A few weeks ago Gewilson asked on the Chandoo.org Forums, “Can I simplify my formula? “
=176 – (SUMIF($B10:$AF10,”PD”,$B11:$AF11) +SUMIF($B10:$AF10,”FA”,$B11:$AF11) +SUMIF($B10:$AF10,”PS”,$B11:$AF11) +SUMIF($B10:$AF10,”PN”,$B11:$AF11) +SUMIF($B10:$AF10,”F1″,$B11:$AF11) +SUMIF($B10:$AF10,”P1″,$B11:$AF11) +SUMIF($B10:$AF10,”F7″,$B11:$AF11))
SirJB7 responded with a nice Sumproduct solution:
=176 – SUMPRODUCT(((B$10:AF$10)=({“PD”;”FA”;”PS”;”PN”;”F1″;”F7″})) *(B$11:AF$11))
So Today we will pull this apart to see what inside, I think what we find may surprise you.
SirJB7’s Formula
=176 – SUMPRODUCT(((B$10:AF$10)=({“PD”;”FA”;”PS”;”PN”;”F1″;”F7″})) *(B$11:AF$11))
To Simplify things I am going to use a Truncated set of data and adjust the formula accordingly
We will examine:
=176 – SUMPRODUCT(((B$10:I$10)=({“PD”;”FA”;”PS”;”PN”})) *(B$11:I$11))
This problem has a smaller Range B10:I10 instead of B10:AF10
as well as 2 less possible solutions {“PD”;”FA”;”PS”;”PN”} instead of {“PD”;”FA”;”PS”;”PN”;”F1″;”F7″}
The reason for this will soon become evident.
As usual you can download a Sample File to follow along with. Download Here.
Lets go:
=176 – SUMPRODUCT(((B$10:I$10)=({“PD”;”FA”;”PS”;”PN”})) *(B$11:I$11))
We can see above that the formula is subtracting the result of a Sumproduct from a Fixed Number 176. So we really only need to focus on the Sumproduct part of the formula.
As we saw In Formula Forensics 007 – Sumproduct, Sumproduct adds up the products of the constituent arrays.
In this case
SUMPRODUCT(((B$10:I$10)=({“PD”;”FA”;”PS”;”PN”;})) *(B$11:I$11))
Has only 1 constituent array. The array does consist of 2 components
SUMPRODUCT(((B$10:I$10)=({“PD”;”FA”;”PS”;”PN”})) *(B$11:I$11))
These is a Logic component ((B$10:AF$10)=({“PD”;”FA”;”PS”;”PN”}))
and a Numerical Component (B$11:I$11)
Which are then multiplied together.
Looking at the Logical Component first
((B$10:I$10)=({“PD”;”FA”;”PS”;”PN”}))
The formula is checking the Range B10:I10 against an Array of possible solutions {“PD”;”FA”;”PS”;”PN”}
That is, it is checking each value in our list {“PD”;”FA”;”PS”;”PN”}, against each cell in the range B10:I10.
If we type the above equation=((B$10:I$10)=({“PD”;”FA”;”PS”;”PN”})) into a spare cell C14, and press F9
Excel returns ={FALSE,FALSE,FALSE,FALSE,TRUE,FALSE,FALSE,FALSE;FALSE,TRUE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE}
What the …
If we look closely at the above array we will see that it contains a lot of True/Falses separated by ,’s and a few ;’s
={FALSE,FALSE,FALSE,FALSE,TRUE,FALSE,FALSE,FALSE;FALSE,TRUE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE}
Specifically there are 4 blocks of 8 True/Falses separated by ,’s, each block is separated by a ;
In Total 4 x 8 = 32 Values
What this is, is an array representing the multiplication of the 8 cells in the range B10:I10 with each element of the possible solution array
Each row of the Array is separated from the next by a ;
Each element in each row is separated by a ,
This is best displayed like:
You can see why I simplified the size of the original problem.
