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Re: TVIM display routine on 24-bit displays



As an afterthought, I decided to include the actual TVIM routine, just
in case...

As I say, help would be greatly appreciated on this issue.
Dave

;+
; ROUTINE:  tvim
;
; USEAGE:   tvim,a
;
;           tvim,a,scale=scale,range=range,xrange=xrange,yrange=yrange,$
;                aspect=aspect,title=title,xtitle=xtitle,ytitle=ytitle,$
;                noaxis=noaxis,interp=interp,colors=colors,c_map=c_map,$
;                stitle=stitle,rmarg=rmarg,clip=clip,labels=labels,$
;               
pcharsize=pcharsize,lcharsize=lcharsize,nbotclr=nbotclr,&
;                clevels=clevels,nodata=nodata,rgb_nodata=rgb_nodata,$
;               
barwidth=barwidth,position=position,noframe=noframe,rct=rct, $
;		 subtitle=subtitle
;
; PURPOSE:  Display an image with provisions for
;               
;            1. numbered color scale 
;            2. plot title
;            3. annotated x and y axis 
;            4. simplified OPLOT capability
;            5. manual or automatic scaling with smooth or discreet
colors
;            6  special treatment of "invalid data" pixels
;
; INPUT    
;   a           image quantity
;
; Optional keyword input:
;
;  title
;    plot title
;
;  xtitle
;    x axis title
; 
;  ytitle
;    y axis title
;
;  stitle
;    color key title (drawn to the right of color scale)
;
;  rmarg 
;    right margin expansion factor to provide more room for extra wide
;    color scale annotation (default=1)
;
;  xrange
;    array spanning entire x axis range. (default = [0,x_dimension-1])
;
;  yrange
;    array spanning entire y axis range. (default = [0,y_dimension-1])
;
;    NOTE:TVIM only uses min(XRANGE), max(XRANGE), min(YRANGE) and
max(YRANGE).
;
;  scale
;    if set draw color scale.  SCALE=2 causes steped color scale
;
;  range
;    two or three element vector indicating physical range over which
;    to map the color scale.  The third element of RANGE, if specified, 
;    sets the step interval of the displayed color scale.  It has no
;    effect when SCALE is not set. E.g., RANGE=[0., 1., 0.1] will
;    cause the entire color scale to be mapped between the physical
;    values of zero and one; the step size of the displayed color
;    scale will be set to 0.1.
;
;  clip
;    specifies a set percentage of pixels which will be left outside
;    the color scale.  Larger values of CLIP yield images with greater
;    contrast. For example if clip=2 then the color scale range will
;    be set to include 98% of the pixels and to exclude the brightest
;    1% and the dimmest 1% of the pixel brightness distribution.
;    Keyword RANGE overides the effect of CLIP.
;
;    If CLIP is a two element vector, the upper and lower percentile
;    range can be specified.  For example CLIP=[0,95] will exclude the
;    top 5%.  
;
;    An alternative is to set CLIP to a single negative integer.  This
;    causes the grey scale range to be obtained from the max and min
;    value of the image array after it is filtered by a 2-D median
;    filter. The radius of the median filter is set to -clip.  Median
;    filtering is effective in removing "salt and pepper" noise,
;    (isolated high or low values). For example, setting clip=-1
;    causes the code to check the 9 element superpixel centered at
;    each pixel for median values.  A single extremely large or small
;    value does not affect the final value of the median at each pixel
;    point.
;
;  aspect
;    the x over y aspect ratio of the output image. If not set, aspect
;    is set to (size_x/size_y) of the input image.
;
;  position
;    specifies the lower left and upper right TVIM frame position in
;    normal coordinates.  When set POSITION overides the setting of
;    ASPECT.
;
;  noaxis
;    if set do not draw x and y numbered axis around image. Instead
;    just draw a box
;
;  noframe
;    if set no not draw anything around image, not even a box
;
;  interp
;    TVIM normally uses nearest neighbor sampling to resize the image
;    to fill the data window area. If INTERP is set the resizing
;    operation uses bilinear interpolation
;
