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fortran について書きます。

Plot ルーチン修正

Plotルーチンから非標準構文を取り除く

以前のバージョンでは、Fortran規格外の Cray Pointer を使っていたのですが、Fortran2003 の規格内のルーチンで書き直しました。

また、以前のものは微妙にスレッド競合が起きていて時々挙動がおかしかったので修正しました。

その他微妙な修正も含む途中メモ。

f:id:fortran66:20130219020611j:plain

2-20 微妙にミス修正

ソース・コード

module m_oop
  implicit none
        
  type :: t_rgb
    integer :: ir, ig, ib
  end type t_rgb
  
  type, abstract :: t_device
    character(len = 80) :: title = 'Plotter'
    integer :: nsize_x = 640, nsize_y = 480
    integer :: line_width = 1
    type (t_rgb) :: rgb = t_rgb(0, 0, 0)
  contains
    procedure (device_on    ), deferred, pass :: on
    procedure (device_off   ), deferred, pass :: off
    procedure (device_show  ), deferred, pass :: show
    procedure (device_pen   ), deferred, pass :: pen
    procedure (device_lineTo), deferred, pass :: lineTo
    procedure (device_moveTo), deferred, pass :: moveTo
    procedure (device_dot   ), deferred, pass :: dot
    procedure (device_text  ), deferred, pass :: text
  end type t_device 

  abstract interface 
    subroutine device_on(self)
      import :: t_device
      class(t_device), intent(in out) :: self
    end subroutine device_on
  
    subroutine device_off(self)
      import :: t_device
      class(t_device), intent(in) :: self
    end subroutine device_off

    subroutine device_show(self)
      import :: t_device
      class(t_device), intent(in) :: self
    end subroutine device_show
    
    subroutine device_pen(self, line_width, rgb)
      import :: t_device, t_rgb
      class(t_device), intent(in out) :: self
      integer, intent(in), optional :: line_width
      type (t_rgb), intent(in), optional :: rgb
    end subroutine device_pen

    subroutine device_lineTo(self, ix, iy)
      import :: t_device
      class(t_device), intent(in) :: self
      integer, intent(in) :: ix, iy
    end subroutine device_lineTo
  
    subroutine device_moveTo(self, ix, iy)
      import :: t_device
      class(t_device), intent(in) :: self
      integer, intent(in) :: ix, iy
    end subroutine device_moveTo

    subroutine device_dot(self, ix, iy, icol)
      import :: t_device, t_rgb
      class(t_device), intent(in) :: self
      integer, intent(in) :: ix, iy
      integer, intent(in) :: icol
!      type (t_rgb), intent(in) :: rgb
    end subroutine device_dot
    
    subroutine device_text(self, ix, iy, txt, rgb, ifontsize, ifontdirection)
      import :: t_device, t_rgb
      class(t_device), intent(in) :: self
      integer, intent(in) :: ix, iy
      character (LEN = *), intent(in) :: txt
      type (t_rgb), intent(in), optional :: rgb
      integer, optional, intent(in) :: ifontsize, ifontdirection
    end subroutine device_text 
  end interface
  
end module m_oop

module m_win32
  use, intrinsic :: iso_c_binding
  use ifwina
  use ifwinty
  use ifmt, only : RTL_CRITICAL_SECTION
  use m_oop
  implicit none

  type :: t_wnd
    integer (LPINT)  :: hThread   = 0
    integer (LPDWORD):: id        = 0
    integer (HANDLE) :: hWnd      = 0
    integer (HANDLE) :: hDC       = 0
    integer (HANDLE) :: hPen      = 0
  end type t_wnd      

  type, extends(t_device) :: t_win32
    type (t_wnd), private :: wnd = t_wnd(0, 0, 0, 0, 0)
    type (RTL_CRITICAL_SECTION), private :: CriticalSection = RTL_CRITICAL_SECTION(0,0,0,0,0,0)
  contains 
    procedure, pass :: on     => gr_on
    procedure, pass :: off    => gr_off
    procedure, pass :: show   => gr_show
    procedure, pass :: pen    => gr_pen
    procedure, pass :: lineTo => gr_lineTo
    procedure, pass :: moveTo => gr_moveTo
    procedure, pass :: dot    => gr_dot
    procedure, pass :: text   => gr_text
  end type t_win32

