MATLAB: A VERY slow Matlab code!

nonlinear odesslow code

A part of my MATLAB code is extremely slow and I would appreciate any help!
Here is the slow function that I have:
function du = odefungPC(u,Dijk,Psi2Norm,Size)
du=zeros(3*Size,1);
for i=1:Size
    for j=1:Size
        for k=1:Size
            du(i)=du(i)+1/Psi2Norm(i)*u(Size+j)*u(2*Size+k)*Dijk{i}(j,k);
            du(Size+i)=du(Size+i)+1/Psi2Norm(i)*u(j)*u(2*Size+k)*Dijk{i}(j,k);
            du(2*Size+i)=du(2*Size+i)-2/Psi2Norm(i)*u(j)*u(Size+k)*Dijk{i}(j,k);
        end
    end
end
end
The dimension of the inputs are as follows:
Size is a scalar equal to 120.
u is of size (3*120) x 1.
Dijk is a cell array of size 120 x 1 and every element of the cell array is a 2D array of size 120 x 120.
Psi2Norm is a vector of size 120 x 1.
This is how I use this function: I want to solve a nonlinear system of ODEs and the above code generates the coefficient matrix that I use later in the following form:
odefun=@(t,u)(odefungPC(u,Dijk,PSI2Norm,Size));
options = odeset('MaxStep',(tn-t0)/(numt));
[T,Ug]=ode45(odefun,tspan,u0,options);
As I said it is a nonlinear system. Therefore, I don't know what u is before solving the system…
Thanks very much in advance!

Best Answer

In the inner two for-loops you have ordinary matrix multiplication. You should make use of it.
 function du = odefungPC(u,Dijk,Psi2Norm,Size)
 du=zeros(3*Size,1);
 for i=1:Size
   du(i) =           (u(Size+1:2*Size).'*Dijk{i}*u(2*Size+1:3*Size)) /Psi2Norm(i);
   du(i+Size) =      (u(1:Size).'       *Dijk{i}*u(2*Size+1:3*Size)) /Psi2Norm(i);
   du(2*Size+i) = -2*(u(1:Size).'       *Dijk{i}*u(Size+1:2*Size)  ) /Psi2Norm(i);
 end
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