;    If INTERP = 2 the interpolation range is adjusted so that there
;    is a half pixel border around the plot.  This ensures that the
;    smoothed image properly represents the cell center values of the
;    pixels, but introduces an extrapolation on the outer edges.  This
;    option has noticeable effects for small (<20) image arrays.
;    
;    NOTE: When writing to a Postscript file the resizing operation is
;    accomplished by changing the pixel size.  Thus the INTERP
;    parameter has no effect on Postscript output.
;
;  pcharsize
;    character size of numbers along x and y axis and the title
;    (default is !p.charsize if non-zero, 1 otherwise)
; 
;    NOTE: The character size of the x and y-axis number scale
;    annotation may be independently controlled by the !x.charsize or
;    !y.charsize system variables.  For example, the x and y axis
;    number scale characters may be made invisible by setting these
;    variables to a very small non-zero number before calling TVIM.
;    Remember to restore normal character sizes by setting !x.charsize
;    and !y.charsize to 1 or zero after the call to TVIM.
;
;  lcharsize
;    character size of color key number or labels (default is
;    !p.charsize if non-zero, 1 otherwise)
;
;  barwidth
;     width of color key which appears to right of image when SCALE is
;     set.  (default=1)
;
;  labels
;     a vector of strings used to label the color key levels.  If not
;     set the default color key number labels are used.  If the number
;     of elements in LABELS is the same as the number of elements in
;     COLORS then the labels will appear in the middle of a given
;     color band instead of at the boundary between colors.  If COLORS
;     is not set the number of elements in LABELS should be at least
;     as large as the number of color key segments plus one.
;
;  colors
;     an array of color indicies.  When the COLORS array is set TVIM
;     will map values of A into the color values specified in COLORS.
;     How physical values are assigned to color values depends on how
;     the RANGE parameter is set, as shown in this table:
;     
;             RANGE           color_value
;             -----           -----------
;       1.  not set          COLORS(A)
;       2.  [amin,amax]      COLORS((A-amin)/dinc)
;       3.  [amin,amax,inc]  COLORS((A-amin)/inc)
;     
;     where amin, amax and inc are user specified elements of RANGE
;     and dinc=(amax-amin)/n_elements(COLORS).  In case 1, A is used
;     directly as a subscript into COLORS.  When RANGE is not set
;     legend labels should be used to annotate the color values. In
;     case 2, A is scaled so that each color defined in COLORS
;     represents a proportionate fraction of the total dynamic range.
;     In case 3, amin and inc (and not amax) are used to control which
;     colors are associated with given physical values.  See examples.
;
;  c_map
;     TVIM normally rescales the input image to span the entire color
;     table range. Setting C_MAP disables this automatic re-scaling.
;     This is useful when the image byte values correspond to a
;     particular color mapping that could be destroyed by the
;     rescaling process (E.G.  a gif image).
;     
;     NOTE: When the number of IDL color table entries is less than
;     256 some colors may be lost. Use a private color map to avoid
;     this. See examples.
;               
;  nbotclr
;     number of reserved colors at the bottom of the color
;     table.  Color values between 0 and nbotclr-1 will not
;     be used in the displayed image.  This allows the
;     bottom of the table to be set to special colors which
;     will not be used in the displayed the image.  This
;     keyword is disabled when either the COLORS or NODATA 
;     options are used.  (default=1)
;
;     NOTE: by default the color table indicies used within a TVIM
;     image is limited to the range 1 to !d.n_colors-2. In most
;     predefined color tables, color index 0 and !d.n_color-1
;     correspond to pure black and white, respectively. TVIM uses
;     these color indicies as background and foreground colors for
