Last week in the Chandoo.org Forums a user asked a question
“How do I convert a Roman Numeral to a Number eg: MMMCCCLVII to 3357”
User Xlstime presented the solution of:
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
Today we are going to look at how and why that simple formula works
As always at Formula Forensics you can follow along using a sample file: Download Sample File
Solution
Excel has a Roman function wherein =Roman(3357, 0) will return MMMCCCLVII
I knew there was no such reverse Roman function prior to Excel 2013 and so my initial thought was to look at a VBA Solution.
See notes on the Arabic Excel function at the end of the post.
However Xlstime presented =MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
How does this work?
lets start by pulling it apart from the inside out
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The Indirect Function simply takes its inputs and converts them to a Range, in this case 1:3999.
We will study why 3999 later
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The next function working out is Row()
Excel will convert the function ROW(INDIRECT(“1:3999”)) to an array of Row Numbers
={1;2;3;4;5;6;7;8;9;10;11; …. 3995;3996;3997;3998;3999}
You can see this if you goto cell D7 in the Sample File, press F2 and then F9
I limited the numbers to 300 as Excel cannot display more than 8,192 digits
Stepping out one more function:
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The Roman() function converts its inputs into Roman Numbers
eg: Roman(58) will return LVIII
But as we are feeding it an array of numbers from 1 to 3999 Excel handles all these and converts them to an Array of Roman Numbers
Goto D9 in the sample file =ROMAN(ROW(INDIRECT(“1:300”))) press F2 and then F9
Excel returns an array of roman numbers
={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “CCXCVI”;”CCXCVII”;”CCXCVIII”;”CCXCIX”;”CCC”}
We have limited the example to 300 as Excel cannot display more than 8,192 characters when processing a Function using F9.
Stepping out one more function
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The Excel Index() function is taking the Array of Roman Numerals and Converting it into a single Column array
This isn’t technically needed but it simplifies the solution
If you goto cell D11 in the sample file =INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0) press F2 and then F9
Excel returns an array of roman numbers
={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “CCXCVI”;”CCXCVII”;”CCXCVIII”;”CCXCIX”;”CCC”}
This is exactly the same as the previous output from the Roman() function above, Except that it is now a Single Vertical Array. This is important for the next function.
Stepping out one more function
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
We can see here that the Array of Roman Numerals is now being fed into a Match() function.
Match uses the Syntax =Match(Lookup value, Lookup Array, Match Type)
Match returns the position of the Lookup value within the array
So in our example
The Lookup value is A2 or our Roman Numeral MMMCCCLVII
The Lookup Array is an array of Roman Numerals from 1 to 3999
={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “MMMCMXCV”; “MMMCMXCVI”; “MMMCMXCVII”; “MMMCMXCVIII”; “MMMCMXCIX”}
and the Match Type is 0 or an exact Match
So the Match function will lookup the value MMMCCCLVII in the array and find it in position number 3357, which happens to correspond to the Number of the Roman Numeral and Return 3357 as the result.
Why are we limited to 3999 numbers.
The Excel Roman() function is limited to numbers up to 3999
Why 3999?
Because in Roman Numerals there is no Letter for 5,000 and 4,000 would be shown as M before the Letter for 5,000.
Why did we need the Index() function?
If you goto D17 in the sample file you will see the formula:
=MATCH(A2,ROMAN(ROW(INDIRECT(“1:3999”))),0)
It is the same formula as above but without the Index() function
You will see that it is returning a #VALUE! error
If you edit the formula with F2 and then press F9 to process the function you will see it now shows 3357
What s happening here?
Pressing F9 is the same as Array Entering the Function
so if you edit the function pressing F2 and now Array Enter the function by pressing Ctrl+Shift+Enter, excel now returns 3357
The Index() function puts a wrapper around the array for processing by the Match() function and so Array Entering is avoided.
Most array formulas that require Ctrl+Shift+Enter can be rewritten incorporating an INDEX wrapper and will not require the Ctrl+Shift+Enter confirmation.
