Example #1
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct calculation_arguments arguments;
	struct calculation_results results;

	/* get parameters */
	AskParams(&options, argc, argv);              /* ************************* */

	initVariables(&arguments, &results, &options);           /* ******************************************* */

	allocateMatrices(&arguments);        /*  get and initialize variables and matrices  */
	initMatrices(&arguments, &options);            /* ******************************************* */
	
	pthread_barrier_init(&loop_barrier, NULL, options.number+1);	/* init der Loop-Barriere */

	gettimeofday(&start_time, NULL);                   /*  start timer         */
	calculate(&arguments, &results, &options);                                      /*  solve the equation  */
	gettimeofday(&comp_time, NULL);                   /*  stop timer          */

	displayStatistics(&arguments, &results, &options);
	DisplayMatrix(&arguments, &results, &options);

	freeMatrices(&arguments);                                       /*  free memory     */

	return 0;
}
Example #2
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct calculation_arguments arguments;
	struct calculation_results results; 

	/* get parameters */
	AskParams(&options, argc, argv);              /* ************************* */

	initVariables(&arguments, &results, &options);           /* ******************************************* */

	allocateMatrices(&arguments);        /*  get and initialize variables and matrices  */
	initMatrices(&arguments, &options);            /* ******************************************* */

	gettimeofday(&start_time, NULL);                   /*  start timer         */
	calculate(&arguments, &results, &options);                                      /*  solve the equation  */
	gettimeofday(&comp_time, NULL);                   /*  stop timer          */

	displayStatistics(&arguments, &results, &options);                                  /* **************** */
	DisplayMatrix("Matrix:",                              /*  display some    */
			arguments.Matrix[results.m][0], options.interlines);            /*  statistics and  */

	freeMatrices(&arguments);                                       /*  free memory     */

	return 0;
}
Example #3
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct mpi_options mpi_options;
	struct calculation_arguments arguments;
	struct calculation_results results;
	
	initMpi(&mpi_options, &argc, &argv);
	/* get parameters */
	AskParams(&options, argc, argv, mpi_options.mpi_rank == 0);              /* ************************* */

	initVariables(&arguments, &results, &options, &mpi_options);           /* ******************************************* */
	allocateMatrices(&arguments);        /*  get and initialize variables and matrices  */
	initMatrices(&arguments, &options);            /* ******************************************* */

	gettimeofday(&start_time, NULL);                   /*  start timer         */
	calculate(&arguments, &results, &options, &mpi_options);                                      /*  solve the equation  */
	gettimeofday(&comp_time, NULL);                   /*  stop timer          */

	if(mpi_options.mpi_rank == 0) displayStatistics(&arguments, &results, &options);
	DisplayMatrix(&arguments, &results, &options, mpi_options.mpi_rank, mpi_options.mpi_size, arguments.row_start, arguments.row_end);

	freeMatrices(&arguments);                                       /*  free memory     */

	MPI_Finalize();
	return 0;
}
Example #4
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct calculation_arguments arguments;
	struct calculation_results results;

	struct comm_options comm;

	MPI_Init(&argc, &argv);
	MPI_Comm_rank(MPI_COMM_WORLD, &comm.rank);
	MPI_Comm_size(MPI_COMM_WORLD, &comm.num_procs);

	/* get parameters */
	AskParams(&options, argc, argv, comm.rank);              /* ************************* */
	initVariables(&arguments, &results, &options);           /* ******************************************* */

	if (options.method == METH_JACOBI && comm.num_procs > 1)
	{
		allocateMatrices_mpi(&arguments, &comm);
		initMatrices_mpi(&arguments, &options, &comm); 

		gettimeofday(&start_time, NULL);                   /*  start timer         */
		calculate_mpi(&arguments, &results, &options, &comm);                                      /*  solve the equation  */
		gettimeofday(&comp_time, NULL);                   /*  stop timer          */

		if (comm.rank == ROOT)
		{
			displayStatistics(&arguments, &results, &options);
		}

		DisplayMatrix_mpi(&arguments, &results, &options, comm.rank, comm.num_procs, comm.absoluteStartRow, comm.absoluteStartRow + comm.matrixRows -3);
		freeMatrices(&arguments);                                       /*  free memory     */
	}
	else
	{
		allocateMatrices(&arguments);        /*  get and initialize variables and matrices  */
		initMatrices(&arguments, &options);            /* ******************************************* */

		gettimeofday(&start_time, NULL);                   /*  start timer         */
		calculate(&arguments, &results, &options);                                      /*  solve the equation  */
		gettimeofday(&comp_time, NULL);                   /*  stop timer          */

		displayStatistics(&arguments, &results, &options);
		DisplayMatrix(&arguments, &results, &options);

		freeMatrices(&arguments);                                       /*  free memory     */
	}