;     region blanking and axis annotation. Color tables which do not
;     define black and white in these index locatations are not good
;     choices for TVIM plots, unless the first and last color table
;     entries are redefined as black and white using TVLCT, e.g.,
;     tvlct,0,0,0,0 & tvlct,255,255,255,!d.n_colors-1
;     
;     NOTE: the procedure DCOLORS can be used to load a set
;     of discreet colors in the bottom 11 color values
;     (0-10). The original color table is resampled to fit
;     between color value 11 and the !d.n_colors-1.
;             
;
;  nodata
;     pixel values which are interpreted as invalid data.  Pixels
;     containing this data value are colored with color RGB_NODATA.
;
;  rgb_nodata
;     an RGB value (a 3 component vector) used to color pixels filled
;     with invalid data. (default = [0,0,0])
;
;     NOTE: NODATA and RGB_NODATA override the effect of NBOTCLR
;
;  rct
;     if set, reverse direction of color table.  This keyword can be
;     used on black & white printers to allow large field values to be
;     represented by dark colors.
;
;  subtitle
;     if used adds a subtitle to the plot. Added by dcjk, QUB, 97.
;               
; KEYWORD OUTPUT:
;  CLEVELS 
;     physical values at the color key tic marks.  Use this to set
;     contour levels in a subsequent call to CONTOUR.
;
; SIDE EFFECTS: 
;     Setting SCALE=2 changes the color scale using the STEP_CT
;     procedure.  The color scale may be returned to its original
;     state by the command, STEP_CT,/OFF
;
; PROCEDURE:
;     TVIM first determines the size of the plot data window with a
;     dummy call to PLOT.  When the output device is "X", CONGRID is
;     used to scale the image to the size of the available data
;     window.  Otherwise, if the output device is Postscript,
;     scaleable pixels are used in the call to TV.
;     
;     If the input image quantity is not of type byte, TVIM converts
;     them to byte by scaleing the input between 0 and !d.n_colors-1.
;     If the input is already a byte array and if either the number of
;     color table entries is 256 or if C_MAP is set, then no scaling
;     is done.  This is to ensure consistency with specially defined
;     private color tables.
;     
;     After the the image is drawn TVIM calls PLOT again to draw the x
;     and y axis and titles.  Finally if scale is set, TVIM calls the
;     COLOR_KEY procedure to draw the color scale just to the right of
;     the data window.
;
; RESTRICTIONS: 
;     A stepped color scale (SCALE = 2 option) is not available when
;     writing to a black & white postscript file (i.e., when the
;     DEVICE color option is not enabled).
;
; DEPENDENCIES: COLOR_KEY, STEP_CT, PRANK
;
; EXAMPLES:
;
;;    Plot a GIF image with its own preset RGB
;;    table (perhaps from a digitized video image)
;
; window,colors=256            ; set up a private color map
; read_gif,file,im,r,g,b
; tvlct,r,g,b
; tvim,im,/c_map
;;
;;
;;    Plot an image with descreet greyscale values to a printer
;;    which has its own hard-wired color table.
;
; im=randata(128,128,s=4)
; immx=max(im) & immn=min(im)
; !p.multi=[0,2,2]
; tvim,im,/scale,colors=!p.color*indgen(4)/3.,range=[immn,immx]
; tvim,im,/scale,colors=!p.color*indgen(5)/4.,range=[immn,immx]
; tvim,im,/scale,colors=!p.color*indgen(8)/7.,range=[immn,immx]
; tvim,im,/scale,colors=!p.color*indgen(10)/9.,range=[immn,immx]
;;
;;
;;    Display a map of surface types (green=veg, blue=water, red=sand)
;;    Notice how RANGE is used to associate physical values with colors.
;;    (use im from the previous example)
;
; im=randata(128,128,s=4)
; immx=max(im) & immn=min(im) & delim=immx-immn
; 
; tvlct,[0,0,0,255],[0,255,0,0],[0,0,255,0]
; !p.multi=[0,2,2]
; colors=[1,2,3] & labels=[' veg',' water',' sand']
; range=[immn,immx,delim/3]
; 
; tvim,im,/scale
; 
; tvim,im,colors=colors,range=range,/scale
; 
; tvim,im,colors=colors,range=range,/scale,labels=labels,lch=2
; 
; !p.multi=0
; range=[immn-.25*delim,immx+.25*delim,delim/2]
; lbl=[' veg!c region 1',' water!c region 2',' sand!c region 3']
;
tvim,im,colors=colors,range=range,/scale,labels=lbl,lch=2,rmarg=2,pchar=1.2
;;
;;
