I need to create a running product from a column of numbers (I could use a row, but a column is easier to demonstrate here.) The input might be any arbitrary array. In fact, in the application where I would deploy this, it will not be a range, but rather another dynamic array within a LAMBDA formula. Here is an example of the Input column of numbers and the desired Output from the formula:
Inputs
Expected Dynamic Array Output
10
10
8
80
3
240
4
960
5
4800
The formula would spill the results.
There are lots of solutions for a running total, but I've found no solution for a running product. I have tried a few different approaches, including SUBTOTAL and AGGREGATE with no success. I have also built a number of approaches that get the result, but are hard-coded to a fixed number of rows. I need the formula to adapt to any arbitrarily sized number of rows. The following formula is the closest I have gotten so far.
This LET formula delivers the result, but, as you can see is fixed to 5 rows:
=LET( a, {10;8;3;4;5},
v, SEQUENCE( ROWS(a) ), h, TRANSPOSE( v ),
stagr, (v - h + 1) * (v >= h),
m, IFERROR(INDEX( a, IF(stagr>0,stagr,-1), ), 1),
almost, INDEX(m,v,h) * INDEX(m,v,h+1) * INDEX(m,v,h+2) * INDEX(m,v,h+3) * INDEX(m,v,h+4),
result, INDEX( almost, , 1 ),
result )
The arbitrary array of numbers input is placed in the variable a.
The next step is to create some indexes that will be used to address these numbers: v is a sequence of vertical rows for each number in a and h is a the same sequence, but transposed into columns. stagr is an index matrix that is created from v and h that will later be used to address each item in a to form it into a multiplication matrix. If you replace the last result with stagr, you can see the shape of stagr. It just shifts a column down by one row until they are shifted all the way down.
Now we create the mulitplication matrix m using stagr by simply using INDEX, like this: INDEX(a,stagr). But this is not exactly what is needed because it takes the first row value (10) and replicates it because an INDEX of 0 is treated the same as 1. To get what we want, I forced an error by using and internal IF statement like this: INDEX( a, IF(stagr>0,stagr,-1) ) to replace the 0 results with -1. i.e. it will produce this:
Now, replace the errors with 1's by using IFERROR, so this explains how m is created and why. The result is a matrix like this:
and by multiplying m row-wise, we get the output we want, but this is where I fail.
For illustration, I created a variable almost that shows how I am trying to do a row-wise multiplication.
almost, INDEX(m,v,h) * INDEX(m,v,h+1) * INDEX(m,v,h+2) * INDEX(m,v,h+3) * INDEX(m,v,h+4)
You can see that I crudely multiplied one column times the next and the next... and using h + offset to get there. This produces the almost matrix and result just delivers the first column of that matrix, which contains the answer.
While an answer might be a good replacement for almost that would be dynamically sized, that is not my real question. I want a running product and I suspect that there is a wholly different approach than simply replacing my almost.
Just to be clear, the result must be a dynamic array that spills with no helper cells or CSE drag-down.
oh... and no VBA. (#stackoverflow - please add a no-VBA tag)
The only way I can find is to use DPRODUCT with OFFSET, but that requires a title row. It does not matter what is in the title row(it can even be empty), just that it is included.
=DPRODUCT(OFFSET(A1,0,0,SEQUENCE(COUNT(A:A),,2)),1,$ZZ1:$ZZ2)
The $ZZ1:$ZZ2 can be any empty cell reference.
If the values in A are dynamic then we can do:
=DPRODUCT(OFFSET(A1,0,0,SEQUENCE(ROWS(A2#),,2)),1,$ZZ:$ZZ)
There are plenty of interesting answers here. But, if summation is easy why not take logarithms of the number you want to multiply, sum those logarithms and then calculate the exponent of your sum to return to the product of the original numbers.
i.e. exploit the fact that ln(a * b) = ln(a) + ln(b)
Whilst not available to everybody (yet) we can use SCAN()
Formula in A1:
=SCAN(1,{10,8,3,4,5},LAMBDA(a,b,a*b))
The 1st parameter is our starting value, meaning the 1st calculation in the nested LAMBDA() is '1*10'.
The 2nd parameter can both take a 1D- & 2D-array (written or range-reference).
The 3rd parameter is a nested LAMBDA() where the result of our recursive function will then be used for the 2nd calculation; '10*8'. And the 3rd...etc. etc.
In the above sample a vertical array is spilled but when horizontal input is used this will obviously result in an horizontal spilled output. When a 2D-array is used this will spill a 2D-array as result.
Excel
Need to find nearest float in a table, for each integer 0..99
https://www.excel-easy.com/examples/closest-match.html explains a great technique for finding the CLOSEST number from an array to a constant cell.
I need to perform this for many values (specifically, find nearest to a vertical list of integers 0..99 from within a list of floats).