	MPI_Finalize();

	return 0;
}
Example #5
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
    MPI_Init(&argc, &argv);

    struct options options;
    struct calculation_arguments arguments;
    struct calculation_results results;

    /* get parameters */
    AskParams(&options, argc, argv);

    initVariables(&arguments, &results, &options);

    allocateMatrices(&arguments);        /*  get and initialize variables and matrices  */
    initMatrices(&arguments, &options);

    gettimeofday(&start_time, NULL);                  /*  start timer         */
    if (options.method == METH_JACOBI)
        calculate_jacobi(&arguments, &results, &options);        /*  solve the equation using Jaocbi  */
    else
        calculate_gaussseidel(&arguments, &results, &options);   /*  solve the equation using Gauss-Seidel  */

    MPI_Barrier(MPI_COMM_WORLD);
    gettimeofday(&comp_time, NULL);                   /*  stop timer          */

    // only attempt communication if we have more than 1 procss
    if(arguments.nproc > 1)
    {
        // communicate final maxresiduum from last rank to rank 0
        if(arguments.rank == 0)
            MPI_Recv(&results.stat_precision, 1, MPI_DOUBLE, arguments.nproc - 1, 1, MPI_COMM_WORLD, NULL);

        if(arguments.rank == arguments.nproc - 1)
            MPI_Send(&results.stat_precision, 1, MPI_DOUBLE, 0, 1, MPI_COMM_WORLD);
    }

    //printDebug(&arguments, &results); // pretty-print matrix if we are debugging
    if(arguments.rank == 0)
        displayStatistics(&arguments, &results, &options);

    DisplayMatrix("Matrix:", arguments.Matrix[results.m][0], options.interlines,
                  arguments.rank, arguments.nproc, arguments.offset + ((arguments.rank > 0) ? 1 : 0),
                  (arguments.offset + arguments.N - ((arguments.rank != arguments.nproc - 1) ? 1 : 0)));

    freeMatrices(&arguments);                                       /*  free memory     */

    MPI_Finalize();

    return 0;
}
Example #6
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct calculation_arguments arguments;
	struct calculation_results results;

    // mpi setup ---------------------------------------------------------------
    MPI_Init(NULL, NULL);

    int rank, nprocs;
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &nprocs);

	/* get parameters */
	AskParams(&options, argc, argv, rank);

	initVariables(&arguments, &results, &options, rank, nprocs);

    // printf("[%d] %" PRIu64 " %" PRIu64 "\n", rank, arguments.offset_start, arguments.offset_end);


    // get and initialize variables and matrices
	allocateMatrices(&arguments);
	initMatrices(&arguments, &options);

	gettimeofday(&start_time, NULL);                   /*  start timer         */
    // solve the equation
    if (options.method == METH_JACOBI)
	{
		calculate_mpi(&arguments, &results, &options);
	} else
	{
		calculate(&arguments, &results, &options);
	}

	// MPI_Barrier(MPI_COMM_WORLD);
	// gettimeofday(&comp_time, NULL);                   /*  stop timer          */

	DisplayMatrix(&arguments, &results, &options);

	freeMatrices(&arguments);

    MPI_Finalize();
	return 0;
}
Example #7
0
int
main (int argc, char** argv) {
    AskParams(&options, argc, argv);
    if (argc > 7) {
        altermode = argv[7];
        if (rank == root) {
            printf("altermode enabled!\n");
        }
    }

    MPI_Init(&argc, &argv);
    MPI_Comm_size(MPI_COMM_WORLD, &size);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    last = size-1;

    printf("process %d starting ...\n", rank);

    initVariables();
    initMatrices();

    gettimeofday(&start_time, NULL);
    if (options.method == METH_JACOBI) {
        calculateJacobi();
    }
    MPI_Barrier(MPI_COMM_WORLD);
    gettimeofday(&comp_time, NULL);

    if (rank == root) {
        double time = (comp_time.tv_sec - start_time.tv_sec) + (comp_time.tv_usec - start_time.tv_usec) * 1e-6;
        printf("Berechnungszeit:    %f s \n", time);
        printf("Anzahl Iterationen: %d\n", iteration);
    }

