=SUM(SEQUENCE(10000000))
The formula above is able to sum upto 10 million virtual array elements. We know that 10 million is the limit according to this question and answer. Now, if the same is implemented as Lambda using Lambda helper function REDUCE:
=REDUCE(,SEQUENCE(10000000),LAMBDA(a,c,a+c))
We get,
Calculation limit was reached when trying to calculate this formula
Official documentation says
This can happen in 2 cases:
The computation for the formula takes too long.
It uses too much memory.
To resolve it, use a simpler formula to reduce complexity.
So, it says the reason is space and time complexity. But what is the exact space used to throw this error? How is this determined?
In the REDUCE function above, the limit was at around 66k for a virtual array:
=REDUCE(,SEQUENCE(66660),LAMBDA(a,c,a+c))
However, if we remove the addition criteria and make it return only the current value c, the allowed virtual array size seems to increase to 190k:
=REDUCE(,SEQUENCE(190000),LAMBDA(a,c,c))
After which it throws a error. So, what factors determine the memory limit here? I think it's memory limit, because it throws the error almost within a few seconds.
If you're affected by this issue, you can send feedback to Google:
Open a spreadsheet, preferably one where you bumped into the issue.
Replace any sensitive information with anonymized but realistic-looking data. Remove any sensitive information that is not needed to reproduce the issue.
Choose Help > Report a Problem or Help > Help Sheets Improve. If you are on a paid Google Workspace Domain, see Contact Google Workspace support.
Explain why the calculation limit is an issue for you.
Request:
Justice: Removing arbitrary limits on lambda functions
Equality: Avoiding discrimination against lambda functions
Transparency: Documenting the said discrimination in more clarity and detail
Include a link to this Stack Overflow answer post.
Update Oct '22 (Credit to MaxMarkhov)
The limit is now 10x higher at 1.9 million 1999992. This is still less than 1/5th of 10 million virtual array limit of non-lambda formulas, but much better than before. Also non-lambda formulas's limit doesn't reduce with number of operations. But lambda helper formulas limit still does decrease with number of operations. So, even though it's 10x higher, that just means ~5 extra operations inside lambda(see table below).
A partial answer
We know for a fact, the following factors decide the calculation limit drum roll:
Number of operations
(Nested)LAMBDA() function calls
The base number for 1 operation seems to be 199992 1 2(=REDUCE(,SEQUENCE(199992),LAMBDA(a,c,c))). But for a zero-op or a no-op(=REDUCE(,SEQUENCE(10000000),LAMBDA(a,c,0))), the memory limit is much higher, but you'll still run into time limit. We also know number of operations is a factor, because
=REDUCE(,SEQUENCE(66664/1),LAMBDA(a,c,a+c)) fails
=REDUCE(,SEQUENCE(66664),LAMBDA(a,c,a+c)) works.
=REDUCE(,SEQUENCE(66664),LAMBDA(a,c,a+c+0)) fails
Note that the size of operands doesn't matter. If =REDUCE(,SEQUENCE(39998),LAMBDA(a,c,a+c+0)) works, =REDUCE(,SEQUENCE(39998),LAMBDA(a,c,a+c+100000)) will also work.
For each increase in number of operations inside the lambda function, the maximum allowed array size falls by 2n-1(Credit to #OlegValter for actually figuring out there's a factor multiple here):
Maximum sequence
Number of operations (inside lambda)
Reduction(from 199992)
Formula
199992
1
1
REDUCE(,SEQUENCE(199992),LAMBDA(a,c,c))
66664
2
1/3
REDUCE(,SEQUENCE(66664),LAMBDA(a,c,a+c))
39998
3
1/5
REDUCE(,SEQUENCE(39998),LAMBDA(a,c,a+c+10000))
28570
4
1/7
REDUCE(,SEQUENCE(28570),LAMBDA(a,c,a+c+10000+0))
Operations outside the LAMBDA functions also count. For eg, =REDUCE(,SEQUENCE(199992/1),LAMBDA(a,c,c)) will fail due to extra /1 operation, but you only need to reduce the array size linearly by 1 or 2 per operation, i.e., this =REDUCE(,SEQUENCE(199990/1),LAMBDA(a,c,c)) will work3.
