I was wondering if there is a way to do infinite sums in Excel. I have a sum in the form
= $$\sum_{n=0}^{\infty} f(n)g(n) $$
I was wondering if there is a function to do this in Excel as I dont really want to do a finite sum to a very large number in order to approximate the infinite sum.
Excel isn't a computer algebra system, so it can't do things like sum infinite series symbolically. The following VBA function might help:
Function PartialSum(f As String, var As String, start As Long, finish As Long) As Double
Dim i As Long, sum As Double
Dim term As String
For i = start To finish
term = Replace(f, var, "(" & i & ")")
sum = sum + Evaluate(term)
Next I
PartialSum = sum
End Function
Then, for example, if you put =PartialSum("1/n","n",1,1000) in a worksheet cell it evaluates to 1.643934567. Caution must be taken that you don't use things like sin(n) in the terms since the function just does simple text substitutions and would hence try to evaluate things like "si(1)((1))" in that particular case. The obvious workaround would be to choose as a variable some symbol that does not otherwise occur in the expression.
Related
As suggested by the title, I have run into some trouble trying to implement a variant of the standard deviation function into excel through VBA. I have defined two columns, one being the set of values (Val) under investigation and one being a multiplier column (Multi) that shows how often the value occurs. The idea was that this would save me some time/space as I would not have to repeat the values y number of times. Through the use of the SUMPRODUCT function, I managed to find the mean of the values (taking into account their multipliers). This value is also used as an input (Mn) for the function. What I want now is to also find the standard deviation of my values, again taking into account the multiplier. I have no experience in VBA, so I sort of scrambled together this code, but it is currently not working. Any help would be greatly appreciated!
Function SWSTDEV(Multi As Variant, Val As Variant, Mn As Double)
Dim x As Long
Dim Results
For Each MultiEl In Multi
For Each ValEl In Val
x = x + 1
Results(x) = MultiEl * (ValEl - Mn) ^ 2
Next ValEl
Next MultiEl
SWSTDEV = WorksheetFunction.SQRT(WorksheetFunction.Sum(Results) / WorksheetFunction.Sum(Multi))
End Function
I'm working on a research related to frequencies.
I want to sum all the numbers in each cell and reduce them to single number only.
some cells have 2 numbers, others have 13 numbers. like these..
24.0542653897891
25.4846064424057
27
28.6055035477009
I tried several formulas to do that. the best ones have me 2 digits number, that I couldn't sum it again to get a single result.
like these Formulas:
=SUMPRODUCT(MID(SUBSTITUTE(B5,".",""),ROW(INDIRECT("1:"&LEN(B5)-1)),1)+0)
=SUMPRODUCT(1*MID(C5,ROW(INDIRECT("1:"&LEN(C5))),1))
any suggestion?
Thank you in advance.
EDIT
Based on your explanation your comments, it seems that what you want is what is called the digital root of the all the digits (excluding the decimal point). In other words, repeatedly summing the digits until you get to a single digit.
That can be calculated by a simpler formula than adding up the digits.
=1+(SUBSTITUTE(B5,".","")-1)-(INT((SUBSTITUTE(B5,".","")-1)/9)*9)
For long numbers, we can split the number in half and process each half. eg:
=1+MOD(1+MOD(LEFT(SUBSTITUTE(B5,".",""),INT(LEN(SUBSTITUTE(B5,".",""))/2))-1,9)+1+MOD(RIGHT(SUBSTITUTE(B5,".",""),LEN(SUBSTITUTE(B5,".",""))-INT(LEN(SUBSTITUTE(B5,".",""))/2))-1,9)-1,9)
However, the numbers should be stored as TEXT. When numbers are stored as numbers, what we see may not necessarily be what is stored there, and what the formula (as well as the UDF) will process.
The long formula version will correct all the errors on your worksheet EXCEPT for B104. B104 appears to have the value 5226.9332653096000 but Excel is really storing the value 5226.9333265309688. Because of Excel's precision limitations, this will get processed as 5226.93332653097. Hence there will be a disagreement.
Another method that should work would be to round all of the results in your column B to 15 digits (eg: . Combining that with using the long formula version should result in agreement for all the values you show.
