### SUMPRODUCT() and For Each loops in Power Query: Implementations of List.Accumulate. Part 2

In my mind ** List.Accumulate** is one of most undocumented and most underestimated functions in Power Query ‘M’ language. In this post I would like to continue explanation of this very interesting iterative function.

## Data types

In my previous post about List.Accumulate function in Power Query ‘M’ language I’ve mentioned that ** seed** value, passed to function, could be any. As it was described in Gil Raviv post,

The seed argument (or as we call it the initial state), should be of the same type as the first argument of your accumulator function and of the same type as of the function’s output.

Now I want to add more details to an explanation of the List.Accumulate arguments’ behavior:

- We can pass a
*seed*value ofin Power Query data type to function. What we can pass as a__any allowed__*seed*: table, list, number, date, record, null, duration… anything. - Actually (and here I’d like to correct Gil)
.__function’s output type is independent from the__*seed*type - Function output type depends only from data type returned by
*accumulator*sub*–*function. Real output type could be any:List.Accumulate({1,2,3},0,(state, current)=>(if state = 0 then "" else Text.From(state))&Text.From(current)) // equals “123”

- The first (
*state*) argument in*accumulator*sub-function has to be the same type as*seed*value only at first iteration and only if*state*argument is used in*accumulator*(I really see no sense in manipulations without using*state*argument, but you can do it, that’s why I noted it). After the first iteration the*accumulator*result will totally depend on what this sub-function does (as shown above). - The
*list*elements could be used in*accumulator*sub-function. Could be not. You can use the*list*only– accumulator will perform its manipulations as many times as the count of list elements. This means that you can use__as iteration counter__*List.Accumulate*as**“**(which has as many steps as a count of elements in list).__For Each … Next” loop__

Let us try to look at how those features could be implemented.

## SUMPRODUCT () in Power Query

For a starter let’s try to convert the famous Excel function, SUMPRODUCT, to Power Query function.

**Why we really need it?**

There are a lot of ways to implement SUMPRODUCT in Power Query. For example, we can add custom column with formula like this: = [Amount] * [Price] and then just get the sum of it. It’s easy and clear, except we need to add this helper column to get just one number.

But let suppose we have got two lists by some query manipulations and these lists are not columns in any table. We can transform them to tables, and then somehow combine those tables, perhaps with Index column, and… looks not as easy as it was with columns in one table?

### SUMPRODUCT itself

With *List.Accumulate* we can do it with just one row of code:

let myList1 = {1,1,2,2,4,5}, myList2 = {1,4,2,2,1,5}, SUMPRODUCT = List.Accumulate(MyList1, [Sum=0, Index=0], (state, current) => [Sum = current * MyList2{state[Index]}+state[Sum], Index = state[Index]+1])[Sum] in SUMPRODUCT

Obviously it equals 42.

**How it works**

- Here we got two lists of the same size, MyList1 and MyList2
- We’ll use one of lists as an
*list*argument of List.Accumulate. We actually will use its elements in calculation, but also the count of list elements will be used as a counter to iterations inside our function. - As the seed argument we used a record: [Sum=0, Index =0], where
*Sum*will be used as field for calculation and*Index*will be used as list’s current position counter. - We can describe the accumulator function as follows:
**For Each***current element***In**MyList1- Multiply
*current*on MyList2{state[Index]} (where state[Index] is the value of*Index*from previous step or from*seed*if it is first step) - Add the result to the state[Sum] (where state[Sum] is the previous/seed value of
*Sum*) - Increase previous/seed value of Index by 1
**Next**

- At the end of the loop we have the result as a record of two fields:
*Sum*and*Index*, as a result of*Accumulate*. We need only*Sum*field value, so we just add this filed name in square brackets at the end of row to get its value. Actually it means “give me the value of the [Sum] field from List.Accumulate result”.

### SUMPRODUCT() UDF for PowerQuery/’M’

You can easily transform code from above to the one-row function for future uses:

(MyList1 as list, MyList2 as list) as number => let SUMPRODUCT = List.Accumulate(MyList1, [Sum=0, Index=0], (state, current) => [Sum = current * MyList2{state[Index]} + state[Sum], Index = state[Index] + 1])[Sum] in SUMPRODUCT

Of course, you can enhance it with error handling and other feautures, as you want.

Enjoy! 🙂

(to be continued)

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