ROW() function behaves differently inside SUM() and SUMPRODUCT()

Question

Problem definition: Enter any number in cell `A1`. Now try the following formulae anywhere on first row. ``` =SUM(INDIRECT("A"&ROW())) ``` and ``` =SUMPRODUCT(INDIRECT("A"&ROW())) ``` The first formula evaluates, the second one gives a #VALUE error. This is caused by the `ROW()` function behaving differently inside `SUMPRODUCT()`. In the first formula, `ROW()` returns `1`. In the second formula, row returns `{1}` (array of one length), even though the formula has not been entered as a CSE formula. Why does this happen? Background I need to evaluate a formula of the type ``` =SUMPRODUCT(INDIRECT(*range formed by concatenation and using ROW()*)>1) ``` This is working out to an error. As a workaround to this issue, I now calculate `ROW()` in another cell (in the same row, obviously) and concatenate that inside my `INDIRECT()`. Alternately, I also have tried encapsulating it inside a sum function, like `SUM(ROW())`, and that works as well. I would sure appreciate it if someone could expla…

Accepted Answer

Interesting question. There are subtle issues here which I haven't seen documented.

It seems `INDIRECT("A"&ROW())` returns an array consisting of one element which is a reference to a cell - not the value in that cell. Many functions cannot resolve this type of data correctly but a few functions such as N and T can "dereference" the array and return the underlying value.

Take this case where there are two elements in the array:

```
=SUM(N(INDIRECT("A"&ROW(1:2))))
```

This returns A1+A2 when array entered but it only returns A1 when entered normally. However changing ROW(1:2) to {1;2} in this formula returns the correct result when entered normally. The equivalent SUMPRODUCT formula returns A1+A2 whether array entered or not.

This may be related to how the arguments are registered in the function. According to http://msdn.microsoft.com/en-us/library/bb687900.aspx there are essentially two methods to register function arguments to handle Excel data types:

Type R/U: "Values, arrays, and range references."

Type P/Q: "Excel converts single-cell references to simple values and multi-cell references to arrays when preparing these arguments."

SUM arguments seem to conform with type R/U while SUMPRODUCT arguments behave like type P/Q. Array-entering the SUM formula above forces the range reference argument in ROW to be evaluated as an array whereas this happens automatically with SUMPRODUCT.

Update

After a little more investigation, here's further evidence that might support this theory. Based on the link in the comment, the formula =SUM((A1,A2)) gives the same values as:

```
?executeexcel4macro("CALL(""Xlcall32"",""Excel4"",""2JRJR"",4,,1,(!R1C1,!R2C1))")
```

Registering the last argument as type P by changing `2JRJR` to `2JRJP` gives an error in this case but does allow for single area ranges like `!R1C1:!R2C1`. On the other hand, changing the 4 (xlfsum) to 228 (xlfsumproduct) only allows single area references either way it's called just like SUMPRODUCT.

ROW() function behaves differently inside SUM() and SUMPRODUCT()

Solution

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