  integer, save :: nwin = 0 
  integer (DWORD), save :: iThreadPrivate_Win32 = 0
  type (  RTL_CRITICAL_SECTION), save    ::   gCriticalSection 
  type (T_RTL_CRITICAL_SECTION), pointer :: lpgCriticalSection  

contains
  !--------------------------------------------------------------------------------
  integer(4) function WinMain( hInstance, nCmdShow, win32 )
    implicit none
    integer (HANDLE), intent(in) :: hInstance 
    integer (SINT)  , intent(in) :: nCmdShow
    type (t_win32)  , intent(in) :: win32
    type (T_WNDCLASS) :: wc
    type (T_MSG)      :: mesg
    integer (HANDLE)  :: hWndMain
    integer (BOOL)    :: iretb
    character (LEN = 256) :: ClassName = 'Fortran'//char(0)
    integer :: iwindow_frame_x, iwindow_frame_y
    logical, save :: first = .true. 
    ! Init Main window
    iwindow_frame_x = 2 * GetSystemMetrics(SM_CXFIXEDFRAME) !side line = 6, title bar = 25
    iwindow_frame_y = 2 * GetSystemMetrics(SM_CYFIXEDFRAME) + GetSystemMetrics(SM_CYCAPTION)
    !
    if (first) then
      WinMain = -1 ! Error code 
      wc%lpszClassName = transfer(c_loc(ClassName)     , int(0)) 
      wc%lpfnWndProc   = transfer(c_funloc(MainWndProc), int(0)) ! CALLBACK procedure name
      wc%style         = ior(CS_VREDRAW , CS_HREDRAW)
      wc%hInstance     = hInstance
      wc%hIcon         = NULL   
      wc%hCursor       = LoadCursor( NULL, IDC_ARROW )
      wc%hbrBackground = ( COLOR_WINDOW + 1 )
      if ( RegisterClass(wc) == 0 ) return    ! initialize window
      first = .false.
    end if
    ! Init instance
    WinMain = -2 ! Error code 
    hWndMain = CreateWindowEx(  0, ClassName,                        &
                                trim(win32%title)//char(0),          &
                                int(ior(WS_OVERLAPPED, WS_SYSMENU)), &
                                CW_USEDEFAULT, CW_USEDEFAULT,        &
                                win32%nsize_x + iwindow_frame_x,     &
                                win32%nsize_y + iwindow_frame_y,     &
                                0, 0,                                &
                                hInstance,                           &
                                transfer(c_loc(win32), int(0))    )  
    if (hWndMain == 0) return
    iretb = ShowWindow( hWndMain, nCmdShow )
    iretb = UpdateWindow( hWndMain )
    ! Message Loop
    do while ( GetMessage (mesg, NULL, 0, 0) ) 
      iretb = TranslateMessage( mesg ) 
      iretb = DispatchMessage(  mesg )
    end do
    WinMain = mesg%wParam
    return
  end function WinMain
  !-------------------------------------------------------------------------------------
  integer (LRESULT) function MainWndProc( hWnd, mesg, wParam, lParam ) 
  !DEC$ ATTRIBUTES STDcall, DECORATE, ALIAS : 'MainWndProc' :: MainWndProc
    integer (HANDLE) , intent(in) :: hWnd
    integer (UINT)   , intent(in) :: mesg
    integer (fwParam), intent(in) :: wParam
    integer (flParam), intent(in) :: lParam
    !
    integer (HANDLE) :: hDC, hBmp
    integer (BOOL)   :: iretb
    type (T_PAINTSTRUCT) :: ps
    type (T_RECT)        :: rc
    !
    type (T_CREATESTRUCT), pointer :: cs
    type (t_win32)       , pointer :: win32
    type (c_ptr) :: c_p ! mold for transfer function
    !
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    !
    call c_f_pointer(c_loc(gCriticalSection), lpgCriticalSection)
    call EnterCriticalSection( lpgCriticalSection )
    MainWndProc = 0
    select case ( mesg )
      case (WM_CREATE)
