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 Sum in fit function

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T O P I C    R E V I E W
Leviasa Posted - 03/29/2017 : 08:04:17 AM
Operating System: OriginPro 2016 (64bit)

Hi,
I'm triying to build a fit function with Origin which includes a summation equation like:
F(x)=∑(i=1 to i=n) (G_i*x^2*(L_i)^2)/(1+x^2*(L_i)^2)

I can't build up this function as a fit function (because of the G_i and L_i). Any basic help in the right direction would be appreciated.

Thank you very much for helping me
3   L A T E S T    R E P L I E S    (Newest First)
Hideo Fujii Posted - 03/30/2017 : 1:54:54 PM
Hi Leviasa,

I'm not aware of such method, but for me, it seems not a typical regression because:

1) The number of parameters varies depending on a parameter value.
2) You might be possible to choose "n" as large as you like since some parameter can asymptotically
approach toward 0. Then, the number of parameters may go infinitely.

If you have some reasonable constraint e.g., n<=3 , you can write the function as:
y=(G1*x^2*L1^2)/(1+x^2*L1^2)+(G2*x^2*L2^2)/(1+x^2*L2^2)+(G3*x^2*L3^2)/(1+x^2*L3^2);

But, it still appears for my eyes quite overparameterized (with 6 parameters already).

Maybe some specialist of numerical analysis around can suggest something?

Sorry for not to be helpful much.

--Hideo Fujii
OriginLab
Leviasa Posted - 03/30/2017 : 10:34:45 AM
Not really, but thank you.
The problem is I want the value of "n" and every variable (G_1, G_2, ... and L_1, L_2, ...)

Here you can see my equation aqain:
Hideo Fujii Posted - 03/29/2017 : 6:05:55 PM
Hi Leviasa,

I have tried to define a simple function which contains a summation:

y = ∑{ii=1 to x}(A*ii)

with the following function (Function Type = Origin C) :
double tmp=0;
int ii;
for(ii=1; ii<x; ii++) {
  tmp=tmp+A*(x+ii);
}
y=tmp;

This worked as follows:


Does this help?

--Hideo Fujii
OriginLab

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