A MPI program that implements Gauss Elimination.

/******************************************************************************
* DESCRIPTION:
* A MPI program that implements Gauss Elimination.
*
******************************************************************************/

#include
#include "mpi.h"

#define S 1000 /* number of rows in matrix */
#define MASTER 0 /* taskid of first task */


void readMatrix();
void writeMatrix();
void readVector();
void writeVector();
void GaussianElimination(int,int);

float A [S][S]; //A matrix
float V [S]; //Temp matrix for gaussion eliminitaion
float B [S]; //B matrix


main(int argc, char* argv[]) {
int numtasks; //number of tasks
int taskid; //tasks identifier
int source, //task id of message source
destination; //task id of message destination
double first, last; //a variable to calculate elapsed time
MPI_Status status;
int i, j, k; //General variable to make operations

//Initalize the processes task id and tasks identifier
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &taskid);
MPI_Comm_size(MPI_COMM_WORLD, &numtasks);

/**************************** master task ************************************/
/*Process 0 send matrix data to the slaves */
if (taskid == MASTER) {
//Read a matrix from an input file called "matrix.in"
readMatrix();
//And a vector from an input file called "vector.in"
readVector();

//Measure the overall time spent for the parallel execution.
first = MPI_Wtime();

//Process 0 are striped among the given
//number of processors with row-wise cycling striping.
//Process 0 sends each process only its related part
for (i=1; i destination = i % numtasks;
if(destination != MASTER){
MPI_Send(A[i], S, MPI_FLOAT, destination, 0, MPI_COMM_WORLD);
MPI_Send(&B[i], 1, MPI_FLOAT, destination, 1, MPI_COMM_WORLD);
}
}

}else{

for (i=1; i source = i % numtasks;
if(source == taskid){
MPI_Recv(A[i], S, MPI_FLOAT, MASTER, 0, MPI_COMM_WORLD, &status);
MPI_Recv(&B[i], 1, MPI_FLOAT, MASTER, 1, MPI_COMM_WORLD,&status);
}
}
}
//Parallel Gaussian elimination algorithm that converts the system of linear equations Ax=b to a
// unit triangular system Ux=y.
GaussianElimination(taskid,numtasks);

//Process 0 gets partial results from slaves processes
for (i=1; i destination = i % numtasks;

if(destination == taskid){
if(destination != MASTER){
MPI_Send(A[i], S, MPI_FLOAT, MASTER, 3, MPI_COMM_WORLD);
MPI_Send(&B[i], 1, MPI_FLOAT, MASTER, 4, MPI_COMM_WORLD);
}
}else if(taskid == MASTER){
MPI_Recv(A[i], S, MPI_FLOAT,destination, 3, MPI_COMM_WORLD, &status);
MPI_Recv(&B[i], 1, MPI_FLOAT, destination,4, MPI_COMM_WORLD, &status);
}
}



//MASTER process 0 writes result matrix and result vertor in files called "matrix.out"
// and "vector.out" respectively
if (taskid == MASTER) {
last = MPI_Wtime();
printf("Elapsed Time of Computation is: %f\n", last - first);
writeMatrix();
writeVector();

}
MPI_Finalize();
} /* main */

void GaussianElimination(int taskid, int pSize){
int i, j, k, n,mod;
n=S;
for(k=0; k mod = k % pSize;
if(taskid == mod){
for(j=k+1; j
if(A[k][k] != 0){
A[k][j] = A[k][j]/A[k][k]; // Division step
}else{
printf("Error : Divided by zero.\n");
}

}
if(A[k][k] != 0){
V[k] = B[k]/A[k][k];
}else{
printf("Error : Divided by zero.\n");
}
A[k][k] = 1;
}

//
MPI_Bcast(A[k], S, MPI_FLOAT, mod , MPI_COMM_WORLD);


for(i=k+1; i if(taskid == i % pSize){
for(j=k+1; j A[i][j] = A[i][j]- A[i][k] * A[k][j]; // Elimination step
}
B[i] = B[i] - A[i][k] * V[k];
A[i][k] = 0;
}
}
}
}
void readMatrix(){

FILE * f;
int i, j;
f = fopen("matrix.in","r");
if(f == NULL){
printf("Error : File not found\n");
return;
}
for (i = 0; i < S; i++){
for (j = 0; j < S; j++){
fscanf(f,"%f",&A[i][j]);
}
}
fclose(f);
}

void writeMatrix(){
FILE * f;
int i, j;

f = fopen("matrix.out","w");
if(f == NULL){
printf("Error : File not found\n");
return;
}
for (i = 0; i < S; i++){
for (j = 0; j < S; j++){
fprintf(f,"%2.1f ",A[i][j]);
}
fprintf(f,"%c",'\n');
}
fclose(f);
}
void readVector(){

FILE * f;
int i, j;

f = fopen("vector.in","r");
if(f == NULL){
printf("Error : File not found\n");
return;
}
for (i = 0; i < S; i++){
fscanf(f,"%f",&B[i]);
}
fclose(f);
}
void writeVector(){
FILE * f;
int i, j;

f = fopen("vector.out","w");
if(f == NULL){
printf("Error : File not found\n");
return;
}
for (i = 0; i < S; i++){
fprintf(f,"%2.1f ",B[i]);
}

fclose(f);
}