如何使用多个循环优化此Fortran子例程? [英] How to optimize this Fortran subroutine with many loops?

问题描述

我正在处理的子例程在数组大小变大时效率很低，例如NN = 1000，KK = 200，MM =200.但是，我无法提出优化它的想法.

I am dealing with subroutine that is very inefficient when the array size becomes large, for example, NN=1000, KK=200, MM = 200. But, I can not come up with ideas to optimize it.

program main

  implicit none

  integer :: NN, KK, MM
  integer, allocatable, dimension(:,:) :: id
  complex*16, allocatable, dimension(:) :: phase
  complex*16 :: phase_base(3)
  real*8, allocatable, dimension(:,:) :: wave_base

  complex*16, allocatable, dimension(:,:) :: wave
  integer :: i, j, k, n

  NN = 1000
  KK = 200
  MM = 200

  allocate(id(MM,3))
  allocate(phase(KK))
  allocate(wave_base(KK, NN*(NN+1)/2 ))
  allocate(wave(NN, NN))

  id(:,:) = 2

  phase_base(:) = (1.0d0,1.0d0)

  wave_base(:,:) = 1.0d0

  phase(:) = (1.0d0,1.0d0)

  call  noise_wave(NN, KK, MM, id, phase, phase_base, wave_base, wave)

  deallocate(id)
  deallocate(phase)
  deallocate(wave_base)
  deallocate(wave)

end program main

subroutine noise_wave(NN, KK, MM, id, phase_1, phase_base, wave_base, wave)
  implicit none

  integer, intent(in) :: NN, KK, MM
  integer, intent(in), dimension(MM, 3) :: id
  complex*16, intent(in) :: phase_1(KK)
  complex*16, intent(in) :: phase_base(3)
  real*8,  intent(in) :: wave_base(KK, NN*(NN+1)/2 )

  complex*16, intent(out) :: wave(NN, NN)

  integer :: i, j, k, p, n
  integer :: x, y, z
  real :: start, finish
  complex*16 :: phase_2, phase_2_conjg

  do p = 1, MM

    x = id(p, 1)
    y = id(p, 2)
    z = id(p, 3)

    phase_2 = (phase_base(1) ** x) * (phase_base(2) ** y) * (phase_base(3) ** z)

    phase_2_conjg = conjg(phase_2)

    n = 0
    do j = 1, NN
      do i = 1, j   ! upper triangle

        n = n + 1

        do k = 1, KK

          wave(i,j) = wave(i,j) + wave_base(k,n) * phase_1(k) * phase_2_conjg

        enddo

        wave(j,i) = conjg(wave(i,j) )

      enddo
    enddo
  enddo

end subroutin

有人可以给我一些提示吗? (我已经完成了建议的优化.此外，按照Ian的建议，我添加了一个小测试.因此您可以直接对其进行测试.)

Could someone give me some hint? (I have fulfill the suggested optimizations. Also, following Ian's suggestion, I have added a small test. Thus you can test it directly.)

推荐答案

以下是我的解决方案，遵循上面的好主意.在使用OpenMP之前，仍有一些提高效率的空间.例如，可以通过求和函数消除子例程中的第一个k循环.

Here are my solution following the nice ideas above. There is still some room for efficiency gain before OpenMP. For example, the first k loop in the subroutine can be eliminated by sum function.

program main

  implicit none

  integer :: NN, KK, MM
  integer, allocatable, dimension(:,:) :: id
  complex*16, allocatable, dimension(:) :: phase
  complex*16 :: phase_base(3)
  real*8, allocatable, dimension(:,:) :: wave_base

  complex*16, allocatable, dimension(:,:) :: wave
  integer :: i, j, k, n

  NN = 1000
  KK = 200
  MM = 200

  allocate(id(MM,3))
  allocate(phase(KK))
  allocate(wave_base(KK, NN*(NN+1)/2 ))
  allocate(wave(NN, NN))

  id(:,:) = 2

  phase_base(:) = (1.0d0,1.0d0)

  wave_base(:,:) = 1.0d0

  phase(:) = (1.0d0,1.0d0)

  call  noise_wave(NN, KK, MM, id, phase, phase_base, wave_base, wave)

  deallocate(id)
  deallocate(phase)
  deallocate(wave_base)
  deallocate(wave)

end program main

subroutine noise_wave(NN, KK, MM, id, phase_1, phase_base, wave_base, wave)
  implicit none

  integer, intent(in) :: NN, KK, MM
  integer, intent(in), dimension(MM, 3) :: id
  complex*16, intent(in) :: phase_1(KK)
  complex*16, intent(in) :: phase_base(3)
  real*8,     intent(in) :: wave_base(KK, NN*(NN+1)/2 )
  complex*16, intent(out):: wave(NN, NN)

  integer :: i, j, k, p, n
  integer :: x, y, z
  real :: start, finish
  complex*16 :: phase_2, phase_2_conjg
  complex*16 :: wave_tmp(NN*(NN+1)/2)
  complex*16 :: wave_tmp_2(NN*(NN+1)/2)

  do k = 1, KK

    wave_tmp(:) = wave_tmp(:) + wave_base(k,:) * phase_1(k)

  enddo

  do p = 1, MM
    phase_2 = product(phase_base(:)**id(p,:) )
    phase_2_conjg = conjg(phase_2)

    wave_tmp2(:) = wave_tmp2(:) + wave_tmp(n) * phase_2_conjg
  enddo

  n = 0
  do j = 1, NN
    do i = 1, j
        n = n + 1
        wave(i,j) = wave_tmp2(n)
        wave(j,i) = conjg(wave_tmp2(n) )
    enddo
  enddo

end subroutine

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