jacobi_openmp.c

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

int main ( );

/******************************************************************************/

int main ( )

/******************************************************************************/
/*
  Purpose:

    MAIN is the main program for JACOBI_OPENMP.

  Discussion:

    JACOBI_OPENMP carries out a Jacobi iteration with OpenMP.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    31 January 2017

  Author:

    John Burkardt
*/
{
  double *b;
  double d;
  int i;
  int it;
  int m;
  int n;
  double r;
  double t;
  double *x;
  double *xnew;

  m = 5000;
  n = 50000;

  b = ( double * ) malloc ( n * sizeof ( double ) );
  x = ( double * ) malloc ( n * sizeof ( double ) );
  xnew = ( double * ) malloc ( n * sizeof ( double ) );

  printf ( "\n" );
  printf ( "JACOBI_OPENMP:\n" );
  printf ( "  C/OpenMP version\n" );
  printf ( "  Jacobi iteration to solve A*x=b.\n" );
  printf ( "\n" );
  printf ( "  Number of variables  N = %d\n", n );
  printf ( "  Number of iterations M = %d\n", m );

  printf ( "\n" );
  printf ( "  IT     l2(dX)    l2(resid)\n" );
  printf ( "\n" );

# pragma omp parallel private ( i )
  {
/*
  Set up the right hand side.
*/
# pragma omp for
    for ( i = 0; i < n; i++ )
    {
      b[i] = 0.0;
    }

    b[n-1] = ( double ) ( n + 1 );
/*
  Initialize the solution estimate to 0.
  Exact solution is (1,2,3,...,N).
*/
# pragma omp for
    for ( i = 0; i < n; i++ )
    {
      x[i] = 0.0;
    }

  }
/*
  Iterate M times.
*/
  for ( it = 0; it < m; it++ )
  {
# pragma omp parallel private ( i, t )
    {
/*
  Jacobi update.
*/
# pragma omp for
      for ( i = 0; i < n; i++ )
      {
        xnew[i] = b[i];
        if ( 0 < i )
        {
          xnew[i] = xnew[i] + x[i-1];
        }
        if ( i < n - 1 )
        {
          xnew[i] = xnew[i] + x[i+1];
        }
        xnew[i] = xnew[i] / 2.0;
      }
/*
  Difference.
*/
      d = 0.0;
# pragma omp for reduction ( + : d )
      for ( i = 0; i < n; i++ )
      {
        d = d + pow ( x[i] - xnew[i], 2 );
      }
/*
  Overwrite old solution.
*/
# pragma omp for
      for ( i = 0; i < n; i++ )
      {
        x[i] = xnew[i];
      }
/*
  Residual.
*/
      r = 0.0;
# pragma omp for reduction ( + : r )
      for ( i = 0; i < n; i++ )
      {
        t = b[i] - 2.0 * x[i];
        if ( 0 < i )
        {
          t = t + x[i-1];
        }
        if ( i < n - 1 )
        {
          t = t + x[i+1];
        }
        r = r + t * t;
      }

# pragma omp master
      {
        if ( it < 10 || m - 10 < it )
        {
          printf ( "  %8d  %14.6g  %14.6g\n", it, sqrt ( d ), sqrt ( r ) );
        }
        if ( it == 9 )
        {
          printf ( "  Omitting intermediate results.\n" );
        }
      }

    }

  }
/*
  Write part of final estimate.
*/
  printf ( "\n" );
  printf ( "  Part of final solution estimate:\n" );
  printf ( "\n" );
  for ( i = 0; i < 10; i++ )
  {
    printf ( "  %8d  %14.6g\n", i, x[i] );
  }
  printf ( "...\n" );
  for ( i = n - 11; i < n; i++ )
  {
    printf ( "  %8d  %14.6g\n", i, x[i] );
  }
/*
  Free memory.
*/
  free ( b );
  free ( x );
  free ( xnew );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "JACOBI_OPENMP:\n" );
  printf ( "  Normal end of execution.\n" );

  return 0;
}