In addition LAMBDA function calls itself cost more. So, refactoring your code doesn't eliminate the memory limit, but reduces it furthermore. For eg, if your code uses LAMBDA(a,c,(a-1)+(a-1)), if you add another lambda like this: LAMBDA(a,c,LAMBDA(aminus,aminus+aminus)(a-1)), it errors out with much less array elements than before(~20% less). LAMBDA is much more expensive than repeating calls.
There are many other factors at play, especially with other LAMBDA functions. Google might change their mind about these arbitrary limits later. But this gives a start.
Possible workarounds:
LAMBDA itself isn't restricted. You can nest as much as you want to. Only LAMBDA Helper Functions are restricted. (Credit to player0)
Named functions which don't use LAMBDA(helper functions) themselves, aren't subjected to the same restrictions. But they're subject to maximum recursion restrictions.
Another workaround is to avoid using lambda as a arrayformula and use autofill or drag fill feature, by making the lambda function return only one value per function. Note that this might actually make your sheet slow. But apparently, Google is ok with that - multiple individual calls instead of a single array call. For example, I've written a permutations function here to get a list of all permutations. While it complains about "memory limit" for a array with more than 6 items, it can work easily by autofill/dragfill/copy+paste with relative ranges.
not even an answer
by brute-forcing a few ideas it looks like there are more hidden variables than previously thought. it is probably safe to say that the upper limit is a result of "running out of memory" especially when calculation time does not play any role. the thing is that there are factors even outside of LAMBDA that affect the computational capabilities of the formula. here is a brief summary of the issue in layman's terms:
WHY WERE/ARE LAMBDA'S MINIONS STUPID?!
UPDATE: limit boundaries were moved 10-fold higher, so none of the below testing formulae limits represent the actual up-to-date state, however, lambda minions are still not limitless!
let's imagine a memory buffer from the 1999 era with a limited size of 30 units that kicks in only when you use LAMBDA with friends (MAP, SCAN,BYCOL, BYROW, REDUCE, MAKEARRAY). keep in mind that in google sheets when we use any other formula, the limiting factor is usually the cell count limit.
example 1
output capability: 199995 cells!
reduction from 199995: 1/1 (meh, but ok)
example 2
output capability: 49998 cells!
reduction from 199995: 1/~4 (*double-checking the calendar if the year is really 2022*)
example 3
output capability: 995 cells!
reduction from 199995: 1/201 !! (*remembering this company built a quantum computer*)
further testing
establishing the baseline: all below formulae are maxed out so they work as "one step before erroring out". please keep noticing the numbers as a direct representation of row (not cell) processing abilities
starting with a simple:
=ROWS(BYROW(SEQUENCE(99994), LAMBDA(x, AVERAGE(x))))
by adding one more x the following would error out so even the length of strings matters:
=ROWS(BYROW(SEQUENCE(99994), LAMBDA(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, AVERAGE(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx))))
doubling the array brings no issues:
=ROWS(BYROW({SEQUENCE(99994), SEQUENCE(99994)}, LAMBDA(x, AVERAGE(x))))
but additional "stuff" will reduce the output by 1:
=ROWS(BYROW({SEQUENCE(99993), SEQUENCE(99993, 1, 5)}, LAMBDA(x, AVERAGE(x))))
interestingly this one runs with no problem so now even the complexity of input matters (?):
=ROWS(BYROW(SEQUENCE(99994, 6, 0, 5), LAMBDA(x, AVERAGE(x))))
and with this one, it seems that even choice of formula selection matters:
=ROWS(BYROW(RANDARRAY(99996, 2), LAMBDA(x, AVERAGE(x))))
but what if we move from virtual input to real input... A1 cell being set to =RANDARRAY(105000, 3) we can have:
=ROWS(BYROW(A1:B99997, LAMBDA(x, AVERAGE(x))))
again, it's not a matter of cells because even with 8 columns we can get the same:
=ROWS(BYROW(A1:H99997, LAMBDA(x, AVERAGE(x))))
not bad, however, indirecting the range will put us back to 99995:
=ROWS(BYROW(INDIRECT("A1:B"&99995), LAMBDA(x, AVERAGE(x))))
another fact is that LAMBDA as a standalone function runs flawlessly even with an array 105000×8 (that's solid 840K cells)
=LAMBDA(x, AVERAGE(x))(A1:H105000)
so is this really the memory issue of LAMBDA (?) or the factors that determine the memory used in LAMBDA are limits of unknown origin bestowed upon LAMBDA by individual incapabilities of:
MAP
SCAN
BYCOL
BYROW
REDUCE
MAKEARRAY
and their unoptimized memory demands shaken by wast variety of yet unknown variables within our spacetime
Edit 2022/10/26
Seems, Google Sheets Team has just increased the max. limit 10x times 😍.