So we have an Array of True/Falses ={FALSE,FALSE,FALSE,FALSE,TRUE,FALSE,FALSE,FALSE;FALSE,TRUE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE}
Which is now multiplied by the next component of the Sumproduct
({FALSE,FALSE,FALSE,FALSE,TRUE,FALSE,FALSE,FALSE;FALSE,TRUE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE}) *(B$11:I$11)
In a spare cell, say C23 enter
=({FALSE,FALSE,FALSE,FALSE,TRUE,FALSE,FALSE,FALSE;FALSE,TRUE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE}) *(B$11:I$11) and press F9
Excel returns
={0,0,0,0,10,0,0,0;0,10,0,0,0,0,0,0;0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0}
Note that this array has the same 8 column x 4 Row layout as above, except that all the True have been replaced by the values in the Score cells B11:I11
Sumproduct now kicks in and adds these up
=Sumproduct({0,0,0,0,10,0,0,0;0,10,0,0,0,0,0,0;0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0})
To get 20
Which is subtracted from our original number
=176 – SUMPRODUCT(((B$10:I$10)=({“PD”;”FA”;”PS”;”PN”})) *(B$11:I$11))
= 176 – Sumproduct({0,0,0,0,10,0,0,0;0,10,0,0,0,0,0,0;0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0})
= 176 – 20
= 156
Download
You can download a copy of the above file and follow along, Download Here.
Other Posts In This Series
You can learn more about how to pull Excel Formulas apart in the following posts
We Need Your Help
I have received a few more ideas since last week and these will feature in coming weeks.
I do need more ideas though and so I need your help.
If you have a neat formula that you would like to share and explain, try putting pen to paper and draft up a Post like above or;
If you have a formula that you would like explained but don’t want to write a post also send it in to Chandoo or Hui.
40 Responses to “Looking up when the data won’t co-operate (case study)”
Nice Trick.. Clever use of cell references
Here is a formula I tried to create:
=SUMPRODUCT(((NOT(ISERROR(SEARCH(L5,B4:H14))))*1),(B5:H15))
It takes care of Caveat #1 (can handle text), but Caveat #2 remains.
In situations like this, I will often use VBA to restructure the data (2 columns: dates and values) on to a new worksheet. I can then use this 'clean' source for data analysis (formula or pivot table).
=SUMPRODUCT(((NOT(ISERROR(SEARCH(L5,B4:H14))))*1),(B5:H15)) and complex formulae in general are all very well but when you come back to them in a few weeks / months time, it is not at all easy to see what they do and what the limitations are.
Hi Chandoo,
I had used this type of cell ref. various times while calculating average.
But for the situation here try below formula . Note this is an array formula and must be confirmed with Ctrl+Shift+Enter.
=SMALL(IF(MMULT((L5=B4:H14)*IF(ISNUMBER(B5:H15),B5:H15),{1;1;1;1;1;1;1}),MMULT((L5=B4:H14)*IF(ISNUMBER(B5:H15),B5:H15),{1;1;1;1;1;1;1})),1)
Regards,
Hi, I think Using SEARCH in here will create a problem say there is a text like SUN and another text SUNLIGHT both result will be added by SUMPRODUCT.
Regards,
Array option.
=SUM(IF(MOD(ROW(B4:B14),2)=MOD(ROW(B4),2),IF(B4:H14=L5,B5:H15)))
Regards
@Elias,
Nice approach.
Although not requested - the formula I suggested closes all possibilities.
Criteria: _____ Value to retrieve:
Date__________ Numeric
Date__________Textual
Textual________Numeric
Textual________Textual
While your formula copes with only the 3 first combinations.
Michael (Micky) Avidan
“Microsoft® Answer” – Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2015)
ISRAEL
@Michael,
Sorry but I don’t understand your point. I believe the challenge was to return the summary of a given date. What is your really volatile formula doing that mine is not?
Regards
@Elias,
I didn't say that the challenge differs from what you just mentioned/aimed to nor that your formula doesn't provide the requested result.
Please read my previous comment again and focus on the last combination (TEXT / TEXT).
I, myself, always try to provide a global Formula that is capable to handle all sorts of data.
Michael (Micky) Avidan
“Microsoft® Answer” – Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2015)
ISRAEL
@Michael,
I see your point, but you are missing the below points if you are trying to cover all sorts of data.
What happened if the lookup value does not exist?
Do you want the first, second, summary, concatenation of the values if the look value is repeated?
