Alright this should be a simple one.
I apologize in case it has been already solved, but I can only find posts related to solving this issue with programming languages and not specifically to EXCEL.
Furthermore, I could find posts that address a sub-problem of my question (e.g. regarding limitation of certain EXCEL functions) and should solve/invalidate my request but maybe, just maybe, there is a workaround.
Problem statement:
I want to calculate the minimum value for each column in an EXCEL matrix. Simply enough, I want to input a 2D array (mxn matrix) in a function and output an array with dimension 1xm where each item is the minimum value MIN(nj) of each nj column.
However, I want to solve this with specific constraints:
Avoid using VBA and other non-function scripting: that I could devise myself;
All in one function: what I want to achieve here is to have one and one function only, not split the problem into multiple passages (such as for example copypasting a MIN() function below each column, that wouldn't do it);
The result should be a transposable array (which is already ok, I assume);
Where I am stranded with my solution so far:
The main issue here is that any function I am trying to use takes the entire matrix as a single array input and would calculate the MIN() of the entire matrix, not each column. My current (not working) function for an exemplary 4x4 matrix in range A1:D4 would be as below (the part in bold is where it is clearly not working):
=MIN(INDEX(A1:D4,SEQUENCE(4,4,1,1)))
which ofc does not work, because INDEX() does probably not "understand" SEQUENCE() as an array of items to take into account. Another, not working, way of solving this is to input a series of ranges (A1:A4;B1:B4;C1:C4;D1:D4) so that INDEX() "understands" the ranges as single columns, but ofc does not know and I do not know sincerely how to formulate that. I could use INDIRECT() in some way to reference the array of ranges, but do not know how and could find a way by searching online.
Fundamental question is: can a function, which works with single arrays, also work with multiple arrays? Basically, I do not know how to communicate an EXCEL array formula, that each batch of data I am inputting is a single array and must be evaluated separately (this is very easily solved with for() cycles, I know).
Many thanks for any suggestion and any workaround, any function and solution works as longs as it fits in the constrains defined above (maybe a LAMBA() function? don't know).
This is ofc a simplification of a way more complex problem (I am trying to calculate the annual mean temperature evolution for a specific location by finding the value - for each year from 1950 to 2021 - that is associated to the lat/lon coordinates that are the nearest to the one of the location inputted, given a netCDF-imported grid of time-arrayed data; the MIN() function is used to selected the nearest location, which is then used, via INDEX() to find temp data). I need to do this in one hit (meaning just pasting the function, which evaluates a matrix of data that is referenced by a fixed range), so that I can just use it modularly for other data sets. I already have a working solution, which is "elegant"* enough, but not "elegant"* as the one I could develop solving this issue.
*where "elegant"= it saves me one click every time for 1000+ datasets when applying the function.
If I understand your problem correct then this should solve it:
=BYCOL(A1:D4,LAMBDA(d,MIN(d)))
Related
Excel's INDEX function shows strange behaviour when the object being indexed is a name introduced in a LET construct or a parameter of a LAMBDA. The behaviour is consistent on Windows and Mac.
Suppose cell B2 contains the formula
=SEQUENCE(50000)
Then the following formulas are all relatively performant:
=MAP(SEQUENCE(2000),LAMBDA(x,INDEX(B2#,x)))
=LAMBDA(MAP(SEQUENCE(2000),LAMBDA(x,INDEX(B2#,x))))()
=LET(mgen,LAMBDA(B2#),LAMBDA(MAP(SEQUENCE(2000),LAMBDA(x,INDEX(mgen(),x)))))()
The following formulas, however, are terribly slow
=LET(m,B2#,MAP(SEQUENCE(2000),LAMBDA(x,INDEX(m,x))))
=LET(m,B2#,LAMBDA(MAP(SEQUENCE(2000),LAMBDA(x,INDEX(m,x)))))()
=LAMBDA(m,MAP(SEQUENCE(2000),LAMBDA(x,INDEX(m,x))))(B2#)
The performance problem gets the worse the longer array B2 is. You can crash Excel with the latter 3 formulas when you replace 50000 by 500000 in B2, while the first three formulas still work perfectly fine.
Note that the length of B2 (the array indexed) should in theory not have any impact on performance, since INDEX is called the exact same number of times in all my examples.
To me, INDEX seems to have performance problems whenever the first argument does not directly refer to a worksheet range.
Yet if that is so -- how can I efficiently (in constant time) get the n-th element of a LET/LAMBDA-named array?
