diff scripts/plot/draw/stemleaf.m @ 17572:7bb76a22cde1

maint: Split scripts/plot directory into 4 pieces. scripts/gui : user-interface functions scripts/plot/appearance : functions controlling plot appearance scripts/plot/draw : plotting functions which produce graphs scripts/plot/util : low-level plotting functions and utilities. * scripts/gui/guidata.m, scripts/gui/guihandles.m, scripts/gui/module.mk, scripts/gui/private/__file_filter__.m, scripts/gui/private/__fltk_file_filter__.m, scripts/gui/private/__is_function__.m, scripts/gui/private/__uigetdir_fltk__.m, scripts/gui/private/__uigetfile_fltk__.m, scripts/gui/private/__uiobject_split_args__.m, scripts/gui/private/__uiputfile_fltk__.m, scripts/gui/uicontextmenu.m, scripts/gui/uicontrol.m, scripts/gui/uigetdir.m, scripts/gui/uigetfile.m, scripts/gui/uimenu.m, scripts/gui/uipanel.m, scripts/gui/uipushtool.m, scripts/gui/uiputfile.m, scripts/gui/uiresume.m, scripts/gui/uitoggletool.m, scripts/gui/uitoolbar.m, scripts/gui/uiwait.m, scripts/gui/waitbar.m, scripts/gui/waitforbuttonpress.m: Moved from scripts/plot to scripts