Use of parfor to reduce computational time

I have a function with 100000 element array and i want to use parfor loop to reduce computaional time. Here is the code

global allNucleiDrops;

    if (~isempty(allNucleiDrops))
        nMax = length(allNucleiDrops);
        for nCount = 1:1:nMax
            index = allNucleiDrops(nCount);
            nMolecules = Type_3(index);
            if (nMolecules > 1 )
                tspan = [tInitial tFinal]; 
                oldSize = pSize(index);
                oldVol = nMolecules*pP.volumeOfMolecule;
                conc = (nMolecules/c.NA)/dP.volume;
                [t,N] = ode45(@(t,N) 4*pi*pP.diffusivity*c.NA*pP.volumeOfMolecule*conc*((3*oldVol)/(4*pi))^(1/3), tspan, oldVol);
                tLenght = length(N(:,1));
                for tCount = tLenght:-1:1
                    newVol = N(tCount);                    
                    newSize = newVol/pP.volumeOfMolecule;
                    changeMolecule = newSize-oldSize;
                    if (changeMolecule > 0)
                    if (changeMolecule <= nMolecules)
                        pSize(index) = newSize;
                        Type_3(index) = Type_3(index) - changeMolecule;
                        break;
                    end
                    end
                end 
                clear N t;
            end       
        end    
    end

[Walter Roberson]

You will need to copy the global variable into a local variable before the parfor: global variables are not sent to workers.

[Walter Roberson]

The differential equation has a closed form solution that should probably be used instead of ode45.

N(tFinal) = 2*pi^(2/3) * oldVol^(1/3) * conc * 6^(1/3) * (tFinal - tInitial) * ((((pP*diffusivity)*c*NA)*pP) * volumeOfMolecule) + oldVol

[Anil Rajajapantulu]

The differential equation has a closed form solution that should probably be used instead of ode45.

N(tFinal) = 2*pi^(2/3) * oldVol^(1/3) * conc * 6^(1/3) * (tFinal - tInitial) * ((((pP*diffusivity)*c*NA)*pP) * volumeOfMolecule) + oldVol;

At the starting i stated with Euler method which you have suggeted, but can't compromise with the accuracy.

i will make the allNucleiDrops as local, hopefully i will reduce the computation time.

And one more thing is calling values from a constant class increases the computation time sholud i declear these variable as global ?

Thank you so much for your suggestion.

[Anil Rajajapantulu]

I made the allNucleiDrops as local also doesn't slove the problem. As i am using indices inside the for loop 'Type_3(index)'. Can someone help me out.

[Adam]

Have you identified where the computational expense is yet? Run the profiler to get an idea, although bearing in mind this does disable some of the compiler speed-ups that you get when running the code normally, it is still usually very useful to understand where the bottlenecks are.

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[Walter Roberson]

Because you can calculate the ode analytically you can calculate the value you need instead of looping to find it.

[Walter Roberson]

newSize = oldSize at tFinal =

1/12*(2*Pi^(2/3)*oldVol^(1/3)*conc*6^(1/3)*pP^2*diffusivity*c*NA*
volumeOfMolecule*tInitial+oldSize*pP.volumeOfMolecule-oldVol)*6^(2/3)/Pi^(2/3)/
oldVol^(1/3)/conc/pP^2/diffusivity/c/NA/volumeOfMolecule