I cannot work around this by writing the indexed array into a cell, since in my case, the indexed array is the result of another lambda.
Edit for clarification: The only purpose of the MAP/SEQUENCE(2000) construct in my examples is to make 2000 separate calls to INDEX, in order for the performance differences to become visible. The construct is completely unrelated to the problem. The performance problems occur whenever I make a lot of INDEX calls with the first argument being a LET/LAMDA name.
Second edit: It seems, however, that some kind of loopy construct is needed to reproduce the problem. I have not been able to reproduce the problem with 2000 separate LET/INDEX formulas in 2000 cells.
Ever since I learnt that Excel is now Turing-complete, I understood that I can now "program" Excel using exclusively formulas, therefore excluding any use of VBA whatsoever.
I do not know if my conclusion is right or wrong. In reality, I do not mind.
However, to my satisfaction, I have been able to "program" the two most basic structures of program flow inside formulas: 1- branching the control flow (using an IF function has no secrets in excel) and 2- loops (FOR, WHILE, UNTIL loops).
Let me explain a little more in detail my findings. (Remark: because I am using a Spanish version of Excel 365, the field separator in formulas is the semicolon (";") instead of the comma (",").
A- Acumulator in a FOR loop
B- Factorial (using product)
C- WHILE loop
D-UNTIL loop
E- The notion of INTERNAL/EXTERNAL SCOPE
And now, the time of my question has arrived:
I want to use a formula that is really an array of formulas
I want to use an accumulator for the first number in the "tuple" whereas I want a factorial for the second number in the tuple. And all this using a single excel formula. I think I am not very far away from succeeding.
The REDUCE function accepts a LET function that contains 2 LAMBDAS instead of a single LAMBDA function. Until here, everything is perfect. However, the LET function seems to return only a "single" function instead of a tuple of functions
I can return (in the picture) function "x" or function "y" but not the tuple (x,y).
I have tried to use HSTACK(x,y), but it does not seem to work.
I am aware that this is a complex question, but I've done my best to make myself understood.
Can anybody give me any clues as to how I could solve my problem?
Very nice question.
I noticed that in your attempts you have given REDUCE() a single constant value in the 1st parameter. Funny enough, the documentation nowhere states you can't give values in array-format. Hence you could use the 1st parameter to give all the constants in (your case; horizontal) array-format, and while you loop through the array of the 2nd parameter you can apply the different types of logic using CHOOSE():
=REDUCE({0,1},SEQUENCE(5),LAMBDA(a,b,CHOOSE({1,2},a+b,a*b)))
This way you have a single REDUCE() function which internal processes will update the given constants from the 1st parameter in array-form. You can now start stacking multiple functions horizontally and input an array of constants, for example:
=REDUCE({0,1,100},SEQUENCE(5),LAMBDA(a,b,CHOOSE({1,2,3},a+b,a*b,a/b)))
I suppose you'd have to use {0\1} and {1\2} like I'd have to in my Dutch version of Excel.
Given your accumulator:
Formula in A1:
=REDUCE(F1:G1,SEQUENCE(F3),LAMBDA(a,b,CHOOSE({1,2},a+b,a*b)))
Recently I answered a question about how to retrieve the MEDIAN() of each MEDIAN() in a 2-column matrix without helpers, e.g:
The row-wise calculation without helpers wasn't too hard because the median with only two values is always the average. Therefor a simple formula was all it took:
=MEDIAN((A1:A3+B1:B3)/2)
But for curiosity sakes however, wat if I would have at least a 3-column matrix?
The median will actually need to be calculated. Here the medians are {8,2,2}.
I can't seem to find a way to to get a row-wise calculation for 3+columns. In this case it's about MEDIAN() but I can imagine there could be other functionalities. Since this could be simplified data I don't want to resort to something like =MEDIAN(MEDIAN(A1:C1),MEDIAN(......
I tried to fiddle around with OFFSET(), though not a fan of volatile functions I was hoping it would either work directly with an array, or would be triggered correctly through using MEDIAN(LET(X,SEQUENCE(ROWS(A1:A3)),MEDIAN(OFFSET(A1:C1,X-1,0)))). I then moved on to combinations of either MMULT() or LARGE(), however none of my attempt were succesfull.
Question
So the question ultimately is; how do we return the result (array) of an row-wise calculation without helpers. And if not possible, that's also a perfectly fine answer so I can rest my head =)
New Answer
With the new BYROW() function one could use:
=MEDIAN(BYROW(A1:C3,LAMBDA(a,MEDIAN(a))))
The nested LAMBDA() in the 2nd parameter makes it a piece o' cake to loop all rows in a dynamic array (not a range per se).
