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Q((/2,5,3/),(/6,4/))

Ëü´ú±í×éƬ¶Î

       [Q2,6, Q2,4]   [27  14]
       |Q5,6, Q5,4| = |90  66|                  (9)
       [Q3,6, Q3,4]   [20  36]

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                                           | Q4,1  Q4,4  Q4,4  Q4,3 |
                                           | Q1,1  Q1,4  Q1,4  Q1,3 |
                                           | Q2,1  Q2,4  Q2,4  Q2,3 |
        Q((/4,1,2,3,4,2,5/),(/1,4,4,3)) =  | Q3,1  Q3,4  Q3,4  Q3,3 |
                                           | Q4,1  Q4,4  Q4,4  Q4,3 |
                                           | Q2,1  Q2,4  Q2,4  Q2,3 |
                                           | Q5,1  Q5,4  Q5,4  Q5,3 |

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4.3¶¯Ì¬Êý×é

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1. ×Ô¶¯Êý×é(automatic arrays)
2. ¿É·ÖÅäÊý×é(allocatable arrays)
3. Ö¸ÕëÊý×é(pointer arrays)

×Ô¶¯Êý×é

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function F18(A,N)

integer N                             ! Ò»¸ö±êÁ¿
real A(:,:)                           ! Ò»¸ö¼Ù¶¨ÐÎ×´µÄÊý×é
real F18(size(A,1))                   ! º¯Êý½á¹û±¾ÉíÊÇÒ»¸ö¶¯Ì¬Êý×é

complex Local_1(N, 2*N+3)             ! Local_1ÊÇÒ»¸ö×Ô¶¯Êý×é
                                      ! Æä´óСÒÔ N Ϊ»ù´¡

real Local_2(size(A,1),size(A,2))     ! Local_2ÊÇÒ»¸ö×Ô¶¯Êý×é
                                      ! Æä´óСÓëAÍêÈ«Ïàͬ

real Local_3(4*size(A,2))             ! Local_3ÊÇÒ»¸öһάÊý×é
                                      ! Æä´óСÊÇA µÄµÚ¶þάµÄ4±¶

..

end function F18

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¿É·ÖÅäÊý×é

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Àý×Ó

subroutine Peach

  use Recipe                   ! ·ÃÎÊÈ«¾Ö¿É·ÖÅäÊý×é Jam.

  real, allocable :: Pie(:,:)  ! Pie ÊÇÒ»¸ö 2-ά¿É·ÖÅäÊý×é
  ...
  allocate  (Pie(N,2*N))       ! ·ÖÅäÒ»¸ö¾Ö²¿¿É·ÖÅäÊý×é

  if (.not.allocated(Jam)) allocate (Jam(4*M))
                               ! Èç¹ûÒ»¸öÈ«¾Ö¿É·ÖÅäÊý×黹ûÓзÖÅä
                               ! Ôò·ÖÅäËü 
  .......deallocate(Pie)
  ....
end subroutine Peach

module Recipe                  ! Jam ÊÇÒ»¸öÈ«¾Ö¿É·ÖÅäÊý×é, Ëü¿ÉÒÔ
  real, allocable :: Jam(:)    ! ÔÚÈκιý³ÌÖÐʹÓøÃÄ£¿é·ÖÅäºÍÊÍ·Å
  ...
end module Recipe

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Ö¸ÕëÊý×é

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Òò´Ë, µ±ËùÓеÄÐèÇóÊÇÊý×é¼òµ¥µÄ¶¯Ì¬·ÖÅäºÍÊÍ·Å, ¶øÇÒʹÓÃ×Ô¶¯Êý×éÊDz»¹»µÄ, ÔòʹÓÿɷÖÅäÊý×é. ÕâÖÖÇé¿öµÄÒ»¸ö³£¼ûµÄÀý×ÓÊǵ±Ò»¸ö"¹¤×÷Êý×é"µÄ´óСȡ¾öÓÚÒ»´Î¾Ö²¿¼ÆËãµÄ½á¹ûµÄʱºò. ÁíÒ»·½Ãæ, Èç¹ûËã·¨µ÷ÓÃÒ»¸ö¶¯Ì¬Ìæ»»(alias), ÀýÈçÒ»¸öËÞÖ÷Êý×é(host array)µÄ"Òƶ¯"²¿·Ö, Ôò¿ÉÄÜÐèҪʹÓÃÒ»¸öÖ¸ÕëÊý×é.

