问题[fortran]

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我正在使用 gfortran，一个 CodeBlocks 框架

program main
  integer, parameter :: n = 3, nsteps = 100
  real, parameter :: a = 0.0, b =10e-14
  complex(8) ::  x(0:n),h
  x = (/1.0, 0.0, 0.0,0.0/)
  h = (b - a)/nsteps
  print *,x
  call rk4sys(n,h,x,nsteps)
end program main

subroutine xpsys(n,x,f)
  complex(8), dimension (0:n) ::  x
  complex(8), dimension (0:n) ::  f
  integer n
  complex(8) :: E,d, hbar,W,omega0,omega,gamma1, delta

  d=3.335641E-30
  hbar=(1.0546E-34,0.0)
  omega = 2.482/(6.24E18*hbar)
  W = 1.25E+10
  omega0= 2.4743/(6.24E18*hbar)
  delta=0.0
  gamma1= 1E15
  E=(1/hbar)*W;


  f(0)= (0.,-1.)*d*(x(1)*E - x(2)*conjg(E))+gamma1*x(3)
  f(1)= conjg((0.,1.)*(x(2)*delta+ d*E*(x(0)- x(3)))-gamma1*x(2)/2);
  f(2)= (0., 1.)*(x(2)*delta + d*E*(x(0)- x(3)))-gamma1*x(2)/2
  f(3)= (0., 1.)*d*(x(1)*E- x(2)*conjg(E))-gamma1*x(3)

  !DrhoDt(1)=-1i*d.*(rho(2).*(E) - rho(3).*conj(E))+gamma.*rho(4);+
  !DrhoDt(2)=conj(1i.*(rho(3).*(delta)+ d.*E.*(rho(1)- rho(4)))-gamma.*rho(3)/2);
  !DrhoDt(3)=1i.*(rho(3).*(delta)+ d.*E.*(rho(1)- rho(4)))-gamma.*rho(3)/2;
  !DrhoDt(4)=1i.*d.*(rho(2).*(E)- rho(3).*conj(E))-gamma.*rho(4);
end subroutine xpsys

subroutine rk4sys(n,h,x,nsteps)
  complex(8), dimension (0:nsteps,0:3) ::  Xmass
  complex(8) ::  x(0:n)
  complex(8), allocatable :: y(:)
  complex(8), allocatable :: f(:,:)
  integer :: i, k, n
  complex(8) :: h
  allocate (y(0:n), f(0:n,4))

  Do i=0,nsteps
    Do j=0,3
        Xmass(i,j)=0
    End Do

  End Do


  Xmass(0,0)=x(0)
  Xmass(0,1)=x(1)
  Xmass(0,2)=x(2)
  Xmass(0,3)=x(3)

out:  do k = 1,nsteps
    call xpsys(n,x,f(0,1))
in1:    do i = 0,n
      y(i) = x(i) + 0.5*h*f(i,1)
    end do in1
    call xpsys(n,y,f(0,2))
 in2:    do i = 0,n
      y(i) = x(i) + 0.5*h*f(i,2)
    end do in2
    call xpsys(n,y,f(0,3))
 in3:    do i = 0,n
      y(i) = x(i) + h*f(i,3)
    end do in3
    call xpsys(n,y,f(0,4))
 in4:    do i = 0,n
      x(i) = x(i) + (h/6.0)* (f(i,1) + 2.0*(f(i,2) + f(i,3)) + f(i,4))
      Xmass(k,i) = x(i)
    end do in4
    end do out
  k=0

  OPEN(10,FILE='res.txt')
  !WRITE(10,'(5A25)') 'T','X1','X2','X3',' X4'
  DO k=0,nsteps
    print *,k, real (Xmass(k,0)),AIMAG(Xmass(k,0)), real (Xmass(k,1)), &
         AIMAG(Xmass(k,1)),real (Xmass(k,2)),AIMAG(Xmass(k,2)), &
         real (Xmass(k,3)),AIMAG(Xmass(k,3))

    WRITE(10,'(I3, 8Z19.18)')k, real (Xmass(k,0)),AIMAG(Xmass(k,0)), real (Xmass(k,1)), &
         AIMAG(Xmass(k,1)),real (Xmass(k,2)),AIMAG(Xmass(k,2)), &
         real (Xmass(k,3)),AIMAG(Xmass(k,3))


  END DO
  CLOSE(10)
  Xmass=0
 end subroutine rk4sys

这显示在终端中 - 一切都很好

1 0.90719088395362735 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000Y来-0.290397082089698 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000来

.txt 中的输出不按顺序

1 003FED07B52D39ECD6 000000000000000000 000000000000000000 00BFD294ECFFDF317C 000000000000000000

我正在尝试使用 GNU Fortran 编译器使用四阶 Runge-Kutta 方法求解具有复杂变量的 SDE。如何解决“Array 'f' cannot have a deferred shape”错误？

program main
      integer, parameter :: n = 3, nsteps = 100
      real, parameter :: a = 0.0, b =1.0
      real ::  x(0:n)

      real :: d, hbar,W,omega0,omega,gamma1, E, delta
      d=3.335641E-30
      hbar=1.0546e-34
      omega = 2.482/(6.24e18*hbar)
      W = 1.25e10
      omega0= 2.4743/(6.24e18*hbar)
      delta=0.0
      gamma1= 1E15
      E=(1/hbar)*W;
      x = (/1.0, 0.0, 0.0,0.0/)
      h = (b - a)/nsteps
      call rk4sys(n,h,x,nsteps)
end program main



subroutine xpsys(n,x,f)
      complex, dimension (0:n) ::  x, f
      integer n

      f(0)= (-(0., 1.))*d*x(1)*E - x(2)*E+gamma1*x(4) ! 00+
      f(1)= ((0., -1.)*(x(2)*(delta)+ d*E*(x(0)- x(3)))-gamma1*x(2)/2)!11
      f(2)= (0., 1.)*(x(2)*(delta)+ d*E*(x(0)- x(3)))-gamma1*x(2)/2!10
      f(3)= (0., 1.)*d*(x(1)*E- x(2)*E)-gamma1*x(3)!01

end subroutine xpsys

subroutine rk4sys(n,h,x,nsteps)
      complex ::  x(0:n), f(:,:)
      real, allocatable :: y(:)
      integer :: i, k, n
      real :: h
      print *,0,x
      allocate (y(0:n), f(0:n,4))
    out:  do k = 1,nsteps
            call xpsys(n,x,f(0,1))
    in1:    do i = 0,n
              y(i) = x(i) + 0.5*h*f(i,1)
            end do in1
            call xpsys(n,y,f(0,2))
    in2:    do i = 0,n
              y(i) = x(i) + 0.5*h*f(i,2)
            end do in2
            call xpsys(n,y,f(0,3))
    in3:    do i = 0,n
              y(i) = x(i) + h*f(i,3)
            end do in3
            call xpsys(n,y,f(0,4))
    in4:    do i = 0,n
              x(i) = x(i) + (h/6.0)* (f(i,1) + 2.0*(f(i,2) + f(i,3)) + f(i,4))
            end do in4
            print *, k, x
          end do out
end subroutine rk4sys