How do you initialize a nested function?

Hello everyone,

I'm trying to find the derivative of qi with respect to time and I'm not sure how to initialise qi. The ode function is nested within a parent function (and the parent function is initialised in a separate .m file). Is there a format for initializing nested odes?

A copy of the nested function is shown below:

%Code

 function dqidt= LDF1(~,qi) 
      %This function computes the derivative of qi wrt time
            TestProcess_Parameters; 
            qistar = qsat* bi*P_opt^vi/(1+ bi*P_opt*vi); %Calculate Equilibrium molar loading
            k =(15*Dm)/Rc^2; %Mass transfer coefficient for spherical adsorbent pellets
            dqidt = k*(qistar - qi);            
          end

[Jan]

What do you mean by "initialize"? What exactly does "the parent function is initialized in a separate .m file" mean?

[Moyin]

Hi Jan,

Usually for odes, it is my understanding that you give the input parameter an initial value before running the ode solver, something like this:

[t,y] = ode15s(odefun,tspan,y0,options) where y0 is the initial value.

The code I wrote above is nested within another function-what i'm referring to as the parent function. I have copied the relevant section here for reference; my "parent function" is the function called derivatives. The problem is i get an error of 'not enough input parameters' for the dqidt function and i think it is because qi does not have an initial value. I'm not sure how to give it an initial value if it is nested within another function. Hope that clarifies things a bit more.

%Code

function [derivatives] = Testbreakthrough (~, State_Parameters)  

TestProcess_Parameters;

Pi= State_Parameters (1:N); 

qi = State_Parameters (N+1:2*N); 

%Calling the functions

dqidt = LDF(qi);

dPdt= TP(Pi);

dPidt= PP(Pi);

derivatives = [dPidt; dqidt];  

%Calculate derivatives 

          function dqidt= LDF(~,qi) 

            %This function computes the derivative of qi wrt time
              TestProcess_Parameters;

              qistar = qsat* bi*P_opt^vi/(1+ bi*P_opt*vi); 

              k =(15*Dm)/Rc^2; 

              dqidt = k*(qistar - qi);
          end
  end

[Walter Roberson]

You are calling LDF with one parameter, but you are defining LDF with two parameters in which you are ignoring the first. Since you have exclusive control over LDF, it would not seem to make sense to define it as taking two parameters.

[Moyin]

Okay, thank you Walter

Answer 1

[Jan]

 Usually for odes, it is my understanding that you give the input parameter
 an initial value before running the ode solver, something like this:

 [t,y] = ode15s(odefun,tspan,y0,options) where y0 is the initial value.

This is almost or partially correct. You do not "give" the function to be integrated an initial value. The initial value is delivered to the integrator, which use it as start point of the trajectory. But you do not "initialized" the function to be integrated.

 i get an error of 'not enough input parameters' for the dqidt function and 
 i think it is because qi does not have an initial value.

Please post the error message instead of a short rephrasing. It contains important information.

No, you do not have to "initialize" the function LDF. As Walter has said already, it is defined with 2 inputs (while the first one is ignored):

function dqidt= LDF(~, qi)

but you callit with 1 input only:

dqidt = LDF(qi);

You need:

dqidt = LDF([], qi);

Or anything else as first input - this does not matter, because it is ignored.

The function LDF computes the derivative of the function. This might depend on the time and the current value, and you provide the current value as qi already, but only at the wrong position in the list of inputs.

[Moyin]

Thank you! It got rid of the error