# lsqnonlin multiple dataset optimisation

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Hello;
I would like to optimise simple ode using multiple datasets. I wonder if is possible to do it using lsqnonlin command? Of course, I will want to allow for different values of the initial conditions for each dataset.
I found, that Population-wide parameter estimation can be done in the Simbiology, however, I would rather prefer to use the lsqnonlin.
Thank you in advance

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### 채택된 답변

Alan Weiss 1 Mar 2021
It sounds like you are trying to find a set of ODE parameters that work for multiple data sets. If that is true, then I think that the workflow is this:
• Have lsqnonlin pass in a set of parameters x.
• in your ODE solving function solve each ODE with its own initial conditions for its own set of times.
• Concatenate all of the solutions as F(x) and calculate F(x) - [xdata;ydata;zdata] as the lsqnonlin output (response)
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
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Malgorzata Wieteska 2 Mar 2021
Thank you Alan, That is exactly that what I wanted to know. Thank you very much. Malgosia

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### 추가 답변(2개)

Arthur Goldsipe 27 Feb 2021
You can use lsqnonlin with or without SimBiology. If you want to do this without SimBiology, you need to write a function that takes in the parameters you are trying to estimate, solves your ODEs (for example, using ode45 or ode15s, and returns a vector of residuals (the difference between the simulation results and the measured values). You will also find many similar questions posted on MATLAB Answers, several of which are mentioned in the answer here.
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Malgorzata Wieteska 28 Feb 2021
Hello Arthur, thank you for your reply. However, I want to use lsqnonlin to optimise ode system for multiple experimental dataset, and I wonder if is possible to do it using lsqnonlin. I wonder if I can feed in multiple datasets into lsqnonlin syntax: for instance -
data1 = [ xdata1 xdata2 ];
data2 = [ ydata1 ydata2 ];
data3 = [ zdata1 zdata2 ];
%%call |LSQNONLIN|
lsqnonlin(@ODEfunction,[],[],[],[],xdata,ydata,zdata)?
Malgosia

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