See they are too many possibilities to be cover with just one formula.
Regards
1) The range: B4:H15 was named: RNG.
2) The following Array Formula was "retrieved from my sleeve" and I hope it can be shorten.
3) The formula seems to take care of BOTH(!) caveats.
-------------------------------------------------------------------------------
=OFFSET(INDIRECT(ADDRESS(SMALL(IF(RNG=L5,ROW(RNG),""),1),MOD(SMALL(IF(RNG=L5,(ROW(RNG))+COLUMN(RNG)/10),1),1)*10)),1,)
-------------------------------------------------------------------------------
Michael (Micky) Avidan
“Microsoft® Answer” – Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2015)
ISRAEL
@Michael,
Check what happened with your result if you type 41927 in D5.
Regards
Correct. Didn't predict that.
Will find time to work something out.
Michael (Micky) Avidan
“Microsoft® Answer” – Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2015)
ISRAEL
@Elias,
Let's hope the following Array Formula "closes all open doors".
Again - it has nothing to do with your formula which works fine as long as the 3 first mentioned combinations are concerned.
-------------------------------------------------------------------------------
=INDEX(RNG,LARGE(IF(RNG=L5,MOD(ROW(RNG)-1,2)*(ROW(RNG)),""),1)-2,(MOD(SMALL(IF(RNG=L5,(ROW(RNG))+COLUMN(RNG)/10),1),1)*10)-1)
-------------------------------------------------------------------------------
Michael (Micky) Avidan
“Microsoft® Answer” – Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2015)
ISRAEL
Ok, if you insist. The following will cover all the scenarios you listed. However, I’ll never recommend/use such of formula.
Defined names:
rDat = $B$4:$H$15
rRow =ROW(rDat)-MIN(ROW(rDat))+1
rCol =COLUMN(rDat)-MIN(COLUMN(rDat))+1
rInc =MOD(rRow,2)=MOD(MIN(rRow),2)
L6=INDEX(rDat,MAX(IF(rInc,IF(rDat=L5,rRow)))+1,MAX(IF(rInc,IF(rDat=L5,rCol))))
Array Enter
Regards
@Michael,
unfortunately, your array formula still seems to return wrong results (eg 3-Nov).
If data are organized like in the example, ie. looks like a calendar, the INDEX formula seems quite simple:
=INDEX($B$4:$H$15,ROUNDDOWN((L5-B4)/7,0)*2+2,MOD((L5-B4),7)+1)
Yours is effectively the same as what I just came up with, and I believe this is the optimal answer to this particular problem.
My solution, before I saw yours:
=OFFSET(B5,QUOTIENT(L5-B4,7)*2,MOD(L5-B4,7))
OFFSET will work for an arbitrary list size, but INDEX might be easier to read.
QUOTIENT does the round and division in a single step.
If there's an improvement over Elias's solution then I for one can't see it.
Perhaps a non-CSE version which would also mean that only two references (B4:H14 and B5:H15), as opposed to three (B4, B4:B14 and and B5:H15), would require manually amending should the data range change, i.e.:
=SUMPRODUCT((ISEVEN(ROW(B4:H14)-MIN(ROW(B4:H14)))*(B4:H14=L5)*B5:H15))
I suppose we could make it a single, uniform range reference:
=SUMPRODUCT((ISEVEN(ROW(B4:H14)-MIN(ROW(B4:H14)))*(B4:H14=L5)*OFFSET(B4:H14,1,,,)))
which might be more appropriate should we e.g. wish to use a Defined Name for our range, i.e.:
=SUMPRODUCT((ISEVEN(ROW(Rng)-MIN(ROW(Rng)))*(Rng=L5)*OFFSET(Rng,1,,,)))
though whether that compensates for the extra, volatile function call is something to be debated.
Regards
I have tried something and then my Excel workbooks got shut down. Maybe that was too much?
Anyway here is what I've tried:
=SUMPRODUCT(INDEX(B5:H15;IF(ISEVEN(ROW(B5:H15));ROW(B5:B15)-ROW(B5)+1);{1\2\3\4\5\6\7}))
Guess that was wrong? Would this approach work anyway?
Looking forward to learn something from you Excel Experts.