        call c_f_pointer(transfer(lParam           , c_p), cs   ) ! LOC(cs ) = lParam
        call c_f_pointer(transfer(cs%lpCreateParams, c_p), win32) ! LOC(win32) = cs%lpCreateParams 
        iretb = TlsSetValue(iThreadPrivate_Win32, cs%lpCreateParams)
        associate (wnd => win32%wnd)
          wnd%hWnd = hWnd
          hDC      = GetDC(hWnd)
          wnd%hDC  = CreateCompatibleDC(hDC)
          iretb    = GetClientRect(hWnd, rc)
          hBmp     = CreateCompatibleBitmap(hDC, rc%right - rc%left, rc%bottom - rc%top)
          iretb    = SelectObject(wnd%hDC, hBmp)
          iretb    = PatBlt(wnd%hDC, 0, 0, rc%right - rc%left, rc%bottom - rc%top, WHITENESS)
          iretb    = ReleaseDC(hWnd, hDC)
          iretb    = DeleteObject(hBmp)
        end associate
      case (WM_DESTROY)
        call c_f_pointer(transfer(TlsGetValue(iThreadPrivate_Win32), c_p), win32) ! LOC(win32) = TlsGetValue(iThreadPrivate_Win32)
        call c_f_pointer(c_loc(win32%CriticalSection), lpCriticalSection)
        associate (wnd => win32%wnd)
          call EnterCriticalSection( lpCriticalSection )          ! EnterCriticalSection( LOC(win32%CriticalSection) )
          iretb = DeleteObject( wnd%hDC )
          call PostQuitMessage( 0 )
          call LeaveCriticalSection( lpCriticalSection )
        end associate  
      case (WM_PAINT)
        call c_f_pointer(transfer(TlsGetValue(iThreadPrivate_Win32), c_p), win32)  
        call c_f_pointer(c_loc(win32%CriticalSection), lpCriticalSection)
        associate (wnd => win32%wnd)
        call EnterCriticalSection( lpCriticalSection )
          hDC    = BeginPaint(    wnd%hWnd, ps )
          iretb  = GetClientRect( wnd%hWnd, rc )
          iretb  = BitBlt(hDC, 0, 0, rc%right - rc%left, rc%bottom - rc%top, wnd%hDC, 0, 0, SRCCOPY)
          iretb  = endPaint( wnd%hWnd, ps )
          call LeaveCriticalSection( lpCriticalSection )
        end associate
      case (WM_RBUTTONUP)
        call c_f_pointer(transfer(TlsGetValue(iThreadPrivate_Win32), c_p), win32)  
        call c_f_pointer(c_loc(win32%CriticalSection), lpCriticalSection)
        associate (wnd => win32%wnd)
          call EnterCriticalSection( lpCriticalSection )
          iretb = DeleteObject( wnd%hDC )
          call PostQuitMessage( 0 )
          call LeaveCriticalSection( lpCriticalSection )
        end associate  
      case default
        MainWndProc = DefWindowProc( hWnd, mesg, wParam, lParam )
    end select 
    call LeaveCriticalSection( lpgCriticalSection )
    return
  end function MainWndProc
  !-------------------------------------------------------------------------------------
  subroutine gr_on(self)
    use IFMT, only : CreateThread ! multithread module
    class(t_win32), intent(in out) :: self
    integer (BOOL)    :: iretb
    integer (HANDLE)  :: hBmp
    type (T_RECT)    :: rc
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    associate(wnd => self%wnd)
      if (nwin == 0) then
        iThreadPrivate_Win32 = TlsAlloc()
        call c_f_pointer(c_loc(gCriticalSection), lpgCriticalSection)
        call InitializeCriticalSection( lpgCriticalSection ) 
      end if
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call InitializeCriticalSection( lpCriticalSection ) 
      nwin = nwin + 1
      wnd%hThread = CreateThread(NULL, 0, Thread_Proc, NULL, CREATE_SUSPENDED, wnd%id) 
      iretb       = SetThreadPriority(wnd%hThread, THREAD_PRIORITY_BELOW_NORMAL)
      iretb       = ResumeThread(wnd%hThread)

