How to interpolate a vector and work with variables (ode45)?

Hello,

I'm working with a ODE model the one I have to put a vector in a variable and then solve it, but I have some parameters which depends on some of the equations of the model, like auxiliar functions/equations but I haven't been able to make it work, this is the error I get:

Error using Hovorka2004_Prueba>fun
Too many output arguments.

Error in odearguments (line 88)
f0 = feval(ode,t0,y0,args{:});   %
ODE15I sets args{1} to yp0.

Error in ode45 (line 114)
[neq, tspan, ntspan, next, t0,
tfinal, tdir, y0, f0, odeArgs,
odeFcn, ...

Error in Hovorka2004_Prueba (line 8)
[t,x]=ode45(@fun,tspan,x0);

this is what I have so far:

   function [t,x]=Hovorka2004_Prueba
    tspan=[0;100];
    x0 = [0.1249; 0.0941; 0; 0;0; 0.7665;0.9519; 0.8473];
    global out1
    [t,x]=ode45(@fun,tspan,x0);
    out1=[t,x]
     assignin('base','out1',out1);

     figure
        subplot(2,1,1)
        plot(t,x(:,1));
        subplot(2,1,2)
        plot(t,x(:,5));
    end

    function fun(t,x)
    uu1 = importdata('datossinmodi.mat'); 
    ufun = @(t) interp1(1:length(uu1), uu1, t, 'nearest', 0); 

% Begining of the parameters
      % Constants:
        F01= 0.0097; 
    EGP0= 0.0161;
    k12=0.066;
    DG=0;
    AG=0.8;
    tmaxG=40;
    VG= 0.16;
    tmaxI=55;
    Ke=0.138;
    VI=0.12;
    Ka1=0.006;
    Ka2=0.06;
    Ka3=0.03;
    Kb1= 51.2e-4*Ka1; 
    Kb2= 8.2e-4*Ka2;  
    Kb3= 520e-4*Ka3;  

    % Auxiliar Functions/Equations:
     G=x(1)/VG;

    if G>=4.5
        F01_C=F01;
    else
        F01_C=F01*G/4.5;
    end

    if G>=9
        FR=0.003*(G-9)*VG;
    else
        FR=0;
    end

     UI=x(4)/tmaxI;

     UG=(DG*AG*t*exp(-t/tmaxG))/(tmaxG)^2;

% Model:
  f = @(t,x) [   
          -((F01_C/VG*G)*x(1))+ x(6)*x(1) + k12*x(2) - FR + UG + EGP0*(1-x(8));  %(1)  
          x(6)*x(1)-(k12+x(7))*x(2);             %(2)
          ufun(t)-(x(3)/tmaxI);                  %(3) IN HERE ufun(t) IS WHERE I AM TRYING TO PUT THE VECTOR
          (x(3)/tmaxI)-(x(4)/tmaxI);             %(4)
           UI/VI - Ke*x(5);                      %(5)
          -Ka1*x(6)+ Kb1*x(5);                   %(6)
          -Ka2*x(7)+ Kb2*x(5);                   %(7)
          -Ka3*x(8)+ Kb3*x(5);                   %(8)
          ];
  end

How can I make it work? What's wrong with it?

Thanks a lot for your help (:

Answer 1

[Walter Roberson]

You indicate that fun is your objective function in the ode45 call, but you define

      function fun(t,x)

which indicates that fun does not return any values. fun must return a column vector that is the same length as x. Perhaps you want to return the result of invoking your f on t and x.

[Annie]

Hi, Walter,

I just tried to declare function as:

function [t,x]= fun(t,x)

and as:

function f= fun(t,x)

but it keeps sending me errors:

(for function [t,x]= fun(t,x))

>> Hovorka2004_Prueba
Error in Hovorka2004_Prueba>fun (line 21)
uu1 = importdata('datossinmodi.mat');

Error using feval
Output argument "dxdt" (and maybe
others) not assigned during call to
"C:\Users\AnnieA\Dropbox\Tesis (A.
Olay)\MATLAB Simulations\Lectura de
Vectores\Hovorka2004_Prueba.m>fun".

Error in odearguments (line 88)
f0 = feval(ode,t0,y0,args{:});   %
ODE15I sets args{1} to yp0.

Error in ode45 (line 114)
[neq, tspan, ntspan, next, t0,
tfinal, tdir, y0, f0, odeArgs,
odeFcn, ...

Error in Hovorka2004_Prueba (line 8)
[t,x]=ode45(@fun,tspan,x0);

(for function f= fun(t,x))

>> Hovorka2004_Prueba
Error using odearguments (line 93)
FUN returns a vector of length 1,
but the length of initial conditions
vector is 8. The vector returned by
FUN and the initial conditions
vector must have the same number of
elements.

Error in ode45 (line 114)
[neq, tspan, ntspan, next, t0,
tfinal, tdir, y0, f0, odeArgs,
odeFcn, ...

Error in Hovorka2004_Prueba (line 8)
[t,x]=ode45(@fun,tspan,x0);

Any suggestion? :/

[Walter Roberson]

Your f is a single value, a function handle. Perhaps you want to return the result of invoking your f on t and x.

Or more simply, leave out the @(t,x) and then f will be a numeric array directly instead of a function handle.

[Annie]

If I leave out the @(t,x) it will still interpolate the vector into ufun(t), right?