![]() Where the difference is very small : ->fstar = L_Squares ( xstar )Ī straightforward way of finding the parameters a and b is to use the fminsearch function, which does not require the derivative of the objective function. The initial guess of the optimization problem is given: // Computes the sum of squares of the differences. The following L_Squares function defines the cost function of our optimization problem. ![]() Returns the difference between the simulated differential Since the function myModel takes 2 extra parameters as input arguments, we give the list list(myModel,a,b) as the 4th input argument of the ode function. it concatenates the first and second columns of the difference matrix. This function returns a column vector containing the differences of both the first component and the second component of the solution, i.e. The function myDifferences below computes the difference between the simulated ODE, as computed by the ode function, and the experimental data. Then we define the objective function as the sum of squares of these differences. First, we define a function which returns a column vector containing the differences between the simulated ordinary differential equation and the experimental data. The problem is then the unconstrained non linear least squares optimization problem: Minimize L(k) In order to find the parameters a and b, we define a least squares function, which measures the difference between the simulated value of y, as predicted by the ode function, and the experimental data. Given a and b, we can use the ode function and get the value of y at the given times t. ![]() We are searching for the parameters a and b which best fit the experimental data. This will be useful later in this document, when we will compare the algorithms. The number of calls to the function funeval is stored in the data structure. We are given the following experimental data, which indicates the value of y for particular values of the time t. Notice that the function takes the extra parameter a and b as input arguments. The right-hand side of the Ordinary Differential Equation.ĭy(2) = b*y(1) - a*y(2) + 4*t + (a+b)*(1-t^2) The right hand side function f is defined by the following function. In our particular case, the size of the y is equal to 2. Where is the initial state, f is the right hand side of the ODE.
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