I have been looking around for a while but unable to find an answer to my question.
In Excel, what compact formula can I use to create an array made up of a single element repeated n times, where n is an input (potentially hard-coded)?
For example, something that would look like this (the formula below does not work but gives an idea of what I am looking for):
{={"Constant"}*3}
Note: I am not looking for a VBA-based solution.
EDIT Reading #AxelRichter answer, I see I should also indicate that the formulas below assume Constant is a number. If Constant is text, then this solution will not work.
Volatile:
=ROW(INDIRECT("1:" & Repts))/ROW(INDIRECT("1" & ":" & Repts)) * Constant
non-Volatile:
=ROW(INDEX($1:$65535,1,1):INDEX($1:$65535,Repts,1))/ROW(INDEX($1:$65535,1,1):INDEX($1:$65535,Repts,1))*Constant
If
Constant = 14
Repts = 3
then
Result = {14;14;14}
The first part of the formulas create an array of 1's repeated Repts times. Then we multiply that array by Constant to get the desired result.
And after reading #MacroMarc's comment, the following non-volatile formula shouyld also work for numbers:
=(ROW($A$1:INDEX($A:$A,Repts))>0)*Constant
One could concatenate 1:n empty cells to the "Constant" to create a string array having n items "Constant":
"Constant"&INDEX(XFD:XFD,1):INDEX(XFD:XFD,3)
There 3 is n.
Used in Formula
=INDEX("Constant"&INDEX(XFD:XFD,1):INDEX(XFD:XFD,3),0)
Evaluate Formula shows that it works:
Here column XFD is used because in most cases this column will be empty and a column which is guaranteed to be empty is needed for this solution.
If used
"Constant"&T(ROW($A$1:INDEX($A:$A,3)))
=INDEX("Constant"&T(ROW($A$1:INDEX($A:$A,3))),0)
the need of an empty column disappears. The function ROW returns numbers but the T returns an empty string if its parameter is not text. So empty strings will be concatenated for each 1:3 (n).
Thanks to #MacroMarc for the hint.
Try:
REPT("Constant", SEQUENCE(3,1,1,0))
Or, if the reference is to a dynamic array:
REPT("Constant", SEQUENCE(A1#,1,1,0))
The dynamic array spills, and has your constant repeated one time.
Using SEQUENCE with a step of 0 is a much cleaner way to make an array of constants. You can choose whether you want rows or columns (or both!) as well.
=SEQUENCE(Repts,1,Constant,0)
I will generally use a sequence (like Claire (above) said). But if you want to provide an output of text objects, I would do it this way:
=IF(SEQUENCE(A1,A2,1,0),A3)
Where:
A1 has the number of rows
A2 has the number of columns
A3 has the thing you want repeated into an array
The sequence will create a matrix of 1's, which the IF statement will default to the TRUE expression (being the contents of A3).
So, if you wanted a vertical list of 3 items that says "Constant", this would do it:
=IF(SEQUENCE(3,,1,0),"Constant")
If you would prefer it be arranged horizontally instead of vertically, just amend the SEQUENCE function:
=IF(SEQUENCE(,3,1,0),"Constant")
Related
I have a list of values that I would like to match against the combination of multiple ranges.
So, for example, my ranges are A1:A100 and B1:B100.
Instead of concatenating A with B in a new column C, i.e.
CONCAT(A1,B1)...CONCAT(A100,B100)
and then matching my value against that new column - I would like to do something like this:
MATCH(value,CONCATENATE(A1:B100),0)
And copy this down a column near my list of values.
I have a feeling this can be done with some sort of array formula...
Yes as an array formula:
=MATCH(value,$A$1:$A$100 & $B$1:$B$100,0)
Being an array formula it must be confirmed with Ctrl-Shift-Enter instead of Enter when exiting edit mode.
Though they may seem similar in approach they are not. CONCATENATE will return a string not an array to the MATCH with all 200 values in one long string. Where the above will return 100 values, each row concatenated, as an array which can be used to search.
One further note, If performance becomes a issue, Array formulas are inherently slower, adding the helper column and using a regular MATCH will improve the responsiveness.
This should work, basically you just need to concatenate it yourself using &
=MATCH(D1,A1:A10&B1:B10,0)
D1 is the value you're trying to look for.
This is an array, so remember to hit Ctrl+Shift+Enter when you input it.
This question is about how Excel's COUNTIF function treats different data types when used as an array formula.
There are lots of good posts out there detailing how to use COUNTIF for tasks such as extracting unique values from a list, for example this post. I've managed to use examples from this and other posts to solve specific problems, but I'm trying to get a deeper understanding of array formulas in order to adapt my formulas to new needs.
