CS 596 MPI HW
	Due date : 4/26/00 
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1. Your homework is to develop a parallel version of the serial integration
   code handed out in class in either Fortan or C using MPI.

2. Compile and run the serial code (either Fortran or C) using 
   hpc queue on ultra. Keep note of the integration result as well as
   the time it took to run this code.
   Even though this is a serial code I have put
   in MPI there so that you can use the MPI_Wtime(). 
   Compile the serial code as follows :
   tmcc -fast -xarch=v9a -lmpi integrate.c
   tmf90 -fast -xarch=v9a -lmpi integrate.f 

3. Start from the serial code handed out in class and develop
   a MPI code that will do the integration on arbitrary number
   of processors in parallel. 

4. Run the parallel code on one processor. 
   Next run the parallel code on 2 processors and 4 processors.

5. What you need to hand in:
  i)  Hard copy of the serial and the parallel MPI codes
  ii) Timing results of the serial code on 1 processor,
      parallel MPI code on 1 processor, 2 processors, and 4 processors.
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/* This is a serial integration code
and should be run on one processor

You are going to develop a parallel MPI version
of this code for your MPI HW 

I have put in the MPI routines so that you can
measure time with MPI_Wtime
*/

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

#define DIVISIONS       (int)1e9
#define MAXX            (double)100.
#define MINX            (double)0.


/***********************
The integration function
************************/
double  f(x)
double x;
        {
        return (x*x);
        }


/***********************
main
************************/
main(argc, argv)
int argc;
char **argv;
        {
        int     i; 
        double  x;
        double  dx;
        double  total; 
        double  average;
        double t0, t1;
        int npes, iam;

        MPI_Init(&argc, &argv) ;
        MPI_Comm_size(MPI_COMM_WORLD, &npes) ;
        MPI_Comm_rank(MPI_COMM_WORLD, &iam) ;
        printf("Running for maxx = %f, minx = %f,divisions=%d\n",
                MAXX,MINX,DIVISIONS);
        t0 = MPI_Wtime() ;
        /* slice size */
        dx = (MAXX - MINX) / (double)DIVISIONS;

        /* integrate */
        for (i=0 , total=0.0 ; i< DIVISIONS ; i++)
                {
                x = MINX + i * dx;
                average = ( f(x) + f(x+dx) ) / 2.0;
                total += (average * dx);
                }
         t1 = MPI_Wtime() ;
          printf("Time %f in sec\n", t1-t0) ;

        printf ("result of the integration from %f to %f is %f\n",
        (float)MINX, (float)MAXX, (float)total);
        MPI_Finalize();
        }
---------------------------------------------------------------
c This is a serial integration code
c and should be run on one processor
c
c You are going to develop a parallel MPI 
c version of this code for your MPI HW

c I have put the MPI routines so that
c you can measure time with MPI_Wtime

       program integrate
       include 'mpif.h'
 
       parameter (DIVISIONS=1e9)
 
       double precision  x
       double precision dx
       double precision total
       double precision average
       double precision MAXX
       double precision MINX
       double precision t0, t1 

       integer ierr, nPEs, iam

       call MPI_Init(ierr)
       call MPI_Comm_size(MPI_COMM_WORLD, nPEs, ierr)
       call MPI_Comm_rank(MPI_COMM_WORLD, iam, ierr) 

       MAXX = 100.0
       MINX = 0.0
 
 
       write (*,*) "Running for maxx = ",MAXX,", minx = ",MINX,
     . "divisions=",DIVISIONS
        t0 = MPI_WTIME() 
c      slice size
       dx = (MAXX - MINX) / DIVISIONS
c      integrate
       total=0.0
       do i=0,DIVISIONS-1
         x = MINX + i * dx
         average = ( f(x) + f(x+dx) ) / 2.0
         total = total + (average * dx)
       enddo
       t1 = MPI_WTIME()
       write(*,*) ' Time to run=',t1-t0,'sec' 
       write (*,*) "result of the integration from ",MINX," to ",MAXX," 
     . is ",total
       call MPI_FINALIZE(ierr) 
       end
 
C*****************************
C     The integration function
C*****************************
       function f(x)
       double precision x
       f = (x*x)
       return
       end