Explanation
if a number is divisible by 9, its digital root will be 9, otherwise, the digital root will be n MOD 9
The general formula would be: =1+Mod(n-1,9)
In your case, since we are dealing with numbers larger than can be calculated using the MOD function, we need to both remove the dot, and also use the equivalent of mod which is n-(int(n/9)*9)
Notes:
this will work best with numbers stored as text. Since Excel may display and/or convert large numbers, or numbers with many decimal places, differently than expected, working with text strings of digits is the most stable method.
this method will not work reliably with numbers > 15 digits.
If you have numbers > 15 digits, then I suggest a VBA User Defined Function:
Option Explicit
Function digitalRoot(num As String) As Long
Dim S As String, Sum As Long, I As Long
S = num
Do While Len(S) > 1
Sum = 0
For I = 1 To Len(S)
Sum = Sum + Val(Mid(S, I, 1))
Next I
S = Trim(Str(Sum))
Loop
digitalRoot = CLng(S)
End Function
You could use a formula like:
=SUMPRODUCT(FILTERXML("<t><s>"&SUBSTITUTE(A1," ","</s><s>")&"</s></t>","//s"))
You might need an extra SUBSTITUTE for changing . to , if that's your decimal delimiter:
=SUMPRODUCT(FILTERXML("<t><s>"&SUBSTITUTE(SUBSTITUTE(A1,".",",")," ","</s><s>")&"</s></t>","//s"))
However, maybe a UDF as others proposed is also a possibility for you. Though, something tells me I might have misinterpreted your question...
I hope you are looking for something like following UDF.
Function SumToOneDigit(myNumber)
Dim temp: temp = 0
CalcLoop:
For i = 1 To Len(myNumber)
If IsNumeric(Mid(myNumber, i, 1)) Then temp = temp + Mid(myNumber, i, 1)
Next
If Len(temp) > 1 Then
myNumber = temp
temp = 0
GoTo CalcLoop
End If
SumToOneDigit = temp
End Function
UDF (User Defined Functions) are codes in VBA (visual basic for applications).
When you can not make calculations with Given Excel functions like ones in your question, you can UDFs in VBA module in Excel. See this link for UDF .. If you dont have developer tab see this link ,, Add a module in VBA in by right clicking on the workbook and paste the above code in that module. Remember, this code remains in this workbook only. So, if you want to use this UDF in some other file your will have to add module in that file and paste the code in there as well. If you are frequently using such an UDF, better to make add-in out of it like this link
In addition to using "Text to Columns" as a one-off conversion, this is relatively easy to do in VBA, by creating a user function that accepts the data as a string, splits it into an array separated by spaces, and then loops the elements to add them up.
Add the following VBA code to a new module:
Function fSumData(strData As String) As Double
On Error GoTo E_Handle
Dim aData() As String
Dim lngLoop1 As Long
aData = Split(strData, " ")
For lngLoop1 = LBound(aData) To UBound(aData)
fSumData = fSumData + CDbl(aData(lngLoop1))
Next lngLoop1
fExit:
On Error Resume Next
Exit Function
E_Handle:
MsgBox Err.Description & vbCrLf & vbCrLf & "fSumData", vbOKOnly + vbCritical, "Error: " & Err.Number
Resume fExit
End Function
Then enter this into a cell in the Excel worksheet:
=fSumData(A1)
Regards,
The UDF below will return the sum of all numbers in a cell passed to it as an argument.
Function SumCell(Cell As Range) As Double
Dim Fun As Double ' function return value
Dim Sp() As String ' helper array
Dim i As Integer ' index to helper array
Sp = Split(Cell.Cells(1).Value)
For i = 0 To UBound(Sp)
Fun = Fun + Val(Sp(i))
Next i
SumCell = Fun
End Function
Install the function in a standard code module, created with a name like Module1. Call it from the worksheet with syntax like =SumCell(A2) where A2 is the cell that contains the numbers to be summed up. Copy down as you would a built-in function.
Weird Math Error in VBA for Excel
Hi all, would love feedback on unsusual error I'm getting.
Very strange. I have a simple formula that works great if I
only use it in a normal sheet cell and copy it down by columns,
but if I try to do a simple iteration in vba code to perform the same function I get the wrong values.
Description : A number is squared, then divided by another value
between 0.99 to 1.99, next the modulus is taken and then
the number is squared again and the whole formula repeated.
If I copy the formula statement down column wise it calcs fine,
including reasonable decimal accuracy.
