/****************************************************************************
 * DESCRIPTION:  
 *   Serial HEAT2D Example - C Version
 *   This example is based on a simplified 
 *   two-dimensional heat equation domain decomposition.  The initial 
 *   temperature is computed to be high in the middle of the domain and 
 *   zero at the boundaries.  The boundaries are held at zero throughout 
 *   the simulation.  During the time-stepping, an array containing two 
 *   domains is used; these domains alternate between old data and new data.
 *
 *  The physical region, and the boundary conditions, are suggested
    by this diagram;

                   u = 0
             +------------------+
             |                  |
    u = 100  |                  | u = 100
             |                  |
             +------------------+
                   u = 100

Interrior point :
  u[Central] = (1/4) * ( u[North] + u[South] + u[East] + u[West] )

 ****************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <omp.h>

#define NN 50
#define MM 50  

#define ITER_PRINT 100
#define PRINT_DATA 1

#define _EPSILON 0.001


void update(int nx,int ny, float *u, float *unew, float * diff);
void inidat(int nx, int ny, float *u, float *unew); 
void prtdat(int nx, int ny, float *u,const char *fnam);




int main(int argc, char *argv[])
{

    float diff=1.0;
    float EPSILON=_EPSILON;
    int N=NN,M=MM;

    if(argc !=3)
    {
        fprintf(stderr,"usage %s N EPSILON\n ", argv[0]);
        fprintf(stderr,"\t\twhere N is GRID size, EPSILON is  Tolerance\n"); 
        fprintf(stderr,"\t\texample N = 100, EPSILON = 0.1\n"); 
        return -1;
    } 

    N = M = atoi(argv[1]);
    EPSILON = atof(argv[2]);

    float *u     = (float *)malloc(N * M * sizeof(float));
    float *unew  = (float *)malloc(N * M * sizeof(float));

    if(u==0 || unew ==0)
    {
        perror("Can't allocated data\n");
        return -1;
    }

    printf ( "\n" );
    printf ( "HEATED_PLATE\n" );
    printf ( "  Parallel OpenMP version, using %d Threads\n",omp_get_max_threads() );
    printf ( "  A program to solve for the steady state temperature distribution\n" );
    printf ( "  over a rectangular plate.\n" );
    printf ( "  Spatial grid of %d by %d points.\n\n", M, N );


    /* Initialize grid and create input file */
    printf("Initializing grid\n");

    inidat(N, M,u,unew);

    prtdat(N, M,u, "initial.dat");

    printf("Start computing\n");

    int iter=0;

    /* 
     *   iterate until the  new solution unew differs from the old solution u
     *     by no more than EPSILON.
     *     */

    while(diff> EPSILON) {

        update(N, M, u, unew,&diff);

        if(iter%ITER_PRINT==0)
            printf("Iteration %d, diff = %f\n ", iter,diff);

        iter++;
    }

    prtdat(N, M, u, "final.dat");

    free(u);
    free(unew);
}



/****************************************************************************
 *  subroutine update
 ****************************************************************************/
void update(int nx,int ny, float *u, float *unew, float * diff)
{
    int ix, iy;
    *diff=0.0;

#pragma omp parallel for shared(nx,ny,u,unew) private (ix,iy)
    for (ix = 1; ix < nx-1; ix++) {
        for (iy = 1; iy < ny-1; iy++) {
            unew[ix*ny+iy] =  
                (u[(ix+1)*ny+iy] +  u[(ix-1)*ny+iy] +
                 u[ix*ny+iy+1] +  u[ix*ny+iy-1] )/4.0;

        }
    }

    //compute reduction 


    float mydiff;

#pragma omp parallel  shared(nx,ny,u,unew, diff) private (ix,iy,mydiff)
    {
        mydiff=0.0;
#pragma omp for
        for (ix = 1; ix < nx-1; ix++) {
            for (iy = 1; iy < ny-1; iy++) {
                if (mydiff < fabs (unew[ix*ny+iy] - u[ix*ny+iy] ))
                {
                    mydiff = fabs ( unew[ix*ny+iy] - u[ix*ny+iy] );
                }
            }
        }


# pragma omp critical
        {
            if (*diff < mydiff )
            {
                *diff = mydiff;
            }
        }


#pragma omp for
        for (ix = 1; ix < nx-1; ix++) {
            for (iy = 1; iy < ny-1; iy++) {
                u[ix*ny+iy] = unew[ix*ny+iy]; 
            }
        }   
    }
}

/*****************************************************************************
 *  Initialize Data
 *****************************************************************************/
void inidat(int nx, int ny, float *u, float *unew) 
{
    int ix, iy;

    /*
     *Set boundary data and interrior values
     * */
    for (ix = 0; ix < nx; ix++) 
        for (iy = 0; iy < ny; iy++) { 

            if(ix==0)
            {
                u[ix*ny+iy]=0.0; 
            }
            else          
                if(iy==0 && ix!=0)
                {
                    u[ix*ny+iy]=100.0;
                }else

                    if(ix==nx-1)
                    {
                        u[ix*ny+iy]=100.0;
                    }else

                        if(iy==ny-1 && ix!=0)
                        {   
                            u[ix*ny+iy]=100.0;
                        }else

                            u[ix*ny+iy]=0.0;
        }
}

/**************************************************************************
 * Print Data to files
 **************************************************************************/
void prtdat(int nx, int ny, float *u,const char *fnam)
{

    int ix, iy;
    FILE *fp;

    if(ITER_PRINT==0)return;

    fp = fopen(fnam, "w");

    for (ix = 0 ; ix < nx; ix++) {
        for (iy =0; iy < ny; iy++) {

            fprintf(fp, "%8.3f", u[ix*ny+iy]);

            if(iy!=ny-1)
            {
                fprintf(fp, " ");
            }else
            {
                fprintf(fp, "\n");
            }
        }
    }

    fclose(fp);
}