openmp. Parallel solution of SLAE?

Question

Parallel Computing

Given a lower triangular matrix A and a vector b. Find a solution to the system Ax=b. Help, please, with the algorithm for parallelizing this task using OpenMP. Thanks in advance.

Answer 1

I decided, sort of, a problem ... Everything works correctly. Here is the code:

#include <stdio.h>
#include <math.h>
#include <omp.h>

#define N 4
#define eps 0.0001 

void jacobi(double a[N][N], double b[N], double x[N])
{
  int i, j;
  double vectorNorm; 
  double currentX[N];

  do {		
    vectorNorm = 0.0;
    
    #pragma omp parallel for private(i, j) 
    for(i = 0; i < N; i++) {
      currentX[i] = -b[i];
      for(j = 0; j < N; j++) {
        if(i != j)
          currentX[i] += a[i][j] * x[j];
      }

      currentX[i] /= -a[i][i];
    }	

    #pragma omp parallel for
    for(i = 0; i < N; i++) {
      if(fabs(x[i] - currentX[i]) > vectorNorm)
        vectorNorm = fabs(x[i] - currentX[i]); 
      x[i] = currentX[i];
    }
  }
  while(vectorNorm > eps); 
}

int main() {
  int i, j;	
  double matrixA[N][N] = {
    {2,0,0,0},
    {1,2,0,0},
    {3,1,2,0},
    {3,2,1,3}
  };
  double vectorB[N] = {1,1,1,1}, vectorX[N];	
    
  jacobi(matrixA, vectorB, vectorX);
  
  printf("Vector X:\n");
  for (i = 0; i < N; i++) {
    printf("%.3f ", vectorX[i]);
  }
  printf("\n");
    return 0;
}