I came across a peculiar behavior of COUNTIF. In general, Excel seems to treat strings as "larger than" numbers, so that the following examples are valid:
Cell Formula Returns
=1<2 TRUE
="a"<"b" TRUE
="a">"b" FALSE
=1<"b" TRUE
Now, suppose range A1:A6 contains the following data set:
1
2
3
A
B
C
For each cell in this set, I want to check how many of all the cells in the set that are smaller than or equal to that cell (a useful technique in more complex formulas). I enter the following array formula in range B1:B6:
{=COUNTIF($A$1:$A$6,"<="&$A$1:$A$6)} (CTRL + SHIFT + ENTER)
Based on the examples above comparing numbers and strings (also illustrated in Column D below), I would expect the output shown below to look like Column C. However, the array formula returns the result shown in Column B, which suggests that strings and number elements are counted separately by arraywise COUNTIF.
Column A Column B Column C Column D
1 1 1 A1<"C" = TRUE
2 2 2 A2<"C" = TRUE
3 3 3 A3<"C" = TRUE
A 1 4 A4<"C" = TRUE
B 2 5 A5<"C" = TRUE
C 3 6 A6<"C" = FALSE
So the question is how to produce the output in Column C? (EDIT: Just to clarify, I'm specifically looking for solutions that make use of COUNTIF's array properties.)
Any insight into why arraywise COUNTIF apparently behaves differently than the single-cell examples would also be much appreciated.
NOTE: I've translated the examples from a non-English version of Excel, so I apologize in advance for any typos.
PS. For a background, I ran into this problem when I tried to build a formula that would both extract unique values from a list with possible duplicates, and sort the unique values in numerical/alphabetical order. My current solution is to do this in two steps. One solution for how to do it in one step is proposed here.
First of all, excellently laid-out question, and on an interesting topic to boot.
I also raised an eyebrow when I first came across this behaviour of the COUNTIF(S)/SUMIF(S) functions. In their defence, I suppose we could construct situations in which we actually want strings and numerics to be considered separately.
In order to construct your required in-formula array, you will need something like:
MMULT(0+(TRANSPOSE($A$1:$A$6)<=$A$1:$A$6),ROW($A$1:$A$6)^0)
though note that the necessary transposition will mean that any set-up which includes this construction will require committing with CSE.
Regards
The different behavior can easily shown if you compare
=COUNTIF($A$1:$A$6,"<=A")
with
{=COUNT(IF($A$1:$A$6<="A",1))}
The first will only get text values from $A$1:$A$6 because it is clearly text to compare and it is faster ignoring other values then. =COUNTIF($A$1:$A$6,"<=3") will only get numeric values from $A$1:$A$6 because of the same reasons. Even if the criterion would be a concatination with a cell reference, then the concatination would be the first process and would lead either to "<=A" or "<=3". So it is ever clear what to compare, text or numbers.
The second first needs an array of the comparisons, then performs the IF, gets so an array of 1 or FALSE and counts then. But the "A" could also be a cell reference. So it is not clear what to compare at the beginning and the first array has to compare all values in $A$1:$A$6.
So COUNTIF(S) and SUMIF(S) cant be used comparing mixed text and numeric data.
The solution is shown already by XOR LX.
Btw.: with your PS. For a background you should consider the following solution from an German Excel site: http://www.excelformeln.de/formeln.html?welcher=236.
In your linked example:
Formula in B2 downwards
{=INDEX($A$2:$A$99,MATCH(LARGE(COUNTIF(A$2:A$99,">="&A$2:A$99)+99*ISNUMBER(A$2:A$99),ROWS($1:1)),COUNTIF(A$2:A$99,">="&A$2:A$99)+99*ISNUMBER(A$2:A$99),0))&""}
In this solution the COUNTIF compares with >= so the biggest text or number will count lowest and so get the lowest position. All number positions are added with 99. So they are ever greater than all possible text positions. So we have a descended sorted array. Then, using LARGE, the list is created from the highest to the lowest position.
I doubt that countif is the right function for what you want to achieve here.
try this (ctrl+shift+enter):
={SUM(IF(A1>=$A$1:$A$6,1,0))}
You will get
1
2
3
4
5
6
PS: CountIf is an basically an array function internally. Using it in another array function results into multiple array functions and their behaviour becomes complex. Array functions are best used with clear logical path.
As tested in Excel 2013, you will only get 1 in all results instead of what was proposed in Column B.
Currently, in the function provided by you, countif cannot figure out which cell to compare to which cell. Array functions expand ranges and then perform the provided action. Therefore, it is comparing each cell to same cell and resulting into 1.