There are four inputs ;
base value (inputx)
decx = divisor
mod value
The first formula placed at (E2) looks like ; =MOD(((B2^2)/$B$3),$B$4)
In (E3) this statement is placed ; =MOD(((E2^2)/$B$3),$B$4)
Then this exact same statement is copied down, columnwise to the next 98 cells.
All great, no problem. It seems accurate value wise, right to decimal
precision, with values past the decimal point showing in all column cells.
Some sample input values for testing ;
INPUTX --> 231
DECX 1.010101
MOD 400
LOOPTIMES 100
But when I try to implement this is Excel VBA code (Excel 2007)
I often get the wrong values and absolutely no values past the decimal point ever show.
Have tried using all kinds of different data types ; single, double, variant, etc... but all values returned by the VBA function I made always returns
whole numbers, and is often wrong and certainly does not agree with the
values returned by the simple column based statements.
Have tried to find ways around this or to fix this, came across "CDEC", tried
this and nothing changed. Totally stumped and would love some insight into
if this can be fixed so that the function loop returns the same values with
same kind of decimal precision as the column based statements and
would greatly appreciate feedback on how mthis can be done.
Am including my sample code below ;
Public Function SQRD(inputx As Variant, looptime As Variant, decx As Variant) As Variant
Application.Volatile
Dim Count As Integer
SQRD = CDec(inputx)
'Dim decx As variant
Count = 1
For Count = 1 To looptime
SQRD = CDec(SQRD ^ 2) '+ looptime
SQRD = CDec(SQRD Mod 400 / decx)
Next Count
End Function
I will only address your use of the VBA Mod operator. It is NOT equivalent to the Excel MOD function. In particular, the VBA Mod operator will round floating point numbers to integers before performing the operation.
To use a VBA function that mimics the Excel MOD function, use something like:
Function xlMOD(a As Double, b As Double) As Double
xlMOD = a - (b * (a \ b))
End Function
EDIT
There seems to be a bug in VBA (or a documentation error). In the formula above, the \ operator is supposed to be the integer division operator. It does return an integer result. However, it does not truncate, rather it rounds. Actually, what it may be doing, is performing VBA type rounding on the number and divisor, before returning the result.
Therefore, a proper vba function to mimic the Excel MOD function would be:
Function xlMOD(a As Double, b As Double) As Double
xlMOD = a - Int(a / b) * b
End Function
Lots amiss with your code. No need for looping as far as I can see, and you're dividing after the mod not before
This seems to do the trick
Public Function NuFunc(InputX As Variant, DecX As Variant) As Variant
NuFunc = ((InputX ^ 2) / DecX) Mod 400
End Function
I have a column with formula as follows:
=(2+3*6+8) & "KB"
Basically, each cell is a formula and string concatenated (using &). I want to add all these cells up. I tried the following things:
a) =SUM(B2:B21) gives me a sum of 0.
b) Using =B2+B3... gives me a #VALUE error.
c) I tried something like this also - didn't work, gives a sum of 0: =SUM(IF(ISNUMBER(FIND("KB",$C$2:$C$14)),VALUE(LEFT($C$2:$C$14,FIND("KB",$C$2:$C$14)-1)),0))
Make your own SUM function in VBA. Try this:
=StripTextAndSum(A2:A4) - returns 60
=StripTextAndAverage(A2:A4) - returns 20
This method keeps the left most decimal number and tosses away the rest.
NOTE: You can tweak this to fit your needs. One way would be to retain the text so you can return it in the sum....like 150MB (i am assuming KB means kilobyte). Let me know if you like that idea and I'll make it.
EDIT: As pointed out by #DirkReichel, this has been made a little more efficient using IsNumeric instead, but I have retained all the other functions too. IsLetter is a useful function too.