Previous Answer (Pre-BYROW())
So. After a long thought, as far as my understanding goes this is not possible through current formulae. However, currently in BETA, Excel365 will feature the new LAMBDA() function which makes it possible to create your own function without VBA and even recursively call itself. It isn't the prettiest of solutions but I thought I would share what I did here:
Formula in E3:
=MED(A1:C3,"",ROWS(A1:A3))
Where MED() is our own LAMBDA() function created at the "name manager" menu. It reads:
=LAMBDA(rng,txt,rws,IF(rws=0,MEDIAN(FILTERXML("<t><s>"&txt&"</s></t>","//s")),MED(rng,TEXTJOIN("</s><s>",,txt,MEDIAN(INDEX(rng,rws;0))),rws-1)))
As can be seen there are 4 main parameters of which 3 variables:
rng - The range to be examined.
txt - A reserved variable to be used in FILTERXML().
rws - A counter.
The 4th parameter is a nested IF() which if the counter is as 0 will return the median of all medians. This is done through FILTERXML() which I will not get into detail right now.
If the counter is not yet at 0 it will recursively call the LAMBDA() function untill it is, and what it does is using the same three parameters but we can alter them right there and then. Therefor we leave rng intact, we concatenate the MEDIAN() of the row (current counter) through TEXTJOIN() to create a valid xml construct. And last but not least we need to lower the counter.
It's a struggle, but with LAMBDA() it will now be possible to do a rowwise calculation.
Note, if you are interested in the FILTERXML() construct, you might like this post where I now also included a LAMBDA() version of a SPLIT() function.
Problem is straightforward, but solution is escaping. Hopefully some master here can provide insight.
I have a big data grid with prices. Those prices are ordered by location (rows) and business name (cols). I need to match the location/row by looking at two criteria (location name and a second column). Once the matching row is found (there will always be a match), I need to get the minimum/lowest price from two ranges within the grid.
The last point is the real challenge. Unlike a normal INDEX or MINIFS scenario, the columns I need to MIN aren't contiguous... for example, I need to know what the MIN value is between I4:J1331 and Q4:U1331. It's not an intersection, it's a contiguous set of values across two different arrays.
You're probably saying "hey, why don't you just reorder your table to make them contiguous"... not an option. I have a lot of data, and this spreadsheet is used for a bunch of other stuff. So, I have to work with the format I have, and that means figuring out how to do a lookup/min across multiple non-contiguous ranges. My latest attempt:
=MINIFS(AND($I$4:$J$1331,$K$4:$P$1331),$B$4:$B$1331,$A2,$E$4:$E$1331,$B2)
Didn't work, but it should make it more clear what I'm trying to do. There has GOT to be an easy way to just tell excel "use these two ranges instead of one".
Thanks,
Rick
Figured it out. For anyone else who's interested, there doesn't seem to be any easy way to just "AND" arrays together for a search (Hello MS, backlog please). So, what I did instead was to just create multiple INDEX/MATCH arrays inside of a MIN function and take the result. Like this:
MIN((INDEX/MATCH ARRAY 1),(INDEX/MATCH ARRAY 2))
They both have identical criteria, the only difference is the set of arrays being indexed in each function. That basically gives me this:
MIN((match array),(match array))
And Min can then pull the lowest value from either.
Not as elegant as I'd like... lots of redundant code, but at least it works.
-rt
I was trying to calculate the R-squared value of two arrays using RSQ function. One array is fixed, another is located in different columns. I want to generate a code so that i will be able to generate R-squared value for all variables by drag down the cell.
i tried
=RSQ($H$4:$H$102,OFFSET($A$4:$A$102,0,ROW(Z3)-2))
where ROW(Z3)-2 = 1 and the offset part should refer to B4:B102.
The result of RSQ was #N/A. But when I tried SUM(OFFSET($A$4:$A$102,0,ROW(Z3)-2)) it do gives me a correct sum for B4:B102. Can anyone help me out with this problem?
thanks!!!
=RSQ($H$4:$H$102,OFFSET($A$4:$A$102,0,MAX(ROW(Z3)-2)))
The problem seems to be that ROW(n) returns a 1x1 array. I'm guessing Excel is complaining that the 1x1 array is not sized the same as other arrays you are using. Wrapping it in MAX seems to work around this by returning the value in that array, and calculation goes on.
I must say I have not noticed this behavior before. Good question.