BasicDBObject("$project",project));
AggregationOutput output = collectionG.aggregate(stages);
System.out.println(output.results());

Answer 1

Unwind Entities:
DBObject unwind = new BasicDBObject("$unwind", "$Entities");
stages.add(unwind);
Group by _id to find the sum of all the Entities sentiment values per document.
DBObject groupFields = new BasicDBObject( "_id", "$_id");
groupFields.put("value", new BasicDBObject( "$sum", "$Entities.Sentiment.Value"));
groupFields.put("date", new BasicDBObject( "$first", "$Date"));
DBObject groupBy = new BasicDBObject("$group", groupFields );
stages.add(groupBy);
Group by Date now, to get the sum of total Entities Value, and the count of documents per group.
DBObject groupByDate = new BasicDBObject( "_id", "$date");
groupByDate.put("value",new BasicDBObject("$sum","$value"));
groupByDate.put("count",new BasicDBObject("$sum",1));
DBObject dtGrp = new BasicDBObject("$group", groupByDate );
stages.add(dtGrp);
Project value as the multiplicative result of count and value, for each group.
DBObject project = new BasicDBObject("_id",1);
project.put("value",new BasicDBObject("$multiply",
new Object[]{"$value","$count"}));
stages.add(new BasicDBObject("$project",project));
In case your dates differ by milliseconds, you need to group by the date, year and month together, in the second group stage and add a sort stage if necessary.