Try this FormulaArray in B1 then copy till B6:
=SUM(($A$1:$A$6<=$A1)*1)
I am interested in spreadsheet functions, not VBA solutions, to be included in a single cell formula.
[A1:A15 contain numeric values from 1 to 127, B1:B15 contain integers from 1 to 7 that set a divisor.]
Given the function:
=SUMPRODUCT(MOD(FREQUENCY(A1:A15;A1:A15);B1:B15))
FREQUENCY(A1:A15;A1:A15) gives a 1-column array of 15+1 rows, whereas the second part (B1:B15) is a 1-column array of 15 rows.
I would like to change the resulting array given by FREQUENCY (only in memory -not explicit in sheet-) from a 1-column 16 rows array to a 1-column 15 rows array with the first 15 cell values of that array.
[FREQUENCY documentation: https://support.office.com/en-us/article/FREQUENCY-function-44e3be2b-eca0-42cd-a3f7-fd9ea898fdb9 NB: for Excel, second remark states number of elements that depend on bins_array. ]
I would appreciate suggestions.
Thus, both arrays within MOD will have the same dimensions and SUMPRODUCT will not find cells with error values. I can disregard error values using IF and ISERROR within SUMPRODUCT, but I'd rather disregard the non-relevant part of the FREQUENCY resulting array if it is possible.
It has been thought that making it more specific might be more helpful, so it has been heavily reduced and simplified.
With external help, I have been able to fine-tune a way to solve my problem using INDEX in array formula mode. I am posting the answer in case it helps others.
One way: Put FREQUENCY(A1:A15;A1:A15), or any formula that produces an multi-cell array, within INDEX and have 2nd and/or 3rd arguments as array of consecutive values which will represent rows/columns.
INDEX(FREQUENCY(A1:A15;A1:A15);ROW(INDIRECT("1:" & ROWS(FREQUENCY(A1:A15;A1:A15)-1));1)
First argument within INDEX is the resulting array coming from a formula to shrink (from 16x1 to 15x1), which would be a multi-cell array formula if explicitly entered; second argument is the array 1..15 given by row numbers from 1 to the number of total rows of the "array from formula to shrink" MINUS 1: the first 15 (out of 16) values in the array from a formula; 3rd argument is the column of the shrank array (if need be, more than one could be selected using an analogue to the second argument).
In the particular case of FREQUENCY, because it is known that we are interested in the "bins" part of the function, the formula can be simplified by including the total rows of the "bins"/"intervals" array inside FREQUENCY (its second argument). We will have
INDEX(FREQUENCY(A1:A15;A1:A15);ROW(INDIRECT("1:" & ROWS(A1:A15)));1)
and the complete formula would become
SUMPRODUCT(MOD(INDEX(FREQUENCY(A1:A15;A1:A15);ROW(INDIRECT("1:" & ROWS(A1:A15)));1);B1:B15))
Now, both dividend and divisor of MOD have exactly the same dimensions (15x1) and because B1:B15 includes integers greater than 0 there are no errors.
Thanks all for helping me in making question more concise and better formatted.
ADDITIONAL INFORMATION: As pointed out correctly in comments by XOR LX, this does not seem to work in the widely popular spreadsheet software Excel. It has been developed for an INDEX function inside SUMPRODUCT as used in Open Office Calc which I had mistakenly thought 100% equivalent to Excel's version. A more complete answer perhaps using other functions would be appreciated.
In the previous answer, XOR LX points out very correctly that this formula cannot work in Excel, due to row_num/column_num argument behaviour. Very kindly XOR LX has shown me how that approach can work, and also thanks and credit for supplying a good answer: "INDEX can be used to redimension array (even dynamically created ones) if the row_num/column_num array is coerced to take an arbitrary array with the right dimensions, as shown on this blog entry " The following formula has been checked in Excel 2010 and has the expected results:
SUMPRODUCT(MOD(INDEX(FREQUENCY(A1:A15,A1:A15),N(INDEX(ROW(INDIRECT("1:" & ROWS(A1:A15))),,)),1),B1:B15))
NB: row_num argument of first INDEX, a ROW generated auxiliary array, has been nested inside N(INDEX([...],,)); at least one comma is necessary to account for the two arguments minimum of the nested INDEX. It is in itself interesting the discussion that applies generally to INDEX's arguments, and other functions', that need to be coerced to take arrays (see, here and here at XOR LX's blog). For Open Office users it might be worth stressing the point made at the blog
Unlike OFFSET, (...) for which the first parameter must be a
reference (...) in the worksheet, INDEX can also accept –
and manipulate – for its reference arrays which consist of values
generated e.g. via other subfunctions within the formula. XOR LX's blog
That would be indeed the case in changing the dimension in an array as in this question, but also useful in reversing or displacing the values in an array, for example. Open Office accepts arrays as row_num/column_num, so the coercion is not needed and some formulas rely on this, but without it, these formulas are unlikely to work when files are open in Excel.