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exp(g)+cshift9u,1,2)-chsift(u,-1,2)

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function Partial_sums(P)
  real P(:)                     !  ¼Ù¶¨ÐÎ×´µÄÑÆÔªÊý×é
  real Partial_sums(size({))    !  Òª·µ»ØµÄ²¿·ÖºÍ
  integer k

  Partial_sumns = (/(sum(P(1:k),k=1,size(P))/)

                     ! ÔÚ¹¦ÄÜÉÏ, ËüµÈ¼ÛÓÚ:
                     ! do k=1, size(P)
                     !  Partial_sums(k) = sum(P(1:k))
                     ! end do
                     ! µ«ÊÇ, do Ñ­»·ÓÃÀ´ËµÃ÷Ò»¸ö´®ÐͼÆËã,
                     ! ¶ø²»ÊDz¢ÐмÆËã

end function Partial_sums

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4.5 Àý×Ó£º¸ß˹ÏûÔª·¨

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function Simple.Gauss(Grid)         ! ¸ß˹ÏûÔª - ·Ç×î´óÖ÷Ôª
   real ::¡¡Grid(:,:)               ! Òª¹éÔ¼µÄ¾ØÕó
   real ::  Simple_Gauss(size(Grid,1))  ! ·µ»Ø½á¹ûÏòÁ¿
   real ::  G(size(Grid,1), size(Grid,2))  ! G ÊÇÒ»¸ö¾Ö²¿¹¤×÷ÏòÁ¿
   logical :: Not_pivot_row(size(Grid,1), size(Grid,2 )) ! Ö÷ÔªÐÐÆÁ±Î
 if (size(Grid,2).ne.size(Grid,1)+1 stop \"bad Grid shape\"
 N = size(Grid,1)
 G = Grid     ! ÔÚG ÉϲÙ×÷, ¶ø²»ÊÇGridÉÏ

 do L=1,N     ! G(L,L) ÊÇÏÂÒ»¸öÖ÷ÔªÔªËØ

  if (abs(G(L,L)).lt.1E-4) stop \"zero encounterd in pivot\"
!! G_pivot = G(L,L)    !!
!! do j=1,N+1      !! Ö÷ÔªÐйæ¸ñ»¯
!!  (G(L,j) = G(L,j)/G_pivot    !!
!! enddo     !!
  G(L,1) = G(L,1)/G(L,L)     !!!!  Êý¾Ý²¢Ðа汾

!! do i = 1,N   !!
!!   do j = 1, n+1    !!
!! if ( i.ne.L.and.j.ne.L )   then    !! È»ºóÓøÃÖ÷Ôª¹éÔ¼¾ØÕó
!! G(i,j) = G(i,j) - G(i,L)*G(L,j)    !!
!! end if !!
!!  end do !!
!! end do !!
  Not_pivot_row = .true.; Not_pivot_row(L,:) = .false.

  where ( NOt_pivot_row) &      !!!!  Êý¾Ý²¢Ðа汾
   G = G - G(:,spread(L,1,N+1))*G(spread(L,1,N),:)    !!!!  Êý¾Ý²¢Ðа汾

  end do            ! ¶ÔËùÓÐÖ÷ÔªÖظ´

!! do i = 1, N         !! ×îºó£¬ ÌáÈ¡½á¹ûÏòÁ¿ÐÎʽ
!!  Simple_Gauss(i) = G(i, N+1)    !!
!! end do           !!   G µÄ×îºóÒ»ÁÐ
  Simple_Gauss = G(:, N+1)    !!!! Êý¾Ý²¢Ðа汾

end function Simple_Gauss

function Pivot_Gauss(Grid)       ! ¸ß˹ÏûÔª£¬ ×î´óÖ÷Ôª
  real :: Grid(:,:)   ! Òª¹éÔ¼µÄ¾ØÕó
  real :: Pivot_Gauss(size(Grid,1)) ! ·µ»Ø½á¹ûÏòÁ¿
  real :: G(size(Grid,size(Grid,2))  ! G ÊÇÒ»¸ö¾Ö²¿¹¤×÷Êý×é
  integer :: P(size(Grid,1),2)  ! P ÊÇÒ»¸öÖ÷ÔªÊý×é
  logical :: Not_pivot_row(size(Grid,1),size(Grid,2))
                                ! Ö»ÆÁ±Îµ±Ç°Ö÷ÔªÐÐ
  logical :: Not_pivot_row(size(Grid,1),size(Grid,1))
                                ! ÆÁ±ÎËùÓÐÒÔÇ°µÄÖ÷ÔªÐкÍÁÐ
  if (size(Grid,2).ne.size(Grid,1)+1) stop \"bad Grid shape\"
  N = size(Grid,1)
  G = Grid       ! Work on G, not Grid.