      call sleep(100) ! wait for Window initialization 
      iretb = GetClientRect(wnd%hWnd, rc)
      hBmp  = CreateCompatibleBitmap(wnd%hDC, rc%right - rc%left, rc%bottom - rc%top)
      iretb = SelectObject(wnd%hDC, hBmp)
      iretb = DeleteObject(hBmp)
      iretb = PatBlt(wnd%hDC, 0, 0, rc%right - rc%left, rc%bottom - rc%top, WHITENESS)
      wnd%hPen = CreatePen(PS_SOLID, 1, 0)
    end associate
    return
  contains 

    integer (LONG) function Thread_Proc(lp_ThreadParameter)
    !DEC$ ATTRIBUTES STDcall, ALIAS:"_thread_proc" :: Thread_Proc
      integer (LPINT), intent(in) :: lp_ThreadParameter
      integer :: hInst
      hInst       = GetModuleHandle(NULL)
      Thread_Proc = WinMain(hInst, SW_SHOWNORMAL, self)
      return
    end function Thread_Proc
    
  end subroutine gr_on
  !-------------------------------------------------------------------------------------
  subroutine gr_off(self)
    use, intrinsic :: iso_c_binding
    class(t_win32), intent(in) :: self
    integer (BOOL)  :: iretb
    integer (DWORD) :: iwait
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    associate(wnd => self%wnd)
      iwait = INFINITE
      iretb = InvalidateRect(wnd%hWnd, NULL, FALSE)
      iretb = DeleteObject(wnd%hPen) 
      iretb = WaitForSingleObject(wnd%hThread, iwait)
      iretb = CloseHandle(wnd%hThread)
      iretb = PostMessage(wnd%hWnd, WM_DESTROY, NULL, NULL)
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call DeleteCriticalSection( lpCriticalSection ) 
      nwin = nwin - 1
      if (nwin == 0) then 
        iretb = TlsFree(iThreadPrivate_Win32)
        call DeleteCriticalSection( lpgCriticalSection ) 
      end if
    end associate
    return
  end subroutine gr_off
  !-------------------------------------------------------------------------------------
  subroutine gr_show(self)
    class(t_win32), intent(in) :: self
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    integer (BOOL):: iretb
    associate(wnd => self%wnd)
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call EnterCriticalSection( lpCriticalSection ) 
      iretb = InvalidateRect(wnd%hWnd, NULL, FALSE)
      call LeaveCriticalSection( lpCriticalSection )  
    end associate
    return
  end subroutine gr_show
  !-------------------------------------------------------------------------------------
  subroutine gr_pen(self, line_width, rgb)
    class(t_win32), intent(in out) :: self
    integer, intent(in), optional :: line_width
    type (t_rgb), intent(in), optional :: rgb
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    integer (BOOL) :: iretb
    associate( rgb_ => self%rgb, line_width_ => self%line_width, wnd => self%wnd )
      if ( present(rgb) ) rgb_ = rgb
      if ( present(line_width) ) line_width_ = line_width
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call EnterCriticalSection( lpCriticalSection ) 
      iretb    = DeleteObject(wnd%hPen) 
      wnd%hPen = CreatePen(PS_SOLID, line_width_, irgb(rgb_))
      iretb    = SelectObject(wnd%hDC, wnd%hPen)
      iretb    = MoveToEx(wnd%hDC, 0, 0, NULL)
      call LeaveCriticalSection( lpCriticalSection )  
    end associate
    return
  end subroutine gr_pen
  !----------------------------------------------------------------
  integer function irgb(rgb)
    type(t_rgb), intent(in) :: rgb
    irgb = rgb%ir + (rgb%ig + (rgb%ib * 256)) * 256
    return
  end function irgb
  !----------------------------------------------------------------
  subroutine gr_moveTo(self, ix, iy)
    class(t_win32), intent(in) :: self
    integer, intent(in) :: ix, iy
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    integer (BOOL):: iretb
    associate(wnd => self%wnd)
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call EnterCriticalSection( lpCriticalSection )  
      iretb = MoveToEx(wnd%hDC, ix, iy, NULL)
      call LeaveCriticalSection( lpCriticalSection )  
    end associate
    return
  end subroutine gr_moveTo
  !----------------------------------------------------------------
  subroutine gr_lineTo(self, ix, iy)
    class(t_win32), intent(in) :: self
    integer, intent(in) :: ix, iy
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    integer (BOOL):: iretb
    associate(wnd => self%wnd)
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call EnterCriticalSection( lpCriticalSection ) 
      iretb = LineTo(wnd%hDC, ix, iy)
      call LeaveCriticalSection( lpCriticalSection ) 
    end associate
    return
  end subroutine gr_lineTo
  !-------------------------------------------------------------------------------------
  subroutine gr_dot(self, ix, iy, icol)
    class(t_win32), intent(in) :: self
    integer, intent(in) :: ix, iy, icol
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection
    integer (BOOL):: iretb
    associate(wnd => self%wnd)
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call EnterCriticalSection( lpCriticalSection ) 
      iretb = SetPixel(wnd%hDC, ix, iy, icol)
      call LeaveCriticalSection( lpCriticalSection ) 
    end associate
    return
  end subroutine gr_dot
  !----------------------------------------------------------------
  subroutine gr_text(self, ix, iy, txt, rgb, ifontsize, ifontdirection)
    class(t_win32), intent(in) :: self
    integer, intent(in) :: ix, iy
    character (LEN = *), intent(in) :: txt
    type (t_rgb), intent(in), optional :: rgb
    integer, optional, intent(in) :: ifontsize, ifontdirection
    integer (BOOL)   :: iretb
    integer (HANDLE) :: hFont
    integer :: kfontsize, kfontdirection
    type (T_RTL_CRITICAL_SECTION), pointer :: lpCriticalSection