Regrettably, this type of coercion is not passed correctly to Open Office, and formula need to be "decoerced" to work, at least in my casual tests.
In order to use a formula that would work in both spreadsheet programs regarding shortening arrays, the only thing I have managed is the following (required: arrays must be single-column)
SUMPRODUCT(
(COLUMN(INDIRECT("R1C1:R"& ROWS(vals_to_mod) &"C"& ROWS(FREQUENCY(vals_for_freq,vals_for_freq)),FALSE))
-ROW(COLUMN(INDIRECT("R1C1:R"& ROWS(vals_to_mod) &"C"& ROWS(FREQUENCY(vals_for_freq,vals_for_freq)),FALSE))
=0)
*MOD(TRANSPOSE(FREQUENCY(vals_for_freq,vals_for_freq)),vals_to_mod)
)
(it "shortens" one array to the shortest of the pair, by creating an auxiliary array with TRUE/1s on the diagonal starting top-left and FALSE/0s elsewhere, therefore disregarding all defined values outside the square section of the array. Thus, SUMPRODUCT adds values within the diagonal of the square section which are the product of the corresponding values up to the last value of the shorter array.)
I'm trying to perform math within an Excel formula to specify the end of an array. Here is a simple version of what I want to do:
A B C
1 =COUNTA(A1:A5)-1 =SUM(A1:A(1+B1))
2
3
4
5
The first column is my data array. The second column counts the number of entries in that array (so if it isn't full, it returns a value less than 5). The third column sums the array starting with the first value and ending with the last entered value. Obviously with the SUM function it doesn't matter if there are zeroes, but I am trying to use the MATCH function and I don't want it to return a zero just because there are blank entries in the array I'm looking up.
So I want to modify the information within the SUM function to produce a variable array length based on the return value of B1. I hope this is clear. Thanks for any help!
One way is to use INDEX like this
=SUM(A1:INDEX(A:A,B1+1))
you can use the range defined by
A1:INDEX(A:A,B1+1)
in other functions like MATCH
Like this?
=SUM(INDIRECT("A1:A"&(1+B1)))
I'd like to create a table lookup formula that matches two columns. For instance, suppose I'd like to find the value of the Letter column at the row where the Type column is Biennial and the Result column is Warning.
A B C
1 Letter Type Result
2 A Annual Exceeds
3 B Biennial Warning
4 C Biennial DevelopmentNeeded
5 D Biennial PartiallyMeets
6 E Annual Meets
What would the formula look like to accomplish this?
The SUMPRODUCT() formula is really apt for situations where you want to lookup a value with multiple criteria. It is most convenient when wanting to look up numeric values, but it can be adjusted to look up string values as well. As a bonus, you can avoid having to use array formulas.
This particular problem can be tackled with the following formula (indentation added for legibility, which you can do in Excel formulas using ALT + ENTER):
=INDEX(
$A$2:$A$6,
SUMPRODUCT(
($B$2:$B$6 = "Biennial") *
($C$2:$C$6 = "Warning") *
ROW($A$2:$A$6)
) - 1
)
First, SUMPRODUCT() is used to filter out the proper rows using ($B$2:$B$6 = "Biennial") and ($C$2:$C$6 = "Warning"); the multiplication operator * functions as an AND operator (the + operator would function as an OR operator).
Then the result is multiplied by ROW($A$2:$A$6) to find the particular row that has the combination. SUMPRODUCT() then adds everything up, which in this case gives us 3. As the result sought is actually on row 2 due to the column headings, we subtract 1. By applying the INDEX() function, we get the desired result: B.
Beware though that this is the case if and only if the combination sought is unique. If the combination sought exists more than once, this will break down.
Another method that avoids array entry is:
=INDEX($A$2:$A$6,MATCH(2,index(1/(($B$2:$B$6="Biennial")*($C$2:$C$6="Warning")),0)))
It exploits the fact that the match function ignores certain errors and that index manages arrays naturally.
You can use an array formula if you like:
=INDEX($A$2:$A$6,MATCH(1,($B$2:$B$6="Biennial")*($C$2:$C$6="Warning"),0))
Enter in with Ctrl+Shift+Enter
If you want to do this without array formulas, one way you could do it is by creating a helper column.
Column D to have the formula:
=B2&C2
Copied down
Then the new formula could be:
=INDEX($A$2:$A$6,MATCH("BiennialWarning",$D$2:$D$6,0))
It's just a play on the text, really.