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 nonlinear fitting to implict functions

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T O P I C    R E V I E W
arportis Posted - 10/16/1998 : 6:09:00 PM
Can Origin be used to fit the following type of function:

y = Ymax - K * (y/x) ??

In this case, new varibles can be defined ( y and y/x ) that linearize the function and allow Ymax and K to be easily determined. But, I want to fit a slightly more complicated case of this general form in which this may not be possible.

Thanks for any help!
5   L A T E S T    R E P L I E S    (Newest First)
Hideo Fujii Posted - 10/28/1998 : 7:56:00 PM
Dear Arportis,
I found that your formula can be rewritten to a general form:
ay^2+bf(x)y+c=0
Therefore, you can solve this equation on y easily so that you can get a form y=... with f(x) at the rigt side. (Here, f(x) will be -Ymax(E+K+x) in your case.) Of course, there are two solutions which satisfy the above relationship. Choose one form, then you can use Origin's fitter as usual.

--Hideo
rtoomey Posted - 10/26/1998 : 5:07:00 PM
I agree with the information provided in both of Hideo's responses to your question. However, just to make sure this is clear, straight fitting to implicit functions is not supported by Origin. One has to be able to express the fitting function in the form y=F(x) (or similarly, x=F(y)) in order for Origin to successfully perform a fit.

Sincerely,
Ryan Toomey
Hideo Fujii Posted - 10/21/1998 : 2:31:00 PM
Although maybe not the best way, your formula can be modified as a form of:
x=F(y) .
In other word, you can reinterprete x as a dependent variable, and y as an
independent variable. So, you can use the non-linear function fitting in
Origin. Obviously this method changes the interpretation of "best" fitting
by optimizing Sigma(X_bar - Xi)^2 minimum instead of for Sigma(Y_bar - Yi)^2, however practically it might give you a satisfiable solution.

I would be happy if I could hear any comment about this matter...

[This message has been edited by Hideo Fujii (edited 10-21-98).]

[This message has been edited by Hideo Fujii (edited 10-21-98).]
arportis Posted - 10/19/1998 : 12:35:00 PM
You are certainly correct, but I should have given the exact form of the equation I need to "fit".

What does one do with:

y = Ymax - K * (y /(x - (y*E/Ymax)),

Ymax, K and E are "constants" for which I need the best values.

I can't find a way to express this in the form of y = Func(x), with no y's on the right side.
Hideo Fujii Posted - 10/19/1998 : 7:45:00 PM
If I didn't misunderstand your question, your formula may be modified to:
y=Ymax*x/(K+x) .
You can find the same form as the Hyperbl built-in function:
y=P1*x/(P2+x)
in Origin Basic Function category so that you can use Origin's Non-Linear Least Square Fitter for your purpose.

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