How to do a row-wise sum in an array formula in Excel?

问题

Say I have the following basic spreadsheet:

    A   B   C   D
1  -2   4   2  12
2  -1   1   0
3   0   0   0  22
4   1   1   2  12
5   2   4   6
6   3   9  12

The A column has integers from -2 to 3.

The B column has the a column value squared.

The C column is the row sum of A and B so C1 is =SUM(A1:B1).

D1 has =MAX(C1:C6) and this max is the result I need to get with a single formula.

D3 is =MAX(SUM(A1:B6)) entered with Ctrl+Shift+Enter, but it just results in a regular sum. D4 is =MAX(A1:A6+B1:B6) with ctrl+shift+enter, and this works and gives the correct result of 12.

However the problem with D4 is that I need to be able to handle large dynamic ranges without entering endless sums. Say SUM(A1:Z1000) would be A1:A1000+B1:B1000+....+Z1:Z1000 which is not a reasonable formula.

So how can I do something like =MAX(SUM(A1:Z1000)) such that it would sum the rows A1:Z1 to A1000:Z1000 and give me the final row-wize max.

I can only use base Excel, so no helper columns and no VBA function.

UPDATE Since there have not been any successful answers, I have to assume it is not possible with current Excel versions.

So I am trying to build this function in VBA and this is what I have so far.

Function MAXROWSUM(Ref As Range) As Double
    Dim Result, tempSum As Double
    Dim Started As Boolean
    Started = False
    Result = 0
    For Each Row In Ref.Rows
        tempSum = Application.WorksheetFunction.Sum(Row)
        If (Started = False) Then
            Result = tempSum
            Started = True
        ElseIf tempSum > Result Then
            Result = tempSum
        End If
    Next Row
    MAXROWSUM = Result
End Function

This function works and is quite fast with less than 100k rows, but if the row count in the range approaches the possible 1 million, the function becomes very slow taking several seconds, even if most of the range is empty. Is there a way to significantly optimize the current code, by possibly filtering out any empty rows? In my example if I enter MAXROWSUM(A1:B1000000) it will work, but will be slow, can I make this very fast?

回答1:

Your solution is Matrix Multiplication, via the MMULT function

How this works is as follows: currently, you have an X*N array/matrix, which you want to change into an X*1 matrix (where each new row is the sum of the rows in the old matrix), and then take the maximum value. To do this, you need to multiply it by an N*1 matrix: the two Ns "cancel out".

The first step is simple: every value in your second matrix is 1

Example: [6*2] ∙ [2*1] = [6*1]

[[-2][ 4]             [[ 2]
 [-1][ 1]    [[ 1]     [ 0]
 [ 0][ 0]  ∙  [ 1]] =  [ 0]
 [ 1][ 1]              [ 2]
 [ 2][ 4]              [ 6]
 [ 3][ 9]]             [12]]

We then MAX this:

=MAX(MMULT(A1:B6,{1;1}))

To generate our second array dynamically (i.e. for any size), we can use the first Row of our table, convert it entirely to 1 (for example, "Column number > 0"), and then TRANSPOSE this to be a column instead of a row. This can be written as TRANSPOSE(--(COLUMN(A1:B1)>0))

Put it all together, and we get:

=MAX(MMULT(A1:B6, TRANSPOSE(--(COLUMN(A1:B1)>0))))

Since MMULT works with arrays - like SUMPRODUCT - we don't actually need to define this as an Array Formula with Ctrl+Shift+Enter either!

If you wanted to do this column-wise instead, then you would need to swap the arrays around - Matrix Multiplication is not commutative:

=MAX(MMULT(TRANSPOSE(--(ROW(A1:A6)>0)), A1:B6))

[1*6] ∙ [6*2] = [2*1]

                              [[-2][ 4]
                               [-1][ 1]
[[ 1][ 1][ 1][ 1][ 1][ 1]]  ∙  [ 0][ 0]   =  [[ 3][19]]
                               [ 1][ 1]
                               [ 2][ 4]
                               [ 3][ 9]]

回答2:

SUMPRODUCT (The Unsung Hero)

The following are not array formulas.

=SUMPRODUCT(MAX(A:A+A:A^2))

If it doesn't work (older Excel), change to the exact range e.g.:

=SUMPRODUCT(MAX(A$1:A$1000+A$1:A$1000^2))

回答3:

I could not find a way to do the function with basic Excel, so I had to use VBA.

I was able to create a reasonably fast VBA function that works.

Function MAXROWSUM(Ref As Range) As Double
    Dim Result, tempSum As Double
    Dim Started As Boolean
    Started = False
    LastDataRow = Ref.Find("*", SearchOrder:=xlByRows, SearchDirection:=xlPrevious).Row
    Result = 0
    For Each Row In Ref.Rows
        tempSum = Application.WorksheetFunction.Sum(Row)
        If Row.Row > LastDataRow Then
            Exit For
        End If
        If (Started = False) Then
            Result = tempSum
            Started = True
        ElseIf tempSum > Result Then
            Result = tempSum
        End If
    Next Row
    MAXROWSUM = Result
End Function

A key line is: LastDataRow = Ref.Find("*", SearchOrder:=xlByRows, SearchDirection:=xlPrevious).Row which finds the last populated row of the data range and stops the function past it. So entering a function with a million rows where only 100 or a 1000 rows have data will not cause excessive useless calculation.

来源：https://stackoverflow.com/questions/61334490/how-to-do-a-row-wise-sum-in-an-array-formula-in-excel

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