The Excel Arabic Function
In 2013, Microsoft introduced the Arabic function to Excel
To use simply use =Arabic(A2) or =Arabic(“MMMCCCLVII”)
You can read about the Syntax of the function in the Excel Help.
Download
You can download a copy of the above file and follow along, Download Sample File.
A Challenge
Can you solve the problem another way ?
Post your solutions in the comments below.
Other Posts in this Series
The Formula Forensics Series contains a wealth of useful solutions and information specifically about how Normal Formula and specifically Array Formula work.
You can learn more about how to pull Excel Formulas apart in the following posts: http://chandoo.org/wp/formula-forensics-homepage/
If you have a formula and you want to understand how it works contact Hui and it may be featured in future posts.
30 Responses to “Rescue oddly shaped data – Battle between Formulas, VBA and Power Query”
Nice use of Power Query! Power Query is simply awesome! But somehow a lot of people are punishing themselves by not using it (not learning it).
An imperfect 4th approach for consideration... no codes at all...
Select myrange.
Go to Special --> Blank
Delete Cell --> Shift cell left
90% done... now we just need to move the data of 2nd column to the bottom of 1st column
Of course... Power Query is the best.
Cheers,
There is another way but it involves multiple steps:
Copy the values in column E, move the cursor to F5, Paste Special with Skip Blanks, OK
Copy the values in column D, move the cursor to F8, Paste Special with Skip Blanks, OK
And so on.
This works perfectly, albeit a little clumsily apart from the values in B17 and C16, which can be moved with simple copy and paste
Power Query Forever! I do not know how I survived for so long without knowing and using this tool, I can not recommend it to my colleagues, but by the way they prefer to suffer to learn.
My congratulations here from Brazil.
I rolled my eyes when I saw that data
Using decimal places is a nice trick to order data, thanks for that
And tweaking the first formula a bit, you can use OFFSET instead of INDIRECT
=OFFSET($A$1, MIN(IF(myrange, ROW(myrange)), ROWS(A$1:A1))-1, RIGHT(TEXT(MIN(IF(myrange, ROW(myrange) + COLUMN(myrange)*0.00001), ROWS(A$1:A1)), ".00000"), 5)-1)
Tried the above formula with the downloaded oddly shaped data file and I could not get it to work. I get #value without ctrl+shift+enter, and #ref with ctrl+shift+enter.
Sorry, it was SMALL, not MIN.
Add with CTRL+SHIFT+ENTER.
Thank you for your formula. Like the indirect formula I tested this one in older versions of EXCEL and it worked without ALTERATION in EXCEL 95. Very impressive.
Too complicated
Use =Sum to summarize all the sells to the left and Bobs Your Uncle
@Bertie... I am afraid that won't work when you have more than one value in a row.
I tested this formula in versions of Excel all the way back to Excel 95
=IF(ISERROR(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(MyRange"",ROW(MyRange)+COLUMN(MyRange)*0.00001),ROWS(A$1:A9)),"00000.00000"),".","C"),FALSE)),"",(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(MyRange"",ROW(MyRange)+COLUMN(MyRange)*0.00001),ROWS(A$1:A9)),"00000.00000"),".","C"),FALSE)))
So there are multiple ways of cleaning up messy data by formulas.
Wow.. Excel 95. Who knew people still use that. But as you have shown, Excel has all these beautiful and powerful functions for 23 years. It has data sciency stuff before DS was even a thing.
I had a problem with pasting the formula in the original post.
Formula should be: =IF(ISERROR(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(myrange"",ROW(myrange)+COLUMN(myrange)*0.00001),ROWS(A$1:A1)),"00000.00000"),".","C"),FALSE)),"",(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(myrange"",ROW(myrange)+COLUMN(myrange)*0.00001),ROWS(A$1:A1)),"00000.00000"),".","C"),FALSE)))
EXCEL even in a 16 bit version, is a very robust and capable program.