Array formulas don't allow the compare-to value (integers) to change as we move down the list of integers, it treats it like a constant location.
I tried Tables, referring to the integers (works) but the formula from the above web site requires an Array operation (F2, control shift Enter), which are not permitted in Tables. Correction: You can enter the formula, control-enter the array function for one cell, copy the formulas, then insert table. Don't change the search cell reference!
Update:
I can still use array operations, but I manually have to copy the desired function into each 100 target cells. No biggie.
Fixed typo in formula. See end of question for details about "perfection".
Example code:
AI4=some integer
AJ4=MATCH(MIN(ABS(Table[float_column]-AI4)), ABS(Table[float_column]-AI4), 0)
repeat for subsequent integers in AI5...AI103
Example data:
0.1 <= matches 0
0.5
0.95 <= matches 1
1.51 <= matches 2
2.89
Consider the case where target=5, and 4.5, 5.5 exist in the list. One gives -0.5 and the other +0.5. Searching for ABS(-.5) will give the first one. Either one is decent, unless your data is non-monotonic.
This still needs a better solution.
Thanks in advance!
I had another problem, which pushed to a better solution.
Specifically, since the Y values for the X that I am interested in can be at varying distances in X, I will interpolate X between the X point before and after. Ie search for less than or equal, also greater than or equal, interpolate the desired X, then interpolate the Y values.
I could go a step further and interpolate N - 1 to N + 1, which will give cleaner results for noisy data.
I am attempting to translate my existing Matlab code into Numbers (basically Excel). In Matlab, I have the following code:
clear all; clc;
n = 30
x = 1:(n-1)
T = 295;
D = T./(n-x)
E = T/n
for i=1:(n-2)
C(i) = D(i+1) - D(i)
end
hold on
plot(x(1:end-1), C, 'rx')
plot(x, D, 'bx')
I believe everything has been solved by your formulas, there are parts of them that I don't understand otherwise I would try to figure the rest out myself. Attached is the result (Also you might like to know that the formulas you gave work and are recognized in Numbers). Im trying to figure out why (x) begins at 2 as I feel as though it should start at 1?
Also it is clear that the realistic results for the formulas only exist under certain conditions i.e. column E > 0. That being the case, what would be the easiest way to chart data with a filter so that only certain data is charted?
(Using Excel...)
Suppose you put your input values T & n in A1 & B1 respectively.
You could generate x, D & C In columns C,D & E with:
C1: =IF(ROW()<$A$1,ROW(),"")
D1: =IF(LEN(C1)>0,$A$2/($A$1-C1),"")
E1: =IF(LEN(D2)>0,D2-D1,"")
You could then pull all 3 columns down as far as you need to generate the full length of your vectors. If you then want to chart these, simply use these columns as inputs.
I need to make a macro to compare two columns looking for duplicate cells.
I'm currently using this simple double for loop algorithm
for i = 0 To ColumnASize
Cell1 = Sheet.getCellByPosition(0,i)
for j = 0 to ColumnBSi
Cell2 = Sheet.getCellByPosition(1,j)
' Comparison happens here
Next j
Next i
However, as I have 1000+ items in each column this algorithm is quite slow and inefficient. Does anyone here know/have an idea for a more efficient way to do this?
If you want to ensure that no string in col A is equal to any string in col B, then your existing algorithm is order n^2. You may be able to improve that by the following:
1) Sort col A or a copy of it (order nlogn)
2)Sort col B or a copy of it (order nlogn)
3) Look for duplicates by list traversal, see this previous answer (order n).
That should give you an order nlogn solution and I don't think you can do much better than that.
I recieve table of data sorted by purchase order PO number in asc.
For further analysis of data, I'm supposed to sort it out by business directions (sectors or departments e.g.). There is a range of order numbers, each of them related to particular direction, like 1000-1999 direction A, 2000-2999 direction B.
Ideally, I need them to be automatically sorted in ascending order with additional sum row underneath and direction name above.
The problem is, that quantity of digits in number is not limited, which means that for some extra orders might be added one digit aside, or even slash and letter, like 2000/A, or 20,000 - and this last one is supposed to be in the range of 2000-2999 POs.
What might be used to solve the problem?
I'm not certain that this will solve your problem. This fucntion will successively shrink a string from the right until it is a number. You can enter this function into a vba module and then use it in your spreadsheet.
Function getnumber(s As String) As Integer
Dim i As Integer
For i = Len(s) To 0 Step -1
If IsNumeric(Left(s, i)) Then
getnumber = Left(s, i)
i = 0
End If
Next i
End Function
If this works, I'm glad. If it doesn't, you'll need to clarify what you're looking for.
The biggest thing that I would suggest is redefining your input to make this less tedious.