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 Find x in function from table of y values
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Sam__Perry

United Kingdom
1 Posts

Posted - 03/18/2014 :  08:49:47 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
I have the following function that I am using to model some experimental data

y = pi^1/2 * x * exp(x^2) * erfc(x)

I have a column of y values that I determined experimentally, and want to use this model to generate a column of x values to go with each data point. I cannot work out a simple way to do this mathematically due to the combination of exp and erfc functions. Is there a work around?

Many thanks!

Origin Ver. and Service Release (Select Help-->About Origin): 9.1.0
Operating System: Windows 7

Edited by - Sam__Perry on 03/18/2014 08:50:54 AM

Hideo Fujii

USA
1582 Posts

Posted - 03/18/2014 :  4:13:42 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi Sam,

Though this is a bit cumbersome way, you may try it:

1) Using Fitting Function Builder, define your function, say f(x)=experfc(x), with a parameter "p" instead of the constant pi.

2) Make the function plot of your function. ("File: New: Function Plot: 2D Function Plot")

3) Double-click the function plot to show Plot Details, and press "Workbook" button to make the data sheet.

4) Highlight the Y column, and start NLFit ("Analysis: Fitting: Nonlinear Curve Fit").

5) In NLFit, select your function, and in the left panel, select "Find X/Y" tab, and turn ON the "Find X from Y" check box. Click Fit to finish fitting. (Of course, it converges with pi.)

6) You find a new sheet"FitNLFindXfromY1" in the worksheet. Now, you can copy your Y values to the first column in this sheet, and you get the corresponding Xs.

Hope this helps.

--Hideo Fujii
OriginLab
============================================

P.S.

I have noticed after I made a function plot of your function that it is a monotonically increasing function.
Therefore, it is safe to switch the positions and the designations (X and Y) of the first and second columns;
Then you can run "Analysis: Mathematics: Interpolate/Extrapolate Y from X" to get the actual Xs.

Edited by - Hideo Fujii on 03/18/2014 5:19:43 PM
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