!2c. Modify exercise2.f90 to do 3D decomposition of a 4x4x4 grid
!    into 8 blocks (along x, y, and z). 
!------------------------------------------------------------------

      program main

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

      implicit none

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

      integer, parameter :: ndims=3    !dimension of the Cartesian grid
      integer, parameter :: dims_x=2, dims_y=2 ,dims_z=2 !same as dims(1:3)
      integer       dims(ndims)
      integer COMM_CART
      logical periods(ndims),reorder
      integer coords(ndims)

      real x(2,2,2),y(2,2,2),z(2,2,2),dx,dy,dz
      real x_corner,y_corner,z_corner
      integer nx,ny,nz

!--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=4
        ny=4
        nz=4

!--Create a Cartesian topology
       dims(1)=dims_x
       dims(2)=dims_y
       dims(3)=dims_z
      periods(1)=.true.  ! periodic bdry. cond. along x
      periods(2)=.false. ! non-periodic bdry. cond. along y
      periods(3)=.false. ! non-periodic bdry. cond. along y

      reorder=.false.

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

!           ----------------------------------------------------------------
!          | MPI_CART_CREATE will provide a 3D Cartesian array of processes |
!   ======>| of dimensions 2x2x2.                                             |
!          | Each process rank is associated with a given sub-domain.       |
!           ---------------------------------------------------------------- 


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

     call MPI_CART_COORDS(COMM_CART,my_rank,3,coords,ierror)

!--The physical coordinates of my left-bottom corner:
       dx=0.2
       dy=0.2
       dz=0.2
       x_corner= float( nx/dims(1) * coords(1)  ) * dx
       y_corner= float( ny/dims(2) * coords(2)  ) * dy
       z_corner= float( nz/dims(3) * coords(3)  ) * dz

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

       do i=1,2
        x(i,:,:)=x_corner+(float(i)-0.5)*dx
       end do

       do j=1,2
        y(:,j,:)=y_corner+(float(j)-0.5)*dy
       end do
        
       do k=1,2
        z(:,:,k)=z_corner+(float(k)-0.5)*dz
       end do
        
!--Print

       write(*,"('my rank.=',i2,', my coords=[',3i2,'] ,&
                                       & x= ',8f4.1)" ) &
    &         my_rank, coords, x

       write(*,"('my rank.=',i2,', my coords=[',3i2,'] ,&
                                       & y= ',8f4.1)" ) &
    &         my_rank, coords, y

       write(*,"('my rank.=',i2,', my coords=[',3i2,'] ,&
                                       & z= ',8f4.1)" ) &
    &         my_rank, coords, z


!--Finilize MPI
      call MPI_FINALIZE(irc)

      stop
      end