    associate(wnd => self%wnd)
      if ( present(rgb) ) iretb = SetTextColor(wnd%hDC, irgb(rgb))
      if ( present(ifontsize) ) then 
        kfontsize = ifontsize
      else
        kfontsize = 10
      end if
      if ( present(ifontdirection) ) then
        kfontdirection = ifontdirection
      else  
        kfontdirection = 0
      end if
      call c_f_pointer(c_loc(self%CriticalSection), lpCriticalSection)
      call EnterCriticalSection( lpCriticalSection ) 
      iretb = SetBkMode(wnd%hDC, TRANSPARENT)
      hFont = CreateFont( kfontsize , 10 , kfontdirection , 0 ,FW_DONTCARE , FALSE , FALSE , FALSE ,  &
                     ANSI_CHARSET , OUT_DEFAULT_PRECIS ,                   &
                         CLIP_DEFAULT_PRECIS , PROOF_QUALITY ,                 &
                       ior(FIXED_PITCH,  FF_ROMAN) , NULL            )
      iretb = SelectObject(wnd%hdc , hFont)
      iretb = TextOut(wnd%hDC, ix, iy, txt, len_trim(txt))
      iretb = SelectObject(wnd%hdc , GetStockObject(SYSTEM_FONT))
      iretb = DeleteObject(hFont)
      call LeaveCriticalSection( lpCriticalSection ) 
    end associate
    return
  end subroutine gr_text
 end module m_win32

module m_plot
  use m_oop
  use m_win32
  implicit none
  private
  public :: t_rgb, t_device, t_win32, t_wnd
end module m_plot
module m_mandel
  implicit none  
  integer, private, parameter :: kd = SELECTED_REAL_KIND(15)
contains
  pure elemental integer function imandel(z)
    complex(kd), intent(in) :: z
    complex(kd) :: c
    c = (0.0_kd, 0.0_kd)
    do imandel = 150, 1, -1 
      if (abs(c) > 2.0_kd) exit
      c = c * c - z 
    end do
    return
  end function imandel
end module m_mandel