Sorry, I haven't took notice of XOR LX's answer. I guess that's kind of what I was looking for.
@Michael Avidan
As it stands that is not a very rigorous construction.
You say "I, myself, always try to provide a global Formula that is capable to handle all sorts of data", which is a wonderful philosophy, but isn't it at least as important that we ensure that our formulas are independent of the row and column references of the data range in question, so that, should that range change, we do not have to re-work our solution?
What happens with your formula, for example, if RNG is instead re-located one row down, from B4:H15 to B5:H16?
When a formula is reliant upon the addition/subtraction of certain constants within the formula, which themselves are necessarily dependent upon the specific rows/columns in which the data lies at any given time (e.g. the -1 in MOD(ROW(RNG)-1,2)), then that formula is not a very flexible one.
Hence the reason for my choice of a slightly longer construction:
ROW(B4:H14)-MIN(ROW(B4:H14))
which ensures that this part of the calculation is not dependent upon the precise location of the data range within the worksheet, and so will give correct answers even if that range is re-located.
Regards
{=OFFSET(B4,MAX((B4:H15=L5)*ISODD(ROW(1:12))*ROW(1:12)),MAX((B4:H15=L5)*ISODD(ROW(1:12))*COLUMN(A:G))-1)}
Non-array formula:
=INDEX(B4:H15,SUMPRODUCT((B4:H15=L5)*(ROW(B4:H15)-ROW(B4)+1)*ISODD(ROW(B4:H15)-ROW(B4)+1))+1,SUMPRODUCT((B4:H15=L5)*(COLUMN(B4:H15)-COLUMN(B4)+1)*ISODD(ROW(B4:H15)-ROW(B4)+1)))
Using one range (B4:H15), one reference (B4), one lookup value (L5) and no INDIRECT or OFFSET.
My trial with defined names:
DateRange
=$B$4:$H$4,$B$6:$H$6,$B$8:$H$8,$B$10:$H$10,$B$12:$H$12,$B$14:$H$14
Position
=RANK('lookup problem'!$L$5,DateRange,1)
L6
=OFFSET(B4,ROUNDUP(Position/7,0)*2- 1,IF(MOD(Position,7)=0,6,MOD(Position,7)-1))
I'd probably just run with something like:
=SUMPRODUCT((B4:H14=L5)*(MOD(ROW(B4:H14),2)=MOD(ROW(B4),2))*B5:H15)
...which is basically the same as Elias' but without the IFs
The opposite of elegant but it works...
=INDEX(B4:H15,IFERROR(MATCH(L5,B4:B14,0),0)+IFERROR(MATCH(L5,C4:C14,0),0)+IFERROR(MATCH(L5,D4:D14,0),0)+IFERROR(MATCH(L5,E4:E14,0),0)+IFERROR(MATCH(L5,F4:F14,0),0)+IFERROR(MATCH(L5,G4:G14,0),0)+IFERROR(MATCH(L5,H4:H14,0),0)+1,IFERROR(MATCH(L5,B4:H4,0),0)+IFERROR(MATCH(L5,B6:H6,0),0)+IFERROR(MATCH(L5,B8:H8,0),0)+IFERROR(MATCH(L5,B10:H10,0),0)+IFERROR(MATCH(L5,B12:H12,0),0)+IFERROR(MATCH(L5,B14:H14,0),0))
=INDEX(B4:H15,
IFERROR(MATCH(L5,B4:B14,0),0)+
IFERROR(MATCH(L5,C4:C14,0),0)+
IFERROR(MATCH(L5,D4:D14,0),0)+
IFERROR(MATCH(L5,E4:E14,0),0)+
IFERROR(MATCH(L5,F4:F14,0),0)+
IFERROR(MATCH(L5,G4:G14,0),0)+
IFERROR(MATCH(L5,H4:H14,0),0)+1,
IFERROR(MATCH(L5,B4:H4,0),0)+
IFERROR(MATCH(L5,B6:H6,0),0)+
IFERROR(MATCH(L5,B8:H8,0),0)+
IFERROR(MATCH(L5,B10:H10,0),0)+
IFERROR(MATCH(L5,B12:H12,0),0)+
IFERROR(MATCH(L5,B14:H14,0),0))
Named Range
rownum = SUMPRODUCT(('lookup problem'!$B$4:$H$14='lookup problem'!$L$5)*ROW('lookup problem'!$B$4:$H$14)*ISEVEN(ROW('lookup problem'!$B$4:$H$14)))
Formula
=OFFSET($A$1,rownum,MATCH(L5,INDIRECT("$B"&rownum&":$H"&rownum),0))
How about SUM(IF(B4:H14=L5,B5:H15)) with array..it should work
Sorry, Chandoo, you can't find stuff this way in every possible scenario.
