MPI - linear pipeline solution for jacobi iteration

This is a discussion on MPI - linear pipeline solution for jacobi iteration within the C++ Programming forums, part of the General Programming Boards category; hello i have a problem on how to write 2 parallel code by using MPI programming with c/c++ to solve ...

  1. #1
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    Question MPI - linear pipeline solution for jacobi iteration

    hello

    i have a problem on how to write 2 parallel code by using MPI programming with c/c++ to solve a system of linear equation by using jacobi and gauss-seidel iteration method. and it is using pipelining.

    here is sample code of an equation solve by using pipeline:



    F = a0x0 + a1x1 + a2x2 .+ k + an-1xn-1


    Code:
    #include <stdio.h>
    #include <stdlib.h>
    #include "mpi.h"
    #define n 100
    
    void main(int argc,char** argv) {
    
    int my_id,i,data[n],a,p,F,x,Tx;
    
    MPI_Status status;
    MPI_Init(&argc,&argv);
    MPI_Comm_rank(MPI_COMM_WORLD,&my_id);
    MPI_Comm_size(MPI_COMM_WORLD,&p);
    
    if (my_id==0) {
    x=rand()%5;
    	
    for (i=0;i<p;i++) {
    		data[i]=rand()%5;
    		MPI_Send(&data[i],1,MPI_INT,I,0,MPI_COMM_WORLD);
    		MPI_Send(&x,1,MPI_INT,i,0,MPI_COMM_WORLD);
    	}
    	
    }
    	
    MPI_Recv(&a,1,MPI_INT,0,0,MPI_COMM_WORLD,&status);
    MPI_Recv(&x,1,MPI_INT,0,0,MPI_COMM_WORLD,&status);
    
    if (my_id==0) {
    F=a;
    x=1;
    
    MPI_Send(&F,1,MPI_INT,1,0,MPI_COMM_WORLD);
    MPI_Send(&x,1,MPI_INT,1,0,MPI_COMM_WORLD);
    
    }
    
    if (my_id>0) {
    MPI_Recv(&F,1,MPI_INT,my_id-1,0,MPI_COMM_WORLD,&status);
    MPI_Recv(&Tx,1,MPI_INT,my_id-1,0,MPI_COMM_WORLD,&status);
    
    
    x=Tx*x;
    F=F+a*x;
    
    MPI_Send(&F,1,MPI_INT,(my_id+1)%p,0,MPI_COMM_WORLD);
    MPI_Send(&x,1,MPI_INT,(my_id+1)%p,0,MPI_COMM_WORLD);
    }
    
    if (my_id==0) {
    MPI_Recv(&F,1,MPI_INT,p-1,0,MPI_COMM_WORLD,&status);
    printf("F= %d\n",F);
    }
    
    MPI_Finalize();
    
    }

    so how can i modified this code so that
    i can do the pipeline jacobi iteration and pipeline gauss-seidel iteration

    assuming the equation is like

    a11x1 + a12x2 + + a1nxn = b1;
    a21x1 + a22x2 + + a2nxn = b2;
    . .
    . .
    . .
    an1x1 + an2x2 + + annxn = bn



    for the jacobi iteration :

    suppose that one process is allocated for each unknown ( p=n)
    and each process iterate the same number of time.on each iteration the newly computed values of the unknow will need to be broadcast to all other process.
    the parallel algorithm should be like this

    Code:
    x[i] = b [i]    /*initialize unknown
    for (iteration =0; iteration<limit; iteration++){ 
        sum = -a[i][i] * x[i];
        for (j = 0; j < n; j++)   /* compute summation */
               sum = sum + a[i][j] * x[j];
        new_x[i] = (b[i] - sum) / a[i][i];   /*compute unknown*/
        broadcast_receive (xnew[i]);   /*broadcast value*/
        global_barrier ();     /* wait for all process */
    }
    an alternative simple solution is to return to basic send() and recv() , for broadcast_receive(); that is process i might have:

    Code:
    for (j=0; j<n; j++) if (i !=j) send (&x[i], Pj);
               for (j=0; j<n; j++) if (i !=j) send (&x[j], Pj);

    i need to modify this sequential code for gauss-seidel so that in can be done in parallel

    Code:
    for (i = 0; i < n -1; i++) /*for each row except last*/
                      for (j = i+1; j<n; j++){ /* step through subsequent row*/
                         m = a[j] [i]/a[i][i]; /*compute multiplier*/
                         for (k= i; k<n; k++) /*modify last n-i-1 element of row j */
                                a [j][k] = a[j][k] - a[i][k] * m ;
                         b[j] = b[j] - b[i] *m; /* modify right side */

    The master process (rank 0) accepts the size of the system and reads the coefficients as
    and bs. Then, it will distribute them to the corresponding slave processes. The master
    process should collect the final solution from the slave processes and display


    i wish if there is solution for this problem

  2. #2
    and the hat of wrongness Salem's Avatar
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    Can you check your code?
    There seems to be a lot of italic code, so it seems like the board has eaten an [ i ] subscript and turned it into italics.

    Also, void main is wrong, see the FAQ
    If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
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