matlab taking too much time

Im doing a ray tracing in matlab with this code. It is taking more 6+ hours to complete. Can anyone help

for j=1:sm
    for i=1:lns2
        m=-1;
        P0=SM(j,:);
        P1=LNS2(i,:);
        OBJ=(P1-F1)/norm(P1-F1);
        ILL=(P1-P0)/norm(P1-P0);
        OUT=m*(OBJ-Rray1)+ILL;
        t=sym('t');
        RAY=P1+t*OUT;
        EQN=RAY(1)==D2;
        t0=solve(EQN,t);
        P2=subs(RAY,t,t0);
        a1=find(P2(2)<=Y2max);
        a2=find(P2(2)>=Y2min);
        a3=find(P2(3)<=Z2max);
        a4=find(P2(3)>=Z2min);
        if a1*a2*a3*a4==1
            OBJ=(F2-P2)/norm(F2-P2);
            ILL=(P2-P1)/norm(P2-P1);
            OUT=m*(OBJ-Rray2)+ILL;
            RAY=P2+t*OUT;
            EQN=RAY(1)==D3;
            t0=solve(EQN,t);
            P3=subs(RAY,t,t0);
            a1=find(P3(2)<=Ymax);
            a2=find(P3(2)>=Ymin);
            a3=find(P3(3)<=Zmax);
            a4=find(P3(3)>=Zmin);
            if a1*a2*a3*a4==1
                y=norm(P1-P0)+norm(P2-P1)+norm(P3-P2);
                y=sin(y*2*pi);
                P3=(round(P3*M))/M;
                IY=1+M*(Ymax-P3(2));
                IZ=1+M*(Zmax-P3(3));
                IMGMTRX(IY,IZ)=IMGMTRX(IY,IZ)+y;
            end
        end
    end
end

[Stephen23]

@Gaurav Goyal: I formatted your code properly for you. Doesn't it look much nicer! And it so much easier to read too! Next time you can do it yourself by clicking the {} Code button.

[Gaurav Goyal]

Thank You. First time asking question...dont know the formatting style...

Answer 1

[John D'Errico]

Why not learn to use the profile tool? That will tell you where the bottlenecks lie, where you need to work to improve your code.

If I had to guess though, your first obvious problem is in the solve. You are using a symbolic tool to solve a problem (REPEATEDLY!) that is surely solvable using other tools. Or, do the symbolic solve up front, ONCE. That will hopefully give you a simple formula you can then use. At worst, consider a numerical solver.

Symbolic tools tend to be slow. I'm sure there are other problems, but that is the glaring one.

But do you really need the accuracy of a symbolic solve anyway? At the end, it appears you are rounding your results to turn into pixels. Symbolic is wild overkill here.

[Gaurav Goyal]

Thanks! i will try that. Any other issues you notice? Also i forgot to mention that I'm just beginning to use MATLAB. I once ran profiler on this code....and it just wouldn't complete. Is that normal?

[John D'Errico]

The profile tool will slow things down some, making it run longer yet. This makes sense since you are requesting MATLAB to do extra bookkeeping.

So the trick is to reduce the problem size a bit so the profile tool will get its job done in a reasonable time. It will still identify any serious bottleneck. Once you see where a bottleneck lies, then you look to see if there are ways to improve it. And there are ALWAYS lots of way to improve. I am sure I could take virtually anything I've written over the years and find fragments I could do better, at least marginally. MATLAB is continually evolving, as I hope so am I.