Using MIN/MAX in excel array formula - excel

Question

I have a simple array formula in excel that doesn't work in the way I wish. In columns A and B there is data (A1 is paired with B1 and so on) while in column F there is the calculation based on the parameter in column E.
In cell F1 the formula is:
{=SUM(MAX(A$1:A$9, E1)*B$1:B$9)}
What this formula does is:
=MAX(A$1:A$9, E1)*B$1 + MAX(A$1:A$9, E1)*B$2 + ...
Instead, I need a formula that does this:
=MAX(A$1, E1)*B$1 + MAX(A$2, E1)*B$2 + ...
In words, the formula I wrote (the first one) always finds the max between the values from A1 to A9 and E1, multiplies it by the i-th B value and sums the results. What I need is a formula that finds the max between the i-th A value and E1, and not between all the A values.
What I'm looking for is easily done by adding in column C the formula =MAX(A1;E$1)*B1 and then in F1 just =SUM(A1:A9), but I can't use this solution because in column F the same formula is repeated, with the E parameter changing every time.
I can use a IF instruction: in F1 I can write
{=SUM(IF(A$1:A$9>E1, A$1:A$9, E1)*B$1:B$9)}
While this formula does what I need in this case, I think it's a bad solution because I find it difficult to read and to expand. For example, if there is another parameter in column D and the factor is MIN(MAX(A$1:A$9;E1);D1), using IF will result in a very long and very unreadable and complicated formula.
Are there better solutions to my problem? Thank you all!
NOTE: syntax may vary a little because I am using the italian version of excel.

Answer 1

The problem is that MAX takes an array as an argument. Functions that normally take an array never return an array - they were designed to turn an array into one number. No matter how many arrays you throw at MAX, it's always just going to return one number.
I couldn't come up with a good solution, so here's a bad one
=SUMPRODUCT(((A1:A9*(A1:A9>E1))+(E1*(A1:A9<=E1)))*B1:B9)
I don't think that really increases the maintainability of the IF-based formula that you're trying to avoid. I think you're stuck with IF or a helper column.

Answer 2

Another possibility is a VBA function.
Public Function SumMaxMin(rRng1 As Range, rRng2 As Range, ParamArray vaMinMax() As Variant) As Double
Dim rCell As Range
Dim dReturn As Double
Dim aMult() As Double
Dim lCnt As Long
Dim i As Long
ReDim aMult(1 To rRng1.Cells.Count)
For Each rCell In rRng1.Cells
lCnt = lCnt + 1
aMult(lCnt) = rCell.Value
For i = LBound(vaMinMax) To UBound(vaMinMax) Step 2
If Not Evaluate(aMult(lCnt) & vaMinMax(i + 1) & vaMinMax(i)) Then
aMult(lCnt) = vaMinMax(i)
End If
Next i
Next rCell
For i = LBound(aMult) To UBound(aMult)
dReturn = dReturn + aMult(i) * rRng2.Cells(i).Value
Next i
SumMaxMin = dReturn
End Function
For your example
=SumMaxMin(A1:A9,B1:B9,E1,">")
Adding another condition
=SumMaxMin(A1:A9,B1:B9,E1,">",D1,"<")
It will error if your ranges aren't the same number of cells or you pass arguments that don't work with Evaluate.

Answer 3

Another possibility for avoiding repetitions of cell references is:
=SUM(B1:B9*ABS(A1:A9-E1*{1,-1}))/2
assuming values are non-negative. More generally to return an array of pairwise max values:
=MMULT((A1:A9-E1*{1,-1})^{2,1}^{0.5,1},{1;1}/2)
which returns:
MAX(A1,E1)
MAX(A2,E1)
...
MAX(A9,E1)

Answer 4

I don't remember ever cracking this problem, but for maintainability I'd probably do something like this:
{=SUM((A1:A9<E1)*E1*B$1:B$9) + SUM((A1:A9>=E1)*A1:A9*B$1:B$9)}

Answer 5

If I understand the problem correctly, using IF instead of MAX should do:
=SUM(IF($A$1:$A$9>E1;$A$1:$A$9;E1)*$B$1:$B$9)