c -----------------------------------------------------------
c Scalar product:  1-D objects
c                  n - local dimension
c -----------------------------------------------------------
      double precision function mpi_dot1(x,y,n)
      implicit none
      include 'mpif.h'
      integer n,i,ierr,comm
      double precision lsum,gsum,x(n),y(n)

      lsum=0.0d0
      do i=1,n
         lsum=lsum + x(i)*y(i)
      enddo
      comm = MPI_COMM_WORLD
      call MPI_ALLREDUCE(lsum,gsum,1,MPI_DOUBLE_PRECISION,
     >                   MPI_SUM, comm, ierr)
      mpi_dot1 = gsum
      return
      end
c -----------------------------------------------------------
c Scalar product:  2-D objects
c                  nx,ny - local dimensions
c -----------------------------------------------------------
      double precision function mpi_dot2(x,y,nx,ny)
      implicit none
      include 'mpif.h'
      integer nx,ny,i,j,ierr,comm
      double precision lsum,gsum,x(nx,ny),y(nx,ny)

      lsum=0.0d0
      do i=1,nx
        do j=1,ny
          lsum=lsum + x(i,j)*y(i,j)
        enddo
      enddo
      comm = MPI_COMM_WORLD
      call MPI_ALLREDUCE(lsum,gsum,1,MPI_DOUBLE_PRECISION,
     >                   MPI_SUM, comm, ierr)
      mpi_dot2 = gsum
      return
      end
c -----------------------------------------------------------
c Scalar product:  3-D objects
c                  nx,ny,nz - local dimensions
c -----------------------------------------------------------
      double precision function mpi_dot3(x,y,nx,ny,nz)
      implicit none
      include 'mpif.h'
      integer nx,ny,nz,i,j,k,ierr,comm
      double precision lsum,gsum,x(nx,ny,nz),y(nx,ny,nz)

      lsum=0.0d0
      do i=1,nx
        do j=1,ny
          do k=1,nz
            lsum=lsum + x(i,j,k)*y(i,j,k)
          enddo
        enddo
      enddo
      comm = MPI_COMM_WORLD
      call MPI_ALLREDUCE(lsum,gsum,1,MPI_DOUBLE_PRECISION,
     >                   MPI_SUM, comm, ierr)
      mpi_dot3 = gsum
      return
      end