Solve large linear systems with Parallel computing toolbox
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Dear all,
I need to solve something of this form
, where
are just 7 distinct doubles and I is the identity matrix. Of course, those linear systems can be solved in parallel, and I want to do that in Matlab with the PCT. The matrix A is A = gallery('poisson',n).
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/332693/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/332690/image.png)
In my cluster, I have a node with 16 CPUs, and I want to use this fact to boost the performance. I wrote the following code to see if the parfor gives an improvement w.r.t the classical for. I started a parallel pool of 7 workers, and when I run it on the cluster I specified to use 7 CPU cores, according to the phylosophy "1 worker per CPU core", but my performance does not get better.
Here's the code with the following output:
clear all
close all
m = 70^2;
A = gallery('poisson',70);
I = speye(m);
v = ones(m,1);
x = zeros(m,7);
theta = [1.1,0.2,5.6,0.2,6,8,9.9];
tic
for i=1:7
x(:,i) = (A - theta(i)*I)\v;
end
toc
parpool(7)
tic
parfor i=1:7
x(:,i) = (A - theta(i)*I)\v;
end
toc
The results are:
Elapsed time is 0.184104 seconds. (with for loop)
Elapsed time is 0.451166 seconds. (with parfor loop)
So my questions are:
- is there something wrong in how I wrote my code to run in parallel? How can I improve my performance? (iterative solvers, or differen methods)
- why the parfor considerably slower than the classical for? I've seen that linear algebra operations are already multithreaded and hence there could be no gain with a parfor
0 Kommentare
Antworten (1)
Dana
am 16 Jul. 2020
Bearbeitet: Dana
am 16 Jul. 2020
First of all, when I run the code you posted, Matlab gives warnings that A-theta(i)*I is singular to working precision for i=2,4. Not sure if that's expected.
Second, I actually do find parfor faster when I run your code (though only barely). Not sure why you're finding otherwise, but it could be something specific to your processor.
7 Kommentare
Bruno Luong
am 16 Jul. 2020
Bearbeitet: Bruno Luong
am 16 Jul. 2020
You should then definitively try look into using one of the iterative solvers such as pcg, cgs, and friends.
In such method you can provide "A" through a function, in your case it's come down to computing
y = (-A*x +theta_i*x)
for any arbitrary given vector x, where A is sparse.
This must speed up, and if furthermore you could provide and cheap approximation of inv(A) for preconditioning, it will speed up even more.
I have no idea about efficiency of par-for since I do not own the parallel computing toolbox.
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