    DisplayMatrix();

    freeMemory();

    MPI_Finalize();
}
Example #8
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct calculation_arguments arguments;
	struct calculation_results results;

	// MPI Init
	MPI_Init(&argc, &argv);
	MPI_Comm_size(MPI_COMM_WORLD, &size);
	MPI_Comm_rank(MPI_COMM_WORLD, &rank);
	
	/* get parameters */
	AskParams(&options, argc, argv);              /* ************************* */

	initVariables(&arguments, &results, &options);           /* ******************************************* */

	allocateMatrices(&arguments);        /*  get and initialize variables and matrices  */
	initMatrices(&arguments, &options);            /* ******************************************* */

	gettimeofday(&start_time, NULL);                   /*  start timer         */
	calculate(&arguments, &results, &options);                                      /*  solve the equation  */
	
	//wait
	MPI_Barrier(MPI_COMM_WORLD);
	gettimeofday(&comp_time, NULL);                   /*  stop timer          */

	if (rank == root){
	displayStatistics(&arguments, &results, &options);
	}
	DisplayMatrix(&arguments, &results, &options);

	freeMatrices(&arguments);                                       /*  free memory     */

	//MPI End
	MPI_Finalize();
	return 0;
}
Example #9
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct calculation_arguments arguments;
	struct calculation_results results;

	/* get parameters */
	AskParams(&options, argc, argv);              /* ************************* */

	initVariables(&arguments, &results, &options);           /* ******************************************* */

	allocateMatrices(&arguments, &options);        /*  get and initialize variables and matrices  */
	initMatrices(&arguments, &options);            /* ******************************************* */

  if (options.inf_func == FUNC_FPISIN) /* Init Cache für Sinus berechnung */
    initMysin(&arguments);
  

	gettimeofday(&start_time, NULL);                   /*  start timer         */
	calculate(&arguments, &results, &options);                                      /*  solve the equation  */
	gettimeofday(&comp_time, NULL);                   /*  stop timer          */

//  int i, j;
//	for(i = 0; i <=arguments.N ; i++)
//	 for(j = 0; j <=arguments.N; j++)
//	     arguments.Matrix[results.m][i][j] = Matrix_getValue(arguments.Mat[results.m], i, j); 

	displayStatistics(&arguments, &results, &options);                                  /* **************** */
	DisplayMatrix("Matrix:",                              /*  display some    */
			arguments.Mat[results.m], options.interlines);            /*  statistics and  */

  freeMysin(&arguments);                     /* Cache für Sinus freigeben */
	freeMatrices(&arguments);                                       /*  free memory     */

	return 0;
}
Example #10
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
  struct options options;
  struct calculation_arguments arguments;
  struct calculation_results results; 
  int rc;
  
  rc = MPI_Init(&argc,&argv);
  if (rc != MPI_SUCCESS) 
  {
    printf("Error initializing MPI. Terminating.\n");
    MPI_Abort(MPI_COMM_WORLD, rc);
  }
  AskParams(&options, argc, argv);                    /* get parameters */   
  initVariables(&arguments, &results, &options);           /* ******************************************* */
  initMPI(&mpis, &arguments);	                     /* initalize MPI */
  allocateMatrices(&arguments);                            /*  get and initialize variables and matrices  */
  initMatrices(&arguments, &options);                      /* ******************************************* */
  
  gettimeofday(&start_time, NULL);                   /*  start timer         */
  calculate(&arguments, &results, &options);         /*  solve the equation  */
  gettimeofday(&comp_time, NULL);                    /*  stop timer          */
  if (0 == mpis.rank)
  {
    displayStatistics(&arguments, &results, &options);               /* **************** */
    DisplayMatrix("Matrix:",                                         /*  display some    */
		  arguments.Matrix[results.m][0], options.interlines);       /*  statistics and  */
  }
  freeMatrices(&arguments);
  freeMPI(&mpis);                                                      /*  free memory     */
  /* **************** */
  //MPI_Barrier(MPI_COMM_WORLD);
  MPI_Finalize();
  return 0;
}
Example #11
0
/* ************************************************************************ */
static
void
calculate (struct calculation_arguments const* arguments, struct calculation_results *results, struct options const* options)
{
	int i, j;                                   /* local variables for loops  */
	int m1, m2;                                 /* used as indices for old and new matrices       */
	double star;                                /* four times center value minus 4 neigh.b values */
	double residuum;                            /* residuum of current iteration                  */
	double maxresiduum;                         /* maximum residuum value of a slave in iteration */

	int const N = arguments->N;
	double const h = arguments->h;

	double pih = 0.0;
	double fpisin = 0.0;

	int term_iteration = options->term_iteration;