  do L = 1, N    !! L ÊÇÏÂÒ»¸öÖ÷ÔªÊý

!!  G_pivot = -1    !!
!!  do i = 1,N   !! Ê×ÏÈ£¬ Ñ°ÕÒÏÂÒ»¸öÖ÷Ôª
!!    Inner_pivot_search :  & !!
!!    do j=1,N   !!
!!     do k=1,L-1   !!
!!       if(i.eq.P(k,1).or.j.eq.P(k,2)) cycle Inner_pivot_search
!!     end do  !! Ìø¹ýÕâ¸öÔªËØ£» ËüÔÚÇ°Ò»¸öÖ÷ÔªÐлòÁÐÖÐ
!!     if (abs(G(i,j)).gt.G_pivot) then   !!
!!      G_pivot = abs(G(i,j))   !!
!!      P(L,1) = i !!
!!      P(L,2) = j !!
!!     end if   !!
!!    end do   Inner_pivot_search   !!
!!   end do     !!
   Not_pivot_rows_or_cols = .true.     !!!! Êý¾Ý²¢Ðа汾
   Not_pivot_rows_cr_cols(P(1:L-1,1),:) = .false.  !!!! Êý¾Ý²¢Ðа汾
   Not_pivot_rows_or_cols(:,P(1:L-1,2)) = .false.  !!!! Êý¾Ý²¢Ðа汾
 P(L,:) = maxloc(abs(G(:,1:N)),mask=Not_pivot_rows_or_cols)
                                                   !!!! Êý¾Ý²¢Ðа汾
  if (abs(G(P(L,1),P(L,2))).lt.1E-4) stop \"ill-conditioned matrix\"

!!  G_pivot = G(P(L,1),P(L,2))   !!
!!  do j=1,N+1     !!  È»ºó¹æ¸ñ»¯Ö÷ÔªÐÐ,
!!   G(P(L,1),j) = g(P(L,1),j)/G_pivot     !! ½¨Á¢Ö÷ÔªÐбêʶ
!!  end do  !!
  G(P(L,1),:) = G(P(L,1),:)/G(P(L,1),P(L,2))  !!!! Êý¾Ý²¢Ðа汾

!!  do i = 1,N    !! È»ºóÓÃÕâ¸öÖ÷ÔªÔªËعéÔ¼¾ØÕó
!!   do j = 1,N +1  !! 
!!    if ( i.ne.P(L,1).and.j.ne.P(L,2)) then  !!
!!    G(i,j) = G(i,j)-G(i,P(L,2))*G(P(L,1),j)  !!
!!    end if  !!
!!   end do  !!
!!  end do  !!
  Not_pivot_rov = .trur.: Not_pivot_row(P(L,1),:) = .false. 
                                         !!!!  Êý¾Ý²¢Ðа汾
  where ( Not_pivot_row ) &              !!!!  Êý¾Ý²¢Ðа汾
  G = G-G(:,spread(P(L,2),1,N+1))*G(spread(P(L,1),1,N),:)
                                         !!!!  Êý¾Ý²¢Ðа汾

end do   !  ¶ÔËùÓÐÖ÷ÔªÖظ´

!! do i=1,N                    !! ×îºó£¬ ´Ó G µÄ×îºóÒ»ÁÐÖлָ´½âÏòÁ¿
!! Pivot_Gauss(P(i,2)) = G(P(i,1),N+1)  !! 
!! end do  !!
Pivot_Gauss(P(:,2)) = G(P(:,1),N=1)    !!!! Êý¾Ý²¢Ðа汾

end function Pivot_Gauss

²Î¿¼ÎÄÏ×

[1] Fortran 90 Handbook, Adams, Brainerd, Martin, Smith, Wagener, McGraw-Hill, 1992

[2] Programming Language Fortran, ANSI standard X3.198-1992

[3] DRAFT - Process Parallelism Standard, ANSI committee X3H5

Copyright: NPACT