Vectorization of Matlab Code involving ODE solver at each iteration

Question

I want to write a fast MATLAB code where I need to write a for loop and I need to solve an ordinary differential equation each time.Is there any way to vectorize the code? Following is the part of the code:

       tspan=0:0.01:20;
        dw=rand(p,1);
        M0=repmat([0 0 1],p,1)';
        for p=1:ns
       [t,M(:,:,p)]=ode45(@(t,M) testfun(t,M,dw(p)),tspan,M0(:,p));
       end

where

       function  dM=testfun(t,M,w1) 
      M_x=M(1);
      M_y=M(2);
       M_z=M(3);
      dM=[w1*M_y;-w1*M_x+w1*M_z-2*w1*M_y;-w1*M_y-(1-M_z)];

Pompilia · Answer 1 · 2013-03-17T15:19:44.740

0

Try this and let me know how it works.

right hand side of the ODE system:

    function  dM = testfun(t,M,w1)

      dM = zeros(length(M), 1);

      M_x  =  M(1:3:end, 1);
      M_y  =  M(2:3:end, 1);
      M_z  =  M(3:3:end, 1);

     dM(1:3:end)  =              (w1.*M_y)';
     dM(2:3:end)  = (-w1.*M_x - 2*w1.*M_y + w1.*M_z)';
     dM(3:3:end)  =             (-w1.*M_y -  (1-M_z))';
   end

main program:

clear all
clc

ns = input('Please tell me how many time you need to integrate the ODE system: ');

tspan = 0:0.01:20;

dw = rand(ns,1);

M0 = repmat([0; 0; 1], 1, ns);

[t, my_M] = ode45(@(t,my_M) testfun(t,my_M,dw), tspan, M0);

s = size(my_M);

for i = 1:ns
```
    M(:, 1:s(2)/ns, i) = my_M(:, s(2)/ns*(i-1)+1:s(2)/ns*i); 
```
end

edited Mar 17 '13 at 15:19

answered Mar 17 '13 at 14:57

Pompilia

13
3

Thank you a lot...sorry for being late to thank you... but it will help me anyway... – prashanta_himalay Jul 23 '13 at 12:33
The next question arises... is it possible to solve this same system if w1 varies with time step without interpolating w1 in the ODE function?because it is highly time consuming – prashanta_himalay Jul 23 '13 at 15:35

Vectorization of Matlab Code involving ODE solver at each iteration

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