Parallel implementation for Jacobi algorithm

Sergio Zavota

2019 5 16

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6 次查看（30 天）

1 个投票

Hi everyone

I implemented a parallel version of Jacobi's method for the resolution of a linear system, but doing some tests i noticed that the time to execute the function in parallel is very high compared to the time to execute the sequential function. This is strange because the Jacobi's method should be faster when executed with a parallel implementation.

I think i'm doing something wrong in the code. Please take a look:

function [x,niter,resrel] = Parallel_Jacobi(A,b,TOL,MAXITER)
[n, m] = size(A); 
D = 1./spdiags(A,0);
B = speye(n)-A./spdiags(A,0);
C= D.*b;
x0=sparse(zeros(length(A),1));
spmd
    
    cod_vett=codistributor1d(1,codistributor1d.unsetPartition,[n,1]);
    cod_mat=codistributor1d(1,codistributor1d.unsetPartition,[n,m]);
    
    B= codistributed(B,cod_mat);
    C= codistributed(C,cod_vett);
    x= codistributed(B*x0 + C,cod_vett);
    
    %x = B*x0 + C;
    Niter = 1; 
    TOLX = TOL;  
    while(norm(x-x0,Inf) > norm(x0,Inf)*TOLX && Niter < MAXITER)
        if(TOL*norm(x,Inf) > realmin)
            TOLX = norm(x,Inf)*TOL;
        else
            TOLX = realmin;
        end    
        x0 = x;
        x = B*x0 + C;
        Niter=Niter+1;
    end
end
Niter=Niter{1}; 
x=gather(x);
end

Below there are the tests:

%sequential Jacobi
format long;
A = gallery('poisson',20);
tic;
x= jacobi(A,ones(400,1),1e-6,2000000);
toc;
Elapsed time is 0.009054 seconds.
%parallel Jacobi
format long;
A = gallery('poisson',20);
tic;
x= Parallel_Jacobi(A,ones(400,1),1e-6,2000000);
toc;
Elapsed time is 11.484130 seconds.