Can ode45 handle vector of undetermined coefficients

Hi

I have a system of ODEs and I want to optimise its coefficients with fminsearch. However, "Not enough input argument" is shown when I used ODE45. I have optimised another single ODE's coefficient in the past and it succeed. So I would like to know can ODE45 handle more than one undetermined coefficients? Thank you!

Answer 1

[Torsten]

The call to ODE45 must read

[T,X] = ode45(@(t,x)Est_Opt_VanillininVitro(t,x,k), time, [0.001 0 0 0.1 0.1]);

and the call

[T,Y]= ode45(@Opt_VanillininVitro , time, [0.001 0 0 0.1 0.1]);

can be deleted.

Then you must determine f (usually by building the sum of squared differences between Y and measurement data taken at the times specified in the "time" vector).

Best wishes

Torsten.

[King]

Thank you very much Torsten

However [T,X] cannot be computed due to "not enough input arguments". I wasn't too clear about the objective. The main goal is fitting X to Y? Such that the k coefficients in dxdt are similar to dydt.

Answer 2

[Torsten]

Since fminsearch suggests coefficients each time before ODE45 is called, there are no undetermined coefficients within ODE45.

We will have to see your code to find your programming error.

Best wishes

Torsten.

[King]

I believe the problem starts from ode45 before fminsearch, I wrote the code in several page

First defining the ODEs

function dxdt = Est_Opt_VanillininVitro(t,x,k); 

dxdt = zeros(5,1);
dxdt(1) = -x(1) * (k(1) * x(4))./(k(2) + x(1));
dxdt(2) = x(1) * (k(1) * x(4))./(k(2) + x(1)) - (k(3) * x(2)*x(5))./(k(4) + x(2));
dxdt(3) = (k(3) * x(2)*x(5))./(k(4) + x(2));
dxdt(4) = 0;
dxdt(5) = 0;

Then I have the objective function

function f = Opt_Obj_VanillininVitro(k);

    time = linspace(0, 0.03);

    [T,X] = ode45(@Est_Opt_VanillininVitro, time, [0.001 0 0 0.1 0.1]);

    [T,Y]= ode45(@Opt_VanillininVitro , time, [0.001 0 0 0.1 0.1]);

[T,Y] is solved with defined k values in the same ODEs

Finally optimise k values with fminsearch,

k = fminsearch('Opt_Obj_VanillininVitro',[0 0 0 0])
  disp(['fminsearch: k = ' num2str(k)]);

I also believe there's a much better way to do this, any suggestion? ^^

Answer 3

[Torsten]

Try

[T,X] = ode45(@(t,x)Est_Opt_VanillininVitro(t,x,k), time, [0.001; 0; 0; 0.1; 0.1]);

Best wishes

Torsten.

[King]

Okay, I tried and it is still the same. I think is because k values are still unknown in X. However, if I just run the fminsearch, it shows "subscripted assignment dimension mismatch."

I'm very appreciated for your help.

Best King