	/* initialize m1 and m2 depending on algorithm */
	if (options->method == METH_JACOBI)
	{
		m1 = 0;
		m2 = 1;
	}
	else
	{
		m1 = 0;
		m2 = 0;
	}

	if (options->inf_func == FUNC_FPISIN)
	{
		pih = PI * h;
		fpisin = 0.25 * TWO_PI_SQUARE * h * h;
	}

#if defined(ROWS) || defined(COLS) || defined(ELEMENTS)
	omp_set_num_threads(options->number);	
#endif

	while (term_iteration > 0)
	{
		double** Matrix_Out = arguments->Matrix[m1];
		double** Matrix_In  = arguments->Matrix[m2];

		maxresiduum = 0;


#if !defined(ROWS) && !defined(COLS) && !defined(ELEMENTS)	
		for (i = 1; i < N; i++)
				{
					double fpisin_i = 0.0;

					if (options->inf_func == FUNC_FPISIN)
					{
						fpisin_i = fpisin * sin(pih * (double)i);
					}

					/* over all columns */
					for (j = 1; j < N; j++)
					{
#endif


#ifdef ROWS
		
	#pragma omp parallel for private(j, star, residuum) reduction(max : maxresiduum)
		
		/* over all rows */

		for (i = 1; i < N; i++)
		{
			double fpisin_i = 0.0;

			if (options->inf_func == FUNC_FPISIN)
			{
				fpisin_i = fpisin * sin(pih * (double)i);
			}

			/* over all columns */
			for (j = 1; j < N; j++)
			{
#endif
	

#ifdef COLS

	#pragma omp parallel for private(i, star, residuum) reduction(max : maxresiduum)
			
		/* over all colums */
		for (j = 1; j < N; j++)
		{

			/* over all rows */
			for (i = 1; i < N; i++)
			{

			double fpisin_i = 0.0;

			if (options->inf_func == FUNC_FPISIN)
			{
				fpisin_i = fpisin * sin(pih * (double)i);
			}

#endif

#ifdef ELEMENTS
		int k;
		#pragma omp parallel for private(i, j, star, residuum) reduction(max : maxresiduum)
			
			for (k = 0; k < ((N-1) * (N-1) - 1); k++)
			{
				j = k % (N - 1) + 1;	// +1 weil k bei 0 anfängt
				i = k / N +1; 			// i ist int, die Nachkommastellen fallen weg; +1 weil k bei 0 anfängt

				double fpisin_i = 0.0;

				if (options->inf_func == FUNC_FPISIN)
				{
					fpisin_i = fpisin * sin(pih * (double)i);
				}

#endif

					star = 0.25 * (Matrix_In[i-1][j] + Matrix_In[i][j-1] + Matrix_In[i][j+1] + Matrix_In[i+1][j]);

					if (options->inf_func == FUNC_FPISIN)
					{
						star += fpisin_i * sin(pih * (double)j);
					}

					if (options->termination == TERM_PREC || term_iteration == 1)
					{
						residuum = Matrix_In[i][j] - star;
						residuum = (residuum < 0) ? -residuum : residuum;
						maxresiduum = (residuum < maxresiduum) ? maxresiduum : residuum;
					}

					Matrix_Out[i][j] = star;
				
			}

#ifndef	ELEMENTS	
		}
#endif

		results->stat_iteration++;
		results->stat_precision = maxresiduum;

		/* exchange m1 and m2 */
		i = m1;
		m1 = m2;
		m2 = i;

		/* check for stopping calculation, depending on termination method */
		if (options->termination == TERM_PREC)
		{
			if (maxresiduum < options->term_precision)
			{
				term_iteration = 0;
			}
		}
		else if (options->termination == TERM_ITER)
		{
			term_iteration--;
		}
	}

	results->m = m2;
}

/* ************************************************************************ */
/*  displayStatistics: displays some statistics about the calculation       */
/* ************************************************************************ */
static
void
displayStatistics (struct calculation_arguments const* arguments, struct calculation_results const* results, struct options const* options)
{
	int N = arguments->N;
	double time = (comp_time.tv_sec - start_time.tv_sec) + (comp_time.tv_usec - start_time.tv_usec) * 1e-6;

