122 lines
3.1 KiB
C
122 lines
3.1 KiB
C
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#include <stdio.h>
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#include <stdlib.h>
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#include <mpi.h>
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#include <math.h>
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#include "util.h"
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void cg_par(double *A_local, double *rhs_local, int N, int b, float tol)
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{
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int size;
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int my_rank;
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// Get number of processes
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MPI_Comm_size(MPI_COMM_WORLD, &size);
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// Get my rank
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MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
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//**************** Parallel CG (M == N)
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int num_it, max_it;
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double x[b], r[b], Ap[b];
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double p_local[b], p_global[N];
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double nr_global, nr_local;
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double np2_global, np2_local;
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double epsilon;
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double alpha, beta;
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max_it = 100;
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// initialization of the solution (local vector)
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for (int i = 0; i < b; i++)
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{
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x[i] = 0.0;
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}
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// compute the global norm of the rhs_local (dot product, then sqrt);
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// all the nodes must have this value
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nr_local = dot(rhs_local, rhs_local, b);
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MPI_Allreduce(&nr_local, &nr_global, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
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nr_global = sqrt(nr_global);
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// if (my_rank == 0) printf("nr = %lg\n", nr_global);
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// threshold of the CG
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epsilon = tol * nr_global;
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// Initialization of p_local and r (local vectors)
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copy_v(p_local, rhs_local, b);
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copy_v(r, rhs_local, b);
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// number of iterations
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num_it = 0;
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printf("num_it %d -- epsilon %lg -- nr_global %lg\n", num_it, epsilon, nr_global);
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while ((nr_global > epsilon) && (num_it < max_it))
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{
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// Compute the local vector Ap = A_local*p_global
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// => gather p_local vectors to p_global
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MPI_Allgather(p_local, b, MPI_DOUBLE, p_global, b, MPI_DOUBLE, MPI_COMM_WORLD);
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// display p_global
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if (my_rank == 0)
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printf("p_global = %lg\n", p_global);
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// do the matrix-vector multiplication
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multAv(Ap, A_local, p_global, b, N);
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// compute the global dot product np2_global = (Ap_global, p_global)
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// all the node must have this value
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np2_local = dot(p_local, Ap, b);
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MPI_Allreduce(&np2_local, &np2_global, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
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if (my_rank == 0)
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printf("np2 = %lg\n", np2_global);
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// alpha
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alpha = (nr_global * nr_global) / np2_global;
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// if(my_rank == 0) printf("alpha = %lg\n", alpha);
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// compute the new x and r (local vectors)
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axpy(alpha, x, p_local, b);
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axpy(-alpha, r, Ap, b);
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// compute the global norm of the residual (dot product, then sqrt);
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// all the nodes must have this value
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nr_local = dot(r, r, b);
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MPI_Allreduce(&nr_local, &nr_global, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
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nr_global = sqrt(nr_global);
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// if(my_rank == 0) printf("nr = %lg\n", nr_global);
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// beta
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beta = (nr_global * nr_global) / (alpha * np2_global);
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// if(my_rank == 0) printf("beta = %lg\n", beta);
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// compute the new p_local (local vector)
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xpay(beta, r, p_local, b);
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// increase the number of iterations
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num_it++;
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// if(my_rank == 0) printf("num_it %d -- nr_global %lg\n", num_it, nr_global);
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}
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free(A_local);
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// gather the solution on the node 0
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double x_global[N];
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MPI_Gather(x, b, MPI_DOUBLE, x_global, b, MPI_DOUBLE, 0, MPI_COMM_WORLD);
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// display the solution
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if (my_rank == 0)
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{
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for (int i = 0; i < N; i++)
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{
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printf("x[%d] = %lg\n", i, x_global[i]);
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}
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}
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return;
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}
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