!2a.  Modify exercise2.f90 so it decomposes an 8x8 grid into 4 blocks 
!     (along x and y).
!----------------------------------------------------------------------

      program main

!-- Create a Cartesian 2D topology and define the
!   physical coordinate arrays x,y in each process.

      implicit none

!--Include the mpi header file
      include 'mpif.h'
      integer i,j,ierr,rank,my_rank,numprocs,itag,ierror
      integer status(MPI_STATUS_SIZE)
      integer irc

      integer, parameter :: ndims=2    !dimension of the Cartesian grid
      integer, parameter :: dims_x=2, dims_y=2  !same as dims(1:2)
      integer       dims(ndims)
      integer COMM_CART
      logical periods(ndims),reorder
      integer coords(ndims)

      real x(4,4),y(4,4),dx,dy
      real x_corner,y_corner
      integer nx,ny

!--Initialize MPI
      call MPI_INIT( ierr )

!--Who am I? --- get my rank=my_rank
      call MPI_COMM_RANK( MPI_COMM_WORLD, my_rank, ierr )

!--How many processes in the global group?
      call MPI_COMM_SIZE( MPI_COMM_WORLD, numprocs, ierr )

!--The size of the domain:
        nx=8
        ny=8

!--Create a Cartesian topology
       dims(1)=dims_x
       dims(2)=dims_y
      periods(1)=.true.  ! periodic bdry. cond. along x
      periods(2)=.false. ! non-periodic bdry. cond. along y

      call MPI_CART_CREATE(MPI_COMM_WORLD,ndims,dims,periods, &
                           reorder,COMM_CART,ierror)

!           ----------------------------------------------------------------
!          | MPI_CART_CREATE will provide a 2D Cartesian array of processes |
!   ======>| of dimensions 2x2.                                             |
!          | Each process rank is associated with a given sub-domain.       |
!           ---------------------------------------------------------------- 

!--Find my coordinate parameters in the Cartesial topology, and use them 
!  to compute the arrays x,y

     call MPI_CART_COORDS(COMM_CART,my_rank,2,coords,ierror)

!--The physical coordinates of my left-bottom corner:
       dx=0.2
       dy=0.2
       x_corner= float( nx/dims(1) * coords(1)  ) * dx
       y_corner= float( ny/dims(2) * coords(2)  ) * dy

!--Use my corner's physical coordinates to compute the cell physical 
!  coordinates (arrays x,y) in my block

       do i=1,4
        x(i,:)=x_corner+(float(i)-0.5)*dx
       end do

       do j=1,4
        y(:,j)=y_corner+(float(j)-0.5)*dy
       end do
        
!--Print

       write(*,"('my rank.=',i2,', my coords=[',2i2,'] ,&
                                       & x= ',16f4.1)" ) &
    &         my_rank, coords, x

       write(*,"('my rank.=',i2,', my coords=[',2i2,'] ,&
                                       & y= ',16f4.1)" ) &
    &         my_rank, coords, y


!--Finilize MPI
      call MPI_FINALIZE(irc)

      stop
      end