;;   Display the image from previous example and overlay a contour plot
;;
; loadct,5
; im=randata(128,128,s=4)
; immx=max(im) & immn=min(im) & delim=immx-immn
; xrange=[-120,-100]
; yrange=[20,50]
; range=[immn,immx]
; xx=findrng(xrange,128)
; yy=findrng(yrange,128)
;
; tvim,im,/scale,xrange=xrange,yrange=yrange,clevels=clevels,range=range
; contour,im,xx,yy,levels=clevels,/overplot
;
;
;;    NOTE: You might prefer the results obtained from procedure
CONFILL.
;         
; confill,im,xx,yy,/asp,levels=clevels
;;
;; 
;;    Display a grey scale image and annotate certain points in color
;;
; loadct,0
; dcolors
; tvim,im,/scale,nbotclr=11
; xx=interpolate([40,80],randomu(iseed,10))
; yy=interpolate([40,80],randomu(iseed,10))
; plots,xx,yy,psym=2,color=1+indgen(10)
;  
;;
;; 
;;    Display a grey scale image and show nodata values in red
;;
; loadct,0
; im=randata(100,100,s=4.5)
; im(randomu(iseed,50)*9999)=-999.
; tvim,im,/scale,nodata=-999.,rgb_nodata=[255,0,0]
;  
;;
;;
;;    Postscript output with a reversed color scale.  Because the
;;    background color is always RGB=(255,255,255) you must set the
;;    default color, !p.color, to a dark color if you want good contrast
;;    between the axis labels and the white paper.   According to 
;;    Didier's reversed color table a color index of 255 should produce
;;    black, but for some reason !p.color=255 doesn't work right.
;;    I think IDL is iterpreting !p.color=255 in some special way.
;;    So instead use !p.color=254; this seems to work fine.
;;
; toggle,/color
; loadct,28
; !p.color=254              ; don't use 255, don't ask me why
; tvim,dist(20),/scale
; toggle
;               
;;
;; display data defined on a regular LAT-LON grid onto a given map 
;; projection.  USE MAP_SET and MAP_IMAGE to create the map projection
;; and to warp the image.  Then use BOXPOS to position the TVIM frame
;; to correctly register the map and image
;
; IMAGE = sin(!pi*findrng(0,24,200))#sin(!pi*findrng(0,12,200))
; !p.multi=[0,1,2]
; map_set,45,0,/ortho,/advance,pos=boxpos(/aspect)
;
newimage=map_image(image,/bilin,latmin=-90,latmax=90,lonmin=-180,lonmax=180)
; tvim,newimage,title='Warped data',pos=boxpos(/get),/scale
; map_set,45,0,/ortho,pos=boxpos(/get),/grid,/cont,/noerase ; draw map
; tvim,image,xrange=[-180,180],yrange=[-90,90],/scale, $
;     title='Unwarped data',xtitle='Longitude',ytitle='Latitude'
; map_set,0,0,/cyl,pos=boxpos(/get),/grid,/cont,/noerase ; draw map
;
;; use MAP_SET2 to mask out land areas. Note that the example below is
;; unusual.   MAP_SET2 doesn't always produce such nicely filled land
areas.
;; Typically one must run MAP_SET2 with /SAVE
;; to create a ascii file containing the continental boundary lat-lon
;; coordinates. Then use an editor  to group the continental coordinates 
;; line segments to form closed contours which POLYFILL can understand 
;; (the call to POLYFILL is enabled by setting con_color).
;;  
;
; image=randata(256,256,s=2.5)
; tvim,image
;
map_set2,-64,-64,/cont,limit=[-65.1,-64.5,-64,-62],/ortho,con_col=100,$
;           pos=boxpos(/get),/noerase,/grid
;;               
; AUTHOR:       Paul Ricchiazzi    oct92 
;               Earth Space Research Group, UCSB
;
; REVISIONS:
; 28jan93: switched from PUT_COLOR_SCALE to COLOR_KEY
; 11feb93: added INTERP keyword
; 11feb93: added C_MAP keyword
; 11feb93: added STITLE keyword
; 20apr93: added RMARG keyword, centered image in plot window
; 23apr93: call COLOR_KEY before TV. Now stepped color scales copy to PS
file
; 10sep93: deal with perfectly flat images. No more math error when a=0
; 14sep93: added CLIP keyword
; 11feb94: added PCHARSIZE,LCHARSIZE,LABELS, and COLORS keywords
; 18feb94: added NBOTCLR keyword
; 16mar94: added INTERP=2 option and adjusted centering of pixels
; 08Jul94: added NODATA and RGB_NODATA keywords
; 04Aug94: added BARWIDTH keyword 
; 04Aug94: defaulted PCHARSIZE and LCHARSIZE to !P.CHARSIZE if non-zero
; 02Mar95: added POSITION keyword
; 31Mar95: added NOAXIS keyword
; 24may95: initial sizing includes allowance for PCHARSIZE > 1
; 06sep95: color indecies used in plot now run from 1 to !d.ncolors-2
; 24jul96: do a REFORM(a) to allow tvim,a(1,*,*)
;-