1999992 from 199992
My original formula supposed it would be 199992 cells, but as you see the "behind" logic changes and may also change in the future.
LAMBDA+Friends Limit
The maximum number of rows you can use in the formula (guess):
Limit = 1999992/(1 + inside_lambdas) - outside_lambdas
inside_lambdas and outside_lambdas are functions and parameters, each count 1:
+ / * -
5, A1, "text",
MOD, AVERAGE, etc.
{"array element"}
The limit is about cells operated by the "lambda+" formula: reduce, byrow, etc.
My tests are here:
Lambda Limits \ Sample Sheet
Steps to fix:
Do Not use Lambda if possible :(
Do most of the calculations outside lambda if possible
Split formulas to multiple cells, having the limit in mind. Copy formulas, each one has its own limit.
Ask Google to Fix this. In Sheets use the menu Help > Help Sheets Improve
Write to the support if you have a paid account.
Final notes:
my formula for the limit is guess, and it works for my examples and tests. Please try it and comment to this answer if you find an error.
the formula does not answer how long variable names affect the limit (=ROWS(BYROW(SEQUENCE(99994), LAMBDA(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, AVERAGE(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx))))) Need more tests to figure out the correct effect on the limit. As this does not break: =ROWS(BYROW(SEQUENCE(199992), LAMBDA(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, AVERAGE(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx)))), my suggestion is this is the max. length of the variable name, and it does not change the cells limit.
Google Sheets team may change the logic "behind" the formula, so all tests may appear invalid in a time.
Google Spreadsheet on google drive. I have just made a survey on google drive for people to fill in their football predictions for fun! I can put all of the publics predictions into an excel document in one click but I want the public to earn points when they predict the right result. For example if a friend of mine predicted Arsenal 2 - 1 Liverpool and the result is Arsenal 1 - 0 Liverpool they should earn 1 point for predicting the right winner and if the prediction was equal to Arsenal 2 - 1 Liverpool, the prediction should earn 3 points.
I am struggling with the code for it but here is the closest I have got:
COUNTIF(F5, ʺ>=ʺ & E5)
The code above does not work and I cannot figure it out. Any help will be greatly appreciated as soon as possible. Thanks a lot.
I am sorry that this is not an answer, but I am unable to comment without higher reputation. It would be helpful to have access to a copy or example of what you have, as your cell references mean very little without. Then we can see exactly what you have tried.
EDIT::
Without knowing how your sheet works or is laid out, it is difficult, however I've put this together for you on Google Sheets here
https://docs.google.com/spreadsheets/d/13Ejaddmj2d8cysxdZE_Inro65KDFgzeJW7FqPWwaCpE/edit?usp=sharing
It's a very clunky set of nested IF statements but it does work. I'm sure there is a neater way of doing it.
In case you can't view it, here is the formula
=IF(A2>B2, IF(D2>E2, IF(A2=D2, IF(B2=E2,"3","1"),"1"),"0"), IF(A2=B2, IF(D2=E2, IF(A2=D2, IF(B2=E2,"3","1"),"1"),"0"), IF(D2<E2, IF(A2=D2, IF(B2=E2,"3","1"),"1"),"0")))
In this case, A2 is Arsenal's score, B2 is Liverpool's score, D2 is Fred's Arsenal score prediction and E2 is his Liverpool prediction. I placed the above formula in cell F2 to give Fred's points.
