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Fitting multiple datasets to "partially" the same model (global fit with

From: JokerOne
Subject: Fitting multiple datasets to "partially" the same model (global fit with shared parameters)
Date: Mon, 7 Dec 2015 06:32:56 -0800 (PST)

Hello everybody,

I am looking for an Octave solution for a task I manage to perform in
Origin, i.e. it appears possible from the mathematical point of view.
However, I have no idea, how to solve it in Octave, which I desire:

I like to fit a model curve to a number of datasets, say

data1 = [x,y1]
data2 = [x y2]
the number of datasets is in the order of 10 (i.e. not many more).

The model to that data is something like:

F(x) = f(x) * g(x), where

f(x) depens on some fitting parameters, say a0, a1, a2,...
and g(x) depends on b0, b1,...

Now I would like to fit all data with the same model simultaneously making
use of my knowledge, that the parameters of g(x) (i.e. b0, b1,...) are equal
for all the datasets.

For example, my model function is:
F(x) =  ( a0*ln(x) )* (b0+b1*x) 
with b0, b1 equal for all datasets.

In Origin, such a situation is called "global fit" with "shared parameters"
or similiar.

Is there any similiar already implemented in Octave, yet?

Any help is appreciated. 

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