pro tvim,a,scale=scale,range=range,xrange=xrange,yrange=yrange,$
        aspect=aspect,title=title,xtitle=xtitle,ytitle=ytitle,$
       
noframe=noframe,noaxis=noaxis,interp=interp,colors=colors,c_map=c_map,$
       
stitle=stitle,rmarg=rmarg,clip=clip,labels=labels,clevels=clevels,$
       
pcharsize=pcharsize,lcharsize=lcharsize,nbotclr=nbotclr,nodata=nodata,$
       
rgb_nodata=rgb_nodata,barwidth=barwidth,position=position,rct=rct, $
        subtitle=subtitle
if n_params() eq 0 then begin
  xhelp,'tvim'
  return
endif  

if keyword_set(pcharsize) eq 0 then begin
  if !p.charsize eq 0 then pcharsize=1 else pcharsize=!p.charsize
endif

if keyword_set(lcharsize) eq 0 then begin
  if !p.multi(1)>!p.multi(2) gt 2 then lcharsize=.5*pcharsize $
                                  else lcharsize=pcharsize
endif

sz=size(reform(a))
nx=sz(1)
ny=sz(2)
nxm=nx-1
nym=ny-1
plot, [0,1],[0,1],/nodata,xstyle=4,ystyle=4,charsize=pcharsize
px=!x.window*!d.x_vsize
py=!y.window*!d.y_vsize
xsize=px(1)-px(0)
ysize=py(1)-py(0)

if keyword_set(scale) or keyword_set(rmarg) then begin
  if keyword_set(rmarg) eq 0 then rmarg=1.
  xmarg=!d.x_ch_size*(4+4*lcharsize)
  if keyword_set(stitle) then xmarg=xmarg+2*!d.y_ch_size*lcharsize
  xsize=xsize-rmarg*xmarg
endif
oxs=xsize
oys=ysize
if keyword_set(aspect) eq 0 then aspect=float(nx)/ny
if xsize gt ysize*aspect then xsize=ysize*aspect else ysize=xsize/aspect 
if xsize lt oxs then px(0)=px(0)+.5*(oxs-xsize)
if ysize lt oys then py(0)=py(0)+.5*(oys-ysize)
px(1)=px(0)+xsize
py(1)=py(0)+ysize

if keyword_set(position) then begin
  px=position([0,2])*!d.x_vsize
  py=position([1,3])*!d.y_vsize
  xsize=px(1)-px(0)
  ysize=py(1)-py(0)
endif

pos=[px(0),py(0),px(1),py(1)]
;
;max_color=!d.n_colors-1
max_color=!d.n_colors-2
;
if keyword_set(title) eq 0 then title=''
if keyword_set(subtitle) eq 0 then subtitle=''

amax=float(max(a))
amin=float(min(a))
;print, 'a      min and max  ',   amin,amax

num_range=n_elements(range)

if n_elements(nodata) then begin
  if n_elements(rgb_nodata) eq 0 then rgb_nodata=[0,0,0]
  iinodata=where(a eq nodata,ncnd)
  iidata=where(a ne nodata,ncgd)
  if ncgd gt 0 then begin
    amin=float(min(a(iidata)))
    amax=float(max(a(iidata)))
    tvlct,rgb_nodata(0),rgb_nodata(1),rgb_nodata(2),1
    nbotclr=2
  endif
endif else begin
  iinodata=-1
endelse
  
if num_range eq 1 then message,'must specify either 2 or 3 elements of
RANGE'

if num_range eq 0 then begin
  if amin eq amax then begin
    case 1 of
      amax eq 0.: rng=[-1,1.]
      amax gt 0.: rng=[0,2*amax]
      amax lt 0.: rng=[2*amax,0]
    endcase
  endif else BEGIN
    CASE n_elements(clip) OF
      1:if clip ge 0 then begin
          rng=prank(a,[clip,100-clip])
        endif else begin
          clp=-2*clip+1
          ix1=-clip & ix2=nx+clip
          iy1=-clip & iy2=ny+clip
          rng=[min((median(a,clp))(ix1:ix2,iy1:iy2),max=mx),mx]
        endelse
      2:rng=prank(a,clip)
      else:rng=[amin,amax] 
    endcase
  endelse
endif else begin
  rng=range(0:1)
  if num_range eq 3 then inc=range(2) else inc=0
endelse

ncolors=n_elements(colors)

case 1 of

  ncolors ne 0 : begin
    case num_range of 
      0:begin
         aa=colors(fix(reform(a)))
         rng=[0,ncolors]
         inc=1
        end
      2:begin
         clrinc=(rng(1)-rng(0))/ncolors
         aa=colors(fix((reform(a)-range(0))/clrinc))
        end
      3:begin
         aa=colors(fix((reform(a)-range(0))/range(2)))
         inc=range(2)
         rng=[range(0),range(0)+ncolors*inc]
        end
    endcase
  end

  keyword_set(c_map) eq 1 : begin
    aa=byte(reform(a))
    rng(0)=0
    rng(1)=max_color
  end

  else: begin
;    if keyword_set(nbotclr) eq 0 then nbotclr=0 else nbotclr=nbotclr
    if keyword_set(nbotclr) eq 0 then nbotclr=1 else nbotclr=nbotclr
    max_color=max_color-nbotclr
    aa=nbotclr+max_color*((float(reform(a))-rng(0))/(rng(1)-rng(0)) > 0.
< 1.)
  end
endcase

if keyword_set(rct) then begin
  aamin=min(aa,max=aamax)
  aa=aamax+aamin-aa
endif else begin
  rct=0
endelse
;
posbar=[px(1)+!d.x_ch_size,py(0)]
if keyword_set(scale) then begin
  if scale eq 2 then step=1 else step=0
  if not keyword_set(barwidth) then barwidth=1
  if ncolors eq 0 then begin
    color_key,pos=posbar,ysize=ysize,range=rng,inc=inc,step=step,$
         title=stitle,charsize=lcharsize,labels=labels,nbotclr=nbotclr,$
         clevels=clevels,barwidth=barwidth,rct=rct
  endif else begin
    color_key,pos=posbar,ysize=ysize,range=rng,inc=inc,title=stitle,$
          
charsize=lcharsize,colors=colors,labels=labels,clevels=clevels,$
           barwidth=barwidth,rct=rct
  endelse
endif

if not keyword_set(interp) then interp=0

if iinodata(0) ne -1 then aa(iinodata)=1

if !d.name eq 'X' then begin
  mone=interp
  if interp lt 2 then begin
    tv,congrid(aa,xsize,ysize,interp=interp,minus_one=mone),px(0),py(0)
  endif else begin
    tv,interpolate(aa,nx*findgen(xsize)/(xsize-1)-.5,$
                      ny*findgen(ysize)/(ysize-1)-.5,/grid),px(0),py(0)
  endelse
endif else begin
  tv,aa,px(0),py(0),xsize=xsize,ysize=ysize,/device
endelse

;
if keyword_set(xtitle) eq 0 then xtitle=''
if keyword_set(ytitle) eq 0 then ytitle=''

if not keyword_set(xrange) then xrng=[0,nxm] $
                           else xrng=[min(xrange), max(xrange)]
if not keyword_set(yrange) then yrng=[0,nym] $
                           else yrng=[min(yrange), max(yrange)]

case 1 of 

  keyword_set(noframe):plot,[0,0],[0,0],xstyle=5,ystyle=5,position=pos,$
                         title=title, subtitle=subtitle,/device,
charsize=pcharsize, $
                         xrange=xrng,yrange=yrng,/noerase,/nodata
                         
  keyword_set(noaxis): plot,[0,0],[0,0],/xstyle,/ystyle,position=pos,$
                        
title=title,xtitle=xtitle,ytitle=ytitle,/device, $
                         xrange=xrng,yrange=yrng,/noerase,/nodata,$
                         charsize=pcharsize,xticks=1,yticks=1,$
                         xtickname=[" "," "],ytickname=[" "," "], $
                         subtitle=subtitle

  else:               
plot,[0,0],[0,0],/xstyle,/ystyle,title=title,/nodata,$
                        
xtitle=xtitle,ytitle=ytitle,xrange=xrng,yrange=yrng,$
                        
position=pos,/noerase,/device,charsize=pcharsize, $
                         subtitle=subtitle
endcase

;
end