How can I run efficiently a function that changes values in an other function

Hello everybody,

I am solving an ode with ode45. Here is the equation: xddot + b*xdot + k*x = 9.81. I need to solve it for several values of the pair (k,b) (say more than 10000 pairs)

I wrote this matlab function to be used in the ode45 call:

      function Ydot = func(t,Y)
      k=2;
      b=5;
      Ydot=zeros(2,1);
      Ydot(1)=Y(2);
      Ydot(2)=9.81-b*Y(2)-k*Y(1);

For instance if I call "T=0:1e-3:.5; [t,Y]= ode45('func',T,[0 1]);", it will give in Y, solution (x and xdot) for the equation with (k,b) = (2,5).

(I know that analytic solution can be readily found for this differential equation but this has been just used to illustrate my issue, my real problem is more complex.)

I have a another function that can change the values of k and b to the one provided as arguments. The call of this function is:

NewValuesfunc('func.m',valueOFk,valueOFb);

This function has been tested and it works perfectly. Now I wrote another function, whose inputs are k and b. The function first runs NewValuesfunc to change the values in func.m, second run ode45 with (the new) func.m. The output is only x (not x and xdot). Here is that function:

 function y = ComputedResult(x)
 T=0:1e-3:.5;
 NewValuesfunc('func.m',x(1),x(2)); % change the values first...
 [t,Y]= ode45('func',T,[0 1]); %... then find the solution for the new values
 y = Y(:,1); % only take x

Now I am testing ComputedResult in a for loop. Initially the values in the func.m file are k=2 and b=5. I save the solution from this pair in xExact (time is always the same: T=0:1e-3:.5). Then I have a set of 4 pairs (k,b) saved in a 2x4 matrix. For each pair ComptedResult is called, which yields the solution (saved in y), this solution is plotted along with the solution from (k,b)=(2,5) (the legend is so that, at each iteration, values of k, b and i are displayed). It turned out that, all the 4 solutions returned by ComputedResult are exactly the solution from (k,b)=(2,5) (initial values), despite the fact that the values in the func.m file has been changed.

Here is the code I used for the test:

T=0:1e-3:.5;
[t,Y]= ode45('func',T,[0 1]); % values are k = 2 and b = 5
xExact=Y(:,1);

kb = [2.5 7.8 8 9;...
    .1  2.5 6 4.5]; % a set of 4 pairs of kb, ks in the 1st line and bs in the 2nd

for i=1:4
    y = ComputedResult(kb(:,i)); 
    % ComputedResult changes the values of k and b (using kb) in the func.m file first 
    % and runs ode45 with 'func' to find the corresponding solution of the differential equation
    plot(T,xExact,T,y), legend('k=2N/m and b=5N.s/m',sprintf('k =%gN/m and b=%gN.s/m    
    (i=%d)',kb(1,i),kb(2,i),i)), pause(2);
end
% this should display the curve solution for (k,b)=(2,5) and 4 others different curves (with 2 seconds (pause(2)) of interval between each)

My question is why? Can you tell me please, where the problem is coming from: despite the values in the func.m file has been changing, the computed solution of the differential equation is the same as for the initial pair (k,b)=(2,5).

Thank you in advance for your help.

Answer 1

[Walter Roberson]

Don't do things this way. Parameterize the call for the ode function. http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Answer 2

[comlich]

Thank you very much Walter. I just did what is explained on the page you sent me and everything worked very good. Thank you so much!!

However I am still curious about why the way I first did it is not working. So if there is anyone out there who see the reason for that, it will be my pleasure to know it. Thanks

Answer 3

[comlich]

By the way, here is my new ComputedResult function (for those who may be interested):

function y = ComputedResult(x)

T=0:1e-3:.5;

[t,Y]= ode45(@func,T,[0 1]);

function Ydot = func(t,Y)
k=x(1);
b=x(2);
Ydot=zeros(2,1);
Ydot(1)=Y(2);
Ydot(2)=1*9.81-b*Y(2)-k*Y(1);
end

y = Y(:,1);
end