What if 2014-10-01 sales would equal 41.927 ? Which is serial number for 2014-10-15 ? SUMIF would fail to retrive correct answer. And your example data suggest that such number is possible in your table.
It's better not to search through dates and numbers at the same time.
If I'd solve a problem like this, it'd reformat table first so I get one column with dates and the other with numbers.
In this case, formula to form date column would be:
=INDIRECT(ADDRESS((INT((ROW()-4)/COUNT($B$4:$H$4))+1)*2+2;MOD(ROW()-4;COUNT($B$4:$H$4))+2;4;1))
and numbers would be the same formula with sight adjustment (+3 instead of +2 at the end of first argument):
=INDIRECT(ADDRESS((INT((ROW()-4)/COUNT($B$4:$H$4))+1)*2+3;MOD(ROW()-4;COUNT($B$4:$H$4))+2;4;1))
And now you got two columns that you can safely use for searching!
Oops, sorry, you actually mentioned that it doesn't work if number=date! I missed that part 🙁
={OFFSET(A1,SUM((B4:H14=L5)*ROW((B4:H14))),SUM((B4:H14=L5)*COLUMN((B4:H14)))-1)}
Works for all data... the solution I got for indirect looks little lengthy
I want to count last 20 records of a person, whose marks is greater than 2 and grade "manager". ....
Assume A1 has got names (James, John...etc...)
A2 "Manager"
A3 "2"
Someone please reply
I want to count last 20 records of a person, whose marks is greater than "2" and grade "Manager"
Assume A1 "geroge" A2 "Michael" A3 "George" etc...name can found anywhere in the rows
B1 "Manager" B2" clerk"
C1 "2" C2, "4"
please reply
Simplest I can come up with. No limitations for either 1 or 2. This does assume dates are an ordered list with 7 per row, and 2 rows per set. Assuming this is always true this will work for an arbitrary long list of dates.
=OFFSET(B5,QUOTIENT($L$5-$B$4,7)*2,MOD($L$5-$B$4,7))
@Marc,
Nice approach - however, as there are no "Negative Dates" - try:
=OFFSET(B5,INT(L5-B4)/7)*2,MOD(L5-B4,7))
——————————————————————————-
Michael (Micky) Avidan
“Microsoft® Answer” – Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2015)
ISRAEL
=OFFSET(B4,ROUNDUP((L5-41911+1)/7,0)*2-1,MOD(L5-41911,7))
B4 has been used as reference cell for OFFSET().
FOR ROWS:
ROUNDUP(....,0) gives the integer value of a division. In case of presence of a remainder, ROUNDUP will add 1 to the Quotient.
As opposed to ROUNDUP(), the INT() or QUOTIENT() functions eliminate the remainder.
41911 = 01-Sept-2014, the first date in the data.
*2 has been used because there are 2 columns per set of data.
/7 has been used because there are 7 columns per set of data.
For columns
MOD(L5-41911,7))
Vijaykumar Shetye,
Panaji, Goa, India
This is how i did it
{=INDEX(B4:H15, MAX((L5=B4:H15)*ROW(B4:H15))-2, MAX((L5=B4:H15)*COLUMN(B4:H15))-1 )}
Here's my solution:
=INDEX(B4:H15,MATCH(1,MMULT(--(B4:H15=L5),TRANSPOSE(COLUMN(B4:H15)^0)),0)+1,MATCH(1,MMULT(TRANSPOSE(--(B4:H15=L5)),ROW(B4:H15)^0),0))
Sorry, forgot to mention Ctrl Shift Enter is needed.