I don't like the VBA code. If you have a blank row in MyRange, the last entry in the range is doubled up in the paste.here range.
Not really. The macro is writing one cell at a time from paste.here. You have to clean the range before, which I was too lazy to write. But a line like Range(range("paste.here"), range("paste.here").end(xldown)).clearcontents should do the trick.
Adding Range(range("paste.here"), range("paste.here").end(xldown)).clearcontents fixed the problem.
for step split column by delimiter i am not getting option of split into rows or columns. Can you help me in this
Thanks Chandoo for promoting Power Query.
To simplify further, you can "Unpivot Columns" instead of right click on the newly created column and split it by comma in to rows in step 3 of Power Query.
i used
=LOOKUP(10000,B5:F5)
and got the answers. I just plagiarized this formula somewhere and use it, maybe you can explain why it works.
Regards
@Johan... I am not sure if the formula works correctly. When I tested it with the sample data in this post, it showed #N/As in two cells. Essentially, it will only give first value in each row. So if a row has multiple values, then subsequent values are missed. LOOKUP() function goes thru a list and finds the first value that is less than or equal to the input - in this case 10000 in B5:F5.
I have the need to convert pdf's to excel on occasion and they often come out a mess like this. I have used:
Cell G2 =COUNT(myrange)
Cell G3 =IFERROR(IF(G2-1<1,"",G2-1),"") copied down to G100
Cell H2 =IFERROR(LARGE(myrange,G2),"") copied down to H100
Waouw...
=IFERROR(INDIRECT("R" & SUBSTITUTE(TEXT(SMALL(IF(myrange "", ROW(myrange) + COLUMN(myrange)*0.00001),
ROWS(A$1:A1)), "00000.00000"), ".", "C"), FALSE), "")
but CTRL Shift Enter with {} before and after 🙂 😀
Here's a way with pivot table
https://www.bookkempt.com/2018/02/aligning-non-contiguous-data.html
This is brilliant. Bookmarked 🙂
Another possibility.
This assumes that you have a row index 'k' to use in the SMALL function and a column index 'h' to identify the columns of 'myRange'.
If you define 'coord' to refer to
=k+h/10 [assuming h<10]
then it will be possible to recover values later based upon location within 'myRange'. The formula 'nb' that identifies non-blanks by coordinates is given by
= SMALL( IF(myRange"", coord), k )
Finally, to unpick the pieces
= INDEX( myRange, INT(nb), 10*MOD(nb, 1) )
Whilst I am here and making trouble the PQ solution is also a tad over-complicated. All that is needed is to unpivot the entire table and remove the Attribute column.
The advanced editor would show
let
Source = Excel.CurrentWorkbook(){[Name="myRange"]}[Content],
#"Unpivoted Columns" = Table.UnpivotOtherColumns(Source, {}, "Attribute", "Value"),
#"Removed Columns" = Table.RemoveColumns(#"Unpivoted Columns",{"Attribute"})
in
#"Removed Columns"
1.fill the blank cells with 0
2.the requested column value=sum of those mess number column
but this can be used in only one column has value
Chandoo
And if we use the formula SEARCH (100000000, B5: F5)
JC
Another approach with Power Query, it will still work if the number of columns changed:
let
Source = Excel.CurrentWorkbook(){[Name="myrange"]}[Content],
#"Added Custom" = Table.AddColumn(Source, "List", each Record.ToList(_)),
#"Removed Other Columns" = Table.SelectColumns(#"Added Custom",{"List"}),
#"Expanded LIst" = Table.ExpandListColumn(#"Removed Other Columns", "List"),
#"Filtered Rows" = Table.SelectRows(#"Expanded LIst", each ([List] null))
in
#"Filtered Rows"
Cool idea to use Record.ToList as added column. Thanks for sharing this.
Nowadays, you can just use TOCOL on Excel 2024, MS 365, and Web Excel. It has a parameter to ignore blanks/errors/both.