module m_jacobi
  implicit none
contains
  subroutine laplace(v) 
    real, intent(out) :: v(-50:50, -50:50)
    logical :: mask(lbound(v, 1):ubound(v, 1), lbound(v, 2):ubound(v, 2))
    integer :: i, j, iter
    mask = .true.
    mask(-10, -5:5) = .false. ! static voltage
    mask( 10, -5:5) = .false. 
    v = 0.0
    v(-10, -5:5) =  10.0 
    v( 10, -5:5) = -10.0
  !
    do iter = 1, 200 
      forall (i = lbound(v, 1) + 1:ubound(v, 1) - 1, j = lbound(v, 2) + 1:ubound(v, 2) - 1, mask(i, j)) 
        v(i, j) = 0.25 * ( v(i - 1, j) + v(i + 1, j) + v(i, j - 1) + v(i, j + 1) )
      end forall
    end do   
    return
  end subroutine laplace
  
end module m_jacobi
!==================================================================
 
program Mandel
  use m_plot
  use m_mandel
  use m_jacobi
  implicit none
  integer, parameter :: kd = SELECTED_REAL_KIND(15)
  integer, parameter :: m = 1000
  integer :: nwinx = 800, nwiny = 600
  integer :: i, j, k, imax, jmax, maxiter, icount, ix, iy
  real (kd) :: xmin, xmax, ymin, ymax 
  real (kd) :: xmin1, xmax1, ymin1, ymax1 
  real (kd) :: x, y, z, dx, dy, dz, a, b, c, d, p
  real (kd) :: t0, t1 
  real :: v(-50:50, -50:50)
  integer, allocatable :: ic(:, :)
  integer :: icol(0:m), it0, it1

