How to add a force to Langevin equation with parfor?
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Erez
el 24 de Dic. de 2020
Comentada: Erez
el 30 de Dic. de 2020
The code below iterates over a simple Langevin equation, representing Brownian motion of 10^5 particles .
tic
dt=0.1;
Particles=10^5;
x=zeros(1,Particles);
MaxTime=10000 ;
parfor ii=1:MaxTime
Gaussian=sqrt(pi*dt)*normrnd(0,1,[1,Particles]);
x=x+Gaussian;
end
toc
The problem is that I don't know how to add a force term to the equation, in a way which still allows me to use parfor.
I want to do something like this:
tic
dt=0.1;
Particles=10^5;
x=zeros(1,Particles);
Force=zeros(1,Particles);
MaxTime=10000 ;
parfor ii=1:MaxTime
Gaussian=sqrt(pi*dt)*normrnd(0,1,[1,Particles]);
x=x+Force*dt+Gaussian;
Force=-x ;
end
toc
This gives the following error message: "The parfor cannot run due to the way variable 'x' is used".
With a standard 'for' loop of course this is not a problem.
It seems that, even though I know that Matlab is naturally paralellized, when one uses vector & matrices correctly, still for the Brownian motion
parfor seems to be 4 times faster than the standard 'for' loop.
How to do this WITH the force term?
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Respuesta aceptada
Raunak Gupta
el 30 de Dic. de 2020
Hi Erez,
From the code I think parallelization is not possible in this case because if you see the Force variable is updated in every iteration and x is also dependent on the value of Force that is calculated in previous iteration. So, there is a dependency on the sequence of execution of loop. Also, if x is termed as a reduction variable it has to be initialized within parfor loop, which will not be correct as per the logic in code.
You may refer to the following documentations to get information about parfor loops.
3 comentarios
Raunak Gupta
el 30 de Dic. de 2020
Editada: Raunak Gupta
el 30 de Dic. de 2020
Hi Erez,
I see your point about the first line of code
x = x + Gaussian;
is a straightforward reduction and x is not deemed as a temporary variable. But the second line of code
x = x - x*dt + Gaussian;
will require to declare x within the parfor as x is multiplied with the "dt" and the value of x has to be stored at that particular iteration to accurately calculate the output. Whereas in the first line of code even if the intermediate x is not known the final output will be correct. The parallelization is only successful when there is no dependency between the individual iteration otherwise one worker (parallel node) will have to wait for the output of another worker which eventually can make the code serial.
I tried doing the second line of code but it makes x as temporary variable. In my knowledge I don't think parallelization is possible in such cases because iterations are interdependent and there is a kind of scaling also applied to output of each iteration.
The 4x speed you got from reduction loop is probably because of 4 or 6 cores available in your system.
Hope this clarifies!
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