Public Function StripTextAndSum(myRange As Range)
Dim r As Range
Dim n As Double
n = 0
For Each r In myRange.Cells
n = n + ParseNumberFromString(r.Text)
Next r
StripTextAndSum = n
End Function
Public Function StripTextAndAverage(myRange As Range)
Dim n As Double
n = StripTextAndSum(myRange)
StripTextAndAverage = n / (myRange.Cells.Count * 1#)
End Function
Public Function ParseNumberFromString(s As String) As Double
ParseNumberFromString = Left(s, GetLastNumberIndex(s))
End Function
Public Function GetFirstLetterIndex(s As String) As Integer
Dim i As Integer
For i = 1 To Len(s) Step 1
If IsLetter(Mid(s, i, 1)) = True Then
GetFirstLetterIndex = i
Exit Function
End If
Next i
End Function
Public Function GetLastNumberIndex(s As String) As Integer
Dim i As Integer
For i = Len(s) To 1 Step -1
If IsNumeric(Left(s, i)) = True Then
GetLastNumberIndex = i
Exit Function
End If
Next i
End Function
Function IsLetter(s As String) As Boolean
Dim i As Integer
For i = 1 To Len(s)
If LCase(Mid(s, i, 1)) <> UCase(Mid(s, i, 1)) = True Then
IsLetter = True
Else
IsLetter = False
Exit For
End If
Next
End Function
I'd normally just move the KB to the following column and left-justify it.
That way, it still looks identical but the first column only has real numbers that you can manipulate mathematically to your heart's content.
Or, assuming they're all in kilobytes (which seems to be a requirement if you just want to add the numeric bits), don't put KB in the data area at all.
Instead change the heading from, for example, Used memory to Used memory (KB).
Do you really want to populate your beautiful spreadsheets with butt-ugly monstrosities like the following? :-)
=SUM(IF(ISNUMBER(FIND("KB",$C$2:$C$14)),VALUE(LEFT($C$2:$C$14,FIND("KB",$C$2:$C$14)-1)),0))
If you need to keep your column as-is, you could always use an array formula to get the sum:
=sum(value(left(b2:b21,len(b2:b21)-2)))
You will need to enter this as an array formula (press Ctrl+Shift+Enter to submit it)
Basically this is taking the leftmost chunk of a cell (all but the last two characters, which we know are 'KB'), using value() to convert it into a numeric, and sum() to add it up. Entering it as an array formula just lets us do this to each cell in the list b2:b21 in one swoop.
As #paxdiablo mentioned, though, it might be best to restructure so that you don't have to deal with your values as text in the first place. My approach would be to enter the values and add the "KB" via formatting. You can use a custom formatting with something like 0.00 "KB" so the cell only holds, say, the value 17, but it displays as "17.00 KB".
On the Daily Dose of Excel website, written by the late Frank Kabel, there are some formulae which can stand in for ATP functions. Not being an Excel guru, I'm struggling with converting one (so far!) to VB6. (Why I'm doing this I may relate once the NDA runs out.)
The problem I'm having is with the code standing in for SERIESSUM, namely,
=SUMPRODUCT(coefficients,x^(n+m*(ROW(INDIRECT("1:"&ROWS(coefficients)))-1)))
Now the SUMPRODUCT and ROWS functions I've been able to render fairly simply with
Public Function SUMPRODUCT(a1 As Variant, a2 As Variant) As Double
Dim dRes As Double
Dim dVal As Double
Dim i As Long
If LBound(a1) = LBound(a2) And UBound(a1) = UBound(a2) Then
For i = LBound(a1) To UBound(a1)
dVal = a1(i) * a2(i)
dRes = dRes + dVal
Next
End If
SUMPRODUCT = dRes
End Function
Public Function ROWS(a1 As Variant)
ROWS = UBound(a1) - LBound(a1) + 1
End Function
What I don't 'get' yet is
how x^(n+m*(ROW(INDIRECT("1:"&ROWS(coefficients)))-1)) evaluates to an array
and what that array might contain
Any Excel gurus out there?
ROW(INDIRECT("1:"&ROWS(coefficients)))-1
If coefficients has 5 rows, this will return the array {1,2,3,4,5}. The rest of the progression is
{1m, 2m, 3m, 4m, 5m)
{n+1m, n+2m, n+3m, n+4m, n+5m)
{x^n+1m, x^n+2m, x^n+3m, x^n+4m, x^n+5m)
That resulting array gets 'series summed' against coeffecients.
You can see the progression in Excel's formula bar by using Ctrl+= on highlighted parts of the formulas. There is a limit on how many characters you can display in the formula bar, so if coefficients has a lot of rows, you may get the error "formula too long"
In the formula bar, select ROW(INDIRECT("1:"&ROWS(coefficients)))-1 and press Ctrl+=. Then select another portion of your formula, making sure you match opening and closing parentheses, and hit Ctrl+=. You can iterate this until you have the whole formula calculated. When you're done, be sure to ESCAPE out of the cell so you don't lose your original formula.
See also Episode 474 here.