The above code first checks to see
if Arsenal beat Liverpool, if true it then checks
if Fred predicted that Arsenal would beat Liverpool. If true, then it checks
if Fred got Arsenal's score correct. If true, it checks
if Fred got Liverpool's score correct. If that's true,
then Fred got everything right and gets 3 points (and a cookie =]).
If Fred gets the winner right but not the scores, he gets 1 point. Otherwise he gets 0.
This formula also checks to see if Liverpool beat Arsenal and runs the same checks against Fred's prediction, then to see if the teams drew and to see if Fred predicted a draw or not. If he predicts a draw and the correct scores he gets 3 points, otherwise he gets 1 for getting the draw correct.
I believe that this is what you are looking for .. attached are a formula and result view of my answer ;)
formulas
results
I am new to google sheets and question which I am asking is typical math question.
I have a value (in d3) which refers to total gram of gas required, now I have to release this much (d3) gas from number of gas Cans. Gas Cans are of two kinds bigger one contains 680 grams gas and small one contains 454 grams of gas.
Now once we open the gas CAN then whole gas will be released mean to say that we cannot release part portion of gas however we can minimize wastage if we use exact (or near to exact) amount of gas required by using some big cans and some small cans. I have worked hard and found a way (see in c3:c5 and also see in b12:c12) but that is too long & that has been shown in below mentioned link.
Now I want total no. of big cans and small cans in d4 & d5 with a formula so that same criteria can be applied to all values.
It has been explained in detail with example in following link:
https://docs.google.com/spreadsheets/d/1zZiKMqb33kDSOIduBMayZ0NMqibcvMF-UBYYvn7VVBs/edit
Thanks in advance.
For D4 you can have =FLOOR(FLOOR(G3/680)+MOD(G3, 680)/454) and for D5 you can have =IF(G3 > G4*680, CEILING(MOD((G3-G4*680)/454, 454)), 0).
Not sure if it will work for all cases though, so make sure you do some testing. In D4, it does the same thing you did where you find the whole number of big cans. It then also calculates if the remainder is larger than one small can, then another big can will be added (it is effectively your "> 66.76" calculation). In D5, the remaining grams are calculating after taking into account how many big cans there already are. If there are remaining grams, then one small can would be calculated. If there are enough big cans to hold the gas, no small cans are necessary. It includes some calculation, but =IF(G3 > G4*680, 1, 0) should work the same, since there should only be one or zero small cans.
first time user of this forum - guidance on how to provide enough information is very appreciated. I am trying to replicate the presentation of data used in the Medical education field. This will help improve the quality of examiners' marking of trainees in a Clinical Exam. What I would like to communicate will be similar to what is already communicated in the College of General Practitioners regarding one of their own exams, please see www.gp10.com.au/slides/thursday/slide29.pdf to help understand what it is I want to present. I have access to Excel, SPSS and R, so any help with any of these would be great. However as a first attempt I have used SPSS and created 3 variables: dummy variable, a "station score" and a "global rating score"(GRS). The "station score"(ST) is a value between 0 and 10 (non-integers) and is on the y-axis similar to the pdf presentation of "Candidate Final Marks". The x-axis is the "global rating scale", an integer from 1 to 6 and is represented in the pdf as the "Overall Performance Scale". When I use SPSS's boxplot I get a boxplot as depicted.
.
What I would like to do is overlay a single examiners own scoring of X number of examinees. So for one examiner (examiner A) provided the following marks:
ST: 5.53,7.38,7.38,7.44,6.81
GRS: 3,4,4,5,3
(this is transposed into two columns).
Whether it be SPSS, Excel or R how would I be able to overlay the box and whisker plots with the individual data points provided by the one examiner? This would help show the degree to which the examiners' marking styles are in concordance with the expected distribution of ST scores across GRS. Any help greatly appreciated! I like Excel graphics but I have found it very difficult to work with when choosing the examiners' data as a separate series - somehow the examiners' GRS scores do not line up nicely on the x-axis. I am very new to R but am also very interested in R, and would expend time to get a good result in R if a good result is viable. I understand JMP may be preferable for this type of thing but access to this may not be possible.