  class(t_device), allocatable :: fig1, fig2, fig3, fig4, fig5 
  type(t_rgb), parameter :: rgb_black = t_rgb(0, 0, 0)
!
  xmin = -2.0d0 
  xmax =  2.0d0 
  ymin = -2.0d0 
  ymax =  2.0d0  
  maxiter = 150
!
  dx = xmax - xmin
  dy = ymax - ymin
  if (dx <= 0.0_kd .OR. dy <= 0.0_kd .OR. maxiter <= 0 .OR. maxiter > M) stop 'input error'
  if (dx * nwinx > dy * nwiny) then
    imax = nwinx
    jmax = nint(nwinx * dy / dx)
  else
    imax = nint(nwiny * dx / dy)
    jmax = int(nwiny)
  end if
!
  dx = dx / real(imax, kd)
  dy = dy / real(jmax, kd)
  icol(0) = 0 ! black
  j = irgb(255, 255, 255)
  do i = maxiter, 1, -1
   icol(i) = j 
   if (j > 1) j = j - irgb(255, 255, 255) / maxiter
  end do
!
  allocate( ic(0:imax, 0:jmax) )  
  call system_clock(it0)
  call cpu_time(t0)
  do concurrent (i = 0:imax, j = 0:jmax) 
    x = xmin + i * dx
    y = ymax - j * dy
    ic(i, j) = imandel(cmplx(x, y, kd))
  end do
  call cpu_time(t1)
  call system_clock(it1)
  print *, ' do concurrent time =', t1 - t0, it1 - it0
!
  allocate(fig1, source = t_win32('Mandelbrot 1', imax, jmax, 1, rgb_black))
  call fig1%on()
  do i = 0, imax
    do j = 0, jmax
      call fig1%dot(i, j, icol(ic(i, j)))  
    end do
    call fig1%show()
  end do
  deallocate( ic )
!
  xmin = 1.10950d0
  xmax = 1.10951d0
  ymin = 0.24758d0 
  ymax = 0.24759d0 
!
  dx = xmax - xmin
  dy = ymax - ymin
  if (dx <= 0.0_kd .OR. dy <= 0.0_kd .OR. maxiter <= 0 .OR. maxiter > M) stop 'input error'
  if (dx * nwinx > dy * nwiny) then
    imax = nwinx
    jmax = nint(nwinx * dy / dx)
  else
    imax = nint(nwiny * dx / dy)
    jmax = int(nwiny)
  end if
!
  dx = dx / real(imax, kd)
  dy = dy / real(jmax, kd)
  allocate( ic(0:imax, 0:jmax) )  
  call system_clock(it0)
  call cpu_time(t0)
  do concurrent (i = 0:imax, j = 0:jmax) 
    x = xmin + i * dx
    y = ymax - j * dy
    ic(i, j) = imandel(cmplx(x, y, kd))
  end do
  call cpu_time(t1)
  call system_clock(it1)
  print *, ' do concurrent time =', t1 - t0, it1 - it0
!
  allocate(fig2, source = t_win32('Mandelbrot 2', imax, jmax, 1, rgb_black))
  call fig2%on()
  do i = 0, imax
    do j = 0, jmax
      call fig2%dot(i, j, icol(ic(i, j)))  
    end do
    call fig2%show()
  end do
!
  allocate(fig3, source = t_win32('Lorenz attractor', 800, 600, 1, rgb_black))
  call fig3%on()
  call fig3%pen(2, t_rgb(255, 125, 0))
  a = 10.0d0
  b = 28.0d0
  c = 8.0d0 / 3.0d0
  d = 0.01d0
  x = 1.0d0
  y = 1.0d0
  z = 1.0d0
  do k = 1, 3000
    dx = a * (y - x)
    dy = x * (b - z) - y
    dz = x * y - c * z
    x = x + d * dx
    y = y + d * dy
    z = z + d * dz
    if (k < 100) call fig3%moveTo( INT(12 * (x + 30)), INT(12 * z) )
    call fig3%lineTo( INT(12 * (x + 30)), INT(12 * z) )
    call fig3%show()
  end do
 ! 
  allocate(fig4, source = t_win32('Chaos', 640, 480, 1, rgb_black))
  call fig4%on()
  do ix = 1, 640
    p = 0.3
    x = ix * (3.0 - 1.5) / 640.0 + 1.5 
    do i = 1, 50
      p = p + x * p * (1.0 - p)
    end do
    do i = 51, 100
      y = p / 1.5 * 480.0
      call fig4%dot(ix, 480 - INT(y), irgb(0, 255, 122))
       p = p + x * p * (1 - p)
    end do
    call fig4%show()
  end do
  !
  allocate(fig5, source = t_win32('Laplace', 1200, 600, 1, rgb_black))
  call fig5%on()
  call laplace(v)
! x-direction  
  do i =  lbound(v, 2), ubound(v, 2)
    ix = 600 + 10 * lbound(v, 2) + 2 * i
    iy = 300 - 3 * i 
    call fig5%moveto(ix, iy)
    do j =  lbound(v, 1), ubound(v, 1)
      ix = 600 + 10 * j + 2 * i 
      iy = 300 - 3 * i - v(j, i) * 20 
      call fig5%lineto(ix, iy)
    end do
  end do
! y-direction
  do j =  lbound(v, 1), ubound(v, 1)
    ix = 600 + 10 * j + 2 * lbound(v, 2) 
    iy = 300 - 3 * lbound(v, 2)
    call fig5%moveto(ix, iy)
    do i = lbound(v, 2), ubound(v, 2)
      ix = 600 + 10 * j + 2 * i 
      iy = 300 - 3 * i - v(j, i) * 20
      call fig5%lineto(ix, iy)
    end do
  end do
  call fig5%show()
 
 
  call fig1%off()
  deallocate(fig1)
  
  call fig2%off()
  deallocate(fig2)
  
  call fig3%off()
  deallocate(fig3)
  
  call fig4%off()
  deallocate(fig4)
  
  call fig5%off()
  deallocate(fig5)

  stop
contains 
  integer function irgb(ir, ig, ib)
    implicit none
    integer, intent(in) :: ir, ig, ib
    irgb = ir + (ig + (ib * 256)) * 256
    return
  end function irgb
end program Mandel