	printf("Berechnungszeit:    %f s \n", time);
	printf("Speicherbedarf:     %f MiB\n", (N + 1) * (N + 1) * sizeof(double) * arguments->num_matrices / 1024.0 / 1024.0);
	printf("Berechnungsmethode: ");

	if (options->method == METH_GAUSS_SEIDEL)
	{
		printf("Gauss-Seidel");
	}
	else if (options->method == METH_JACOBI)
	{
		printf("Jacobi");
	}

	printf("\n");
	printf("Interlines:         %" PRIu64 "\n",options->interlines);
	printf("Stoerfunktion:      ");

	if (options->inf_func == FUNC_F0)
	{
		printf("f(x,y) = 0");
	}
	else if (options->inf_func == FUNC_FPISIN)
	{
		printf("f(x,y) = 2pi^2*sin(pi*x)sin(pi*y)");
	}

	printf("\n");
	printf("Terminierung:       ");

	if (options->termination == TERM_PREC)
	{
		printf("Hinreichende Genaugkeit");
	}
	else if (options->termination == TERM_ITER)
	{
		printf("Anzahl der Iterationen");
	}

	printf("\n");
	printf("Anzahl Iterationen: %" PRIu64 "\n", results->stat_iteration);
	printf("Norm des Fehlers:   %e\n", results->stat_precision);
	printf("\n");
}

/****************************************************************************/
/** Beschreibung der Funktion DisplayMatrix:                               **/
/**                                                                        **/
/** Die Funktion DisplayMatrix gibt eine Matrix                            **/
/** in einer "ubersichtlichen Art und Weise auf die Standardausgabe aus.   **/
/**                                                                        **/
/** Die "Ubersichtlichkeit wird erreicht, indem nur ein Teil der Matrix    **/
/** ausgegeben wird. Aus der Matrix werden die Randzeilen/-spalten sowie   **/
/** sieben Zwischenzeilen ausgegeben.                                      **/
/****************************************************************************/
static
void
DisplayMatrix (struct calculation_arguments* arguments, struct calculation_results* results, struct options* options)
{
	int x, y;

	double** Matrix = arguments->Matrix[results->m];

	int const interlines = options->interlines;

	printf("Matrix:\n");

	for (y = 0; y < 9; y++)
	{
		for (x = 0; x < 9; x++)
		{
			printf ("%7.4f", Matrix[y * (interlines + 1)][x * (interlines + 1)]);
		}

		printf ("\n");
	}

	fflush (stdout);
	
}

/* ************************************************************************ */
/*  main                                                                    */
/* ************************************************************************ */
int
main (int argc, char** argv)
{
	struct options options;
	struct calculation_arguments arguments;
	struct calculation_results results;

	/* get parameters */
	AskParams(&options, argc, argv);              /* ************************* */

	initVariables(&arguments, &results, &options);           /* ******************************************* */

	allocateMatrices(&arguments);        /*  get and initialize variables and matrices  */
	initMatrices(&arguments, &options);            /* ******************************************* */

	gettimeofday(&start_time, NULL);                   /*  start timer         */
	calculate(&arguments, &results, &options);                                      /*  solve the equation  */
	gettimeofday(&comp_time, NULL);                   /*  stop timer          */

	displayStatistics(&arguments, &results, &options);
	DisplayMatrix(&arguments, &results, &options);

	freeMatrices(&arguments);                                       /*  free memory     */

	return 0;
}
Example #12
0
int
main (int argc, char** argv) {
	AskParams(&options, argc, argv);
	if (argc > 7) {
		altermode = argv[7];
		if (rank == root) { printf("altermode enabled!\n"); }
	}
	
	MPI_Init(&argc, &argv);
	MPI_Comm_size(MPI_COMM_WORLD, &size);
	MPI_Comm_rank(MPI_COMM_WORLD, &rank);
	last = size-1;
	
	printf("process %d starting ...\n", rank);
	
	initVariables();
	initMatrices();
	
	gettimeofday(&start_time, NULL);
	calculate();
	MPI_Barrier(MPI_COMM_WORLD);
	gettimeofday(&comp_time, NULL);
	
	if (rank == root) {
		double time = (comp_time.tv_sec - start_time.tv_sec) + (comp_time.tv_usec - start_time.tv_usec) * 1e-6;
		printf("Berechnungszeit:    %f s \n", time);
		printf("Anzahl Iterationen: %d\n", iteration);
	}
	
	DisplayMatrix();
	//testPrint();
	
	/*MPI_Barrier(MPI_COMM_WORLD);
	if (rank == 0) {
		for (int i = 0; i < actuallines; i++) {
			for (int j = 0; j <= N; j++) {
				printf("%7.4f ", newmatrix[i][j]);
			}
			printf("\n");
		}
		printf("\n");
	}
	MPI_Barrier(MPI_COMM_WORLD);
	if (rank == 1) {
		for (int i = 0; i < actuallines; i++) {
			for (int j = 0; j <= N; j++) {
				printf("%7.4f ", newmatrix[i][j]);
			}
			printf("\n");
		}
		printf("\n");
	}
	MPI_Barrier(MPI_COMM_WORLD);
	if (rank == 2) {
		for (int i = 0; i < actuallines; i++) {
			for (int j = 0; j <= N; j++) {
				printf("%7.4f ", newmatrix[i][j]);
			}
			printf("\n");
		}
		printf("\n");
	}
	MPI_Barrier(MPI_COMM_WORLD);
	if (rank == 3) {
		for (int i = 0; i < actuallines; i++) {
			for (int j = 0; j <= N; j++) {
				printf("%7.4f ", newmatrix[i][j]);
			}
			printf("\n");
		}
		printf("\n");
	}*/
	
	freeMemory();
	
	MPI_Finalize();
}
Example #13
0
/* ************************************************************************ */
int
main (int argc, char** argv)
{
    int rank;
    int size;
    int rest;
    int from, to;

    MPI_Init(&argc, &argv);

    MPI_Comm_size(MPI_COMM_WORLD, &size);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);

    struct options options;
    struct calculation_arguments arguments;
    struct calculation_results results;

    /* Parameter nur einmal abfragen */
    if(rank == 0)
    {
        AskParams(&options, argc, argv);
    }
    MPI_Bcast(&options, (sizeof(options)), MPI_BYTE, MASTER, MPI_COMM_WORLD);

    initVariables(&arguments, &results, &options);

    /* Damit allocation + initialization richtig läuft, wird für GS size = 1 gesetzt */
    if(options.method == METH_GAUSS_SEIDEL)
    {
        size = 1;
    }

    /* Aufteilen bis auf rest */
    int N_part = arguments.N;
    int lines = N_part - 1;
    rest = lines % size;
    N_part = (lines - rest) / size;

    /* globale zeilennummer berechnen, hier wird der rest beachtet						*/
    /* offset ist (rank + 1) für rank < rest, steigt also linear mit steigendem rang 	*/
    if(rank < rest)
    {
        from = N_part * rank 		+ rank + 1;
        to = N_part * (rank + 1) 	+ (rank + 1);
    }
    /* offset hier ist rest also die der maximale offset von oben */
    else
    {
        from = N_part * rank 		+ rest + 1;
        to = N_part * (rank + 1) 	+ rest ;
    }
    arguments.to = to;
    arguments.from = from;


    /* at least we only need N - 1 processes for calculation */
    if((unsigned int)size > (arguments.N -1))
    {
        size = (arguments.N - 1);

        if(rank == MASTER )
        {
            printf("\nWarning, you are using more processes than rows.\n This can slow down the calculation process! \n\n");
        }

    }

    //calculate Number of Rows
    arguments.numberOfRows = ((to - from + 1) > 0 ) ? (to - from + 1) : 0;

    allocateMatrices(&arguments);
    initMatrices(&arguments, &options, rank, size);

    gettimeofday(&start_time, NULL);                   /*  start timer         */


    if (options.method == METH_JACOBI )
    {
        calculateJacobi(&arguments, &results, &options, rank, size);
    }
    else
    {
        /* GS berechnet nur MASTER */
        if(rank == MASTER)
        {
            printf("\nGS wird nur sequentiell berechnet! \n");
            calculate(&arguments, &results, &options);
        }
    }

    gettimeofday(&comp_time, NULL);                   /*  stop timer          */

    /* only once */
    if(rank == MASTER)
    {
        displayStatistics(&arguments, &results, &options, size);
    }

    /* GS macht alte ausgabe */
    if((options.method == METH_GAUSS_SEIDEL) && (rank == MASTER))
    {
        DisplayMatrix(&arguments, &results, &options);
    }
    else
    {
        DisplayMatrixMPI(&arguments, &results, &options, rank, size, from, to);
    }

    freeMatrices(&arguments);                                       /*  free memory     */

    MPI_Finalize();
    return 0;
}