Question

我正在学习OpenMP和MPI的并行化。现在，我正在编写一个简单的高斯消除程序，没有旋转。顺序代码如下：

program ge
implicit none
integer, PARAMETER::n = 4
real, dimension (n,n+1)::A
integer::i,j,k
real start, finish

print *
print *, "Basic gaussian elimination"
print *, "By Jose Ortega Valiente"
print *
print *, "Square matrix dimension = ", n

call cpu_time(start)
!matrix A shape 
DO i = 1, n
    DO j = 1, n
        A(i,j) = i + j
    END DO
            A(i,i)=A(i,i)*100
END DO

    ! calcualte RHS (B)
    do i = 1, n
       A(i, n+1) = 0.0
       do j = 1, n
           A(i, n+1) = A(i, n+1) + A(i,j)
       end do
    end do

!let us print the matrix A|RHS
print*
print*,"Matrix A"
DO, i = 1, n
        write(*,"100g15.5") ( A(i,j), j=1,n+1 )
END DO


!Basic Gaussian Elimination
DO k = 1, n
    DO j = k+1, n
        A(k,j) = A(k,j)/A(k,k)
    END DO
    A(k,n+1) = A(k,n+1)/A(k,k)
    A(k,k)=1.0

    DO i = k+1, n
        DO j = k+1, n-1
                        A(i,j) = A(i,j) - A(i,k)*A(k,j)
        END DO
        A(i,n+1) = A(i,n+1) - A(i,k)*A(k,n+1)
                    A(i,k) = 0.0
            END DO

END DO 


!Let us print the result matrix A|RHS
print*
print*, "Matrix A result"
    DO, i = 1, n
            write(*,"100g15.5") ( A(i,j), j=1,n+1 )
    END DO

call cpu_time(finish)
print *, ""
print *, ""
print *, "It took: ", finish-start

end program ge

我没有问题做这个程序的OpenMP版本，但我不知道如何开始使用MPI版本。

OpenMP版本就在这里，以防有人对此感兴趣：

program ge
implicit none
include 'omp_lib.h'
integer, PARAMETER::n = 4
real, dimension (n,n+1)::A
integer::i,j,k
real start, finish  
integer :: my_rank, p

!$omp parallel private( my_rank )
    !$ p = omp_get_num_threads()

!$omp single
print *
print *, "Basic gaussian elimination"
print *, "By Jose Ortega Valiente"
print *
print *, "Square matrix dimension = ", n
print *, "Number of threads available: ", p
!$omp end single

start = omp_get_wtime()
!matrix A shape
!$omp do reduction (+:A) 
    DO i = 1, n
        DO j = 1, n
            A(i,j) = i + j
        END DO
                A(i,i)=A(i,i)*100
    END DO
!omp end do

!The RHS is very simple - No difference in parallel
    ! calculate RHS (B)
!$omp single
    do i = 1, n
        A(i, n+1) = 0.0
        do j = 1, n
                A(i, n+1) = A(i, n+1) + A(i,j)
        end do
    end do

!let us print the matrix A and the RHS
print*
print*,"Matrix A"
DO, i = 1, n
        write(*,"100g15.5") ( A(i,j), j=1,n+1 )
END DO
!$omp end single

!Basic Gaussian Elimination
!Outermost loop (k), iterations depend on each other 
DO k = 1+my_rank, n
    !Inner loop (j), order doesn't affect the result
    !Dividing the whole row by the element A(k,j)
    !$omp do 
        DO j = k+1, n
            A(k,j) = A(k,j)/A(k,k)
        END DO
    !$omp end do
    A(k,n+1) = A(k,n+1)/A(k,k)
    A(k,k)=1.0

    !Inner loop (i), order doesn't affect the result
    !Eliminating column k
    !$omp do 
        DO i = k+1, n
            DO j = k+1, n-1
                            A(i,j) = A(i,j) - A(i,k)*A(k,j)
            END DO
            A(i,n+1) = A(i,n+1) - A(i,k)*A(k,n+1)
                        A(i,k) = 0.0
                END DO
    !$omp end do
END DO 

!$omp end parallel
!Let us print the results (matrix A|RHS)
print*
print*, "Matrix A result"
    DO, i = 1, n
            write(*,"100g15.5") ( A(i,j), j=1,n+1 )
    END DO

finish = omp_get_wtime()
print *, ""
print *, ""
print *, "It took: ", finish-start

end program ge

我的问题不是代码，而是方法。谁能帮我理解怎么做？我的程序效果不好，我认为这是因为我真的不知道如何处理它：

program ge
implicit NONE
include 'mpif.h'
integer, PARAMETER::n = 4
real, dimension (n,n)::A
real, dimension (n)::B,X
integer::i,j
integer:: norm,row,col
real multiplier
real start, finish
integer ierr, taskid, numtasks, stat

call MPI_INIT( ierr )
call MPI_COMM_RANK( MPI_COMM_WORLD, taskid, ierr )
call MPI_COMM_SIZE( MPI_COMM_WORLD, numtasks, ierr )

if (taskid == 0) then
    print *
    print *, "Basic gaussian elimination"
    print *, "By Jose Ortega Valiente"
    print *
    print *, "Square matrix dimension = ", n
    print *, "Number of Nodes = ", numtasks
end if

call cpu_time(start)
!matrix A shape 
DO i = 1, n
    DO j = 1, n
        A(i,j) = i + j
    END DO
    A(i,i)=A(i,i)*100
END DO

! calculate RHS (B) - no real difference with only 1 node
if (taskid == 0) then
        do i = 1, n
            B(i) = 0.0
            do j = 1, n
                    B(i) = B(i) + A(i,j)
            X(i) = 0 !just to initialize
            end do
        end do
end if

!let us print the matrix A and B
if (taskid == 0) then
    print*, ""
    print*,"Matrix A"
    DO i = 1, n
            write(*,"100g15.5") ( A(i,j), j=1,n )
    END DO

    print*, ""
    print*, "Vector B result"
    DO i = 1, n
            print *, B(i)
    END DO
end if


!Basic Gaussian Elimination
DO norm = 0, n-1
    ! Broadcast A(norm) row and B(norm)
    call MPI_Bcast(A(norm,0), n, MPI_REAL, 0, MPI_COMM_WORLD, ierr)
    call MPI_Bcast(B(norm), MPI_REAL, 0, MPI_COMM_WORLD, ierr)
    ! Send data from Node 0 to other Nodes
    if (taskid == 0) then
        DO i=1, numtasks
            DO row=norm+1+i, n, numtasks
                DO j=1, n
                    call MPI_SEND(A(row,j),n,MPI_REAL,i,0,MPI_COMM_WORLD,ierr)
                END DO
                call MPI_SEND(B(row),1,MPI_REAL,i,0,MPI_COMM_WORLD,ierr)
            END DO
        END DO

        DO row=norm+1, n, numtasks
            multiplier = A(row,norm)/A(norm,norm)
            DO col=norm, n
                A(row,col) = A(row,col) - A(norm,col)*multiplier
            END DO
            B(row) = B(row) - B(norm)*multiplier
        END DO

        !recieve the updated data drom other Nodes
        DO i=1, numtasks
            DO j=1, n
                call MPI_RECV(A(row,j),n,MPI_REAL,i,1,MPI_COMM_WORLD,stat, ierr)
            END DO
            call MPI_RECV(B(row),1,MPI_REAL,i,1,MPI_COMM_WORLD,stat, ierr)
        END DO

    else    !recieve data from process 0
        DO row=norm+1+taskid, n, numtasks
            DO j=1,n
                call MPI_RECV(A(row,j),n,MPI_REAL,0,0,MPI_COMM_WORLD,stat, ierr)
            END DO
                            call MPI_RECV(B(row),1,MPI_REAL,0,0,MPI_COMM_WORLD,stat, ierr)

            multiplier = A(row,norm)/A(norm,norm)
            DO col=norm, n
                A(row,col) = A(row,col)-A(norm,col)*multiplier
            END DO
            B(row) = B(row) - B(norm)*multiplier

            !Send back the results
            DO j=1, n
                call MPI_RECV(A(row,j),n,MPI_REAL,0,1,MPI_COMM_WORLD,stat, ierr)
            END DO
                            call MPI_RECV(B(row),1,MPI_REAL,0,1,MPI_COMM_WORLD,stat, ierr)
        END DO
    end if

END DO

!Back substitution
if (taskid == 0) then
    DO row=n-1, 0, --1
        X(row) = B(row)
        DO col=n-1, row, --1
            X(row) = X(row) - A(row,col)*X(col)
        END DO
        X(row) = X(row)/A(row,row)
    END DO
end if


call cpu_time(finish)

!Let us print the result matrix A and B
if (taskid == 0) then
    print*, ""
    print*, "Matrix A result"
        DO i = 1, n
                write(*,"100g15.5") ( A(i,j), j=1,n )
        END DO
    print*, ""
            print*, "Vector B result"
            DO i = 1, n
                print *, B(i)
            END DO
    print*, ""
            print*, "Vector X result"
            DO i = 1, n
                    print *, X(i)
            END DO


    print *, ""
    print *, ""
    print *, "It took: ", finish-start
end if

call MPI_FINALIZE(ierr)

结束程序ge

高斯消除MPI Fortran

0 个答案: