# can someone explain this code?

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Marina Evans
on 26 Jul 2018

Commented: Marina Evans
on 27 Jul 2018

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Jason Whitfield
on 26 Jul 2018

The basic idea of the code is that you optimize the parameters of the ODE so that it matches your experimental data as closely as possible. To do this, the optimizer needs some sort of cost function to evaluate how close the parameters are to their true values. So, the cost function should take in test parameters and return a value correlating to their distance from their true values.

Here is the cost function in the given code.

function COST = COST(x,T,ytrue)

y0 = x(1);

A = x(2);

B = x(3);

% The cost function calls the ODE solver.

[tout,yout] = ode45(@dydt,T,y0,[],A,B);

COST = sum((yout - ytrue).^2);

In this case, the cost function first evaluates the ODE with the given test parameters. Then, it finds the sum of squared differences between the output of the ODE and the experimental data. As these data sets become more similar, the differences will become smaller, and the overall cost will be lower.

Now that we have a cost function, we can simply call the optimizer with the function and some arbitrary initial conditions.

x0 = [0.4 3.9 1.2]; % Just some Initial Condition

ub = [5 5 5]; % Upper bounds

lb = [0 0 0]; % Lower bounds

F = @(x) COST(x,T,ytrue);

xout = fmincon(F,x0,[],[],[],[],lb,ub); %<-- FMINCON is the optimizer

The optimizer will use the cost function to find the parameters that create an ODE closest to your experimental data.

The rest of the code in the example is for defining the ODE and experimental data, or for plotting the results. Let me know if you have more questions.

##### 3 Comments

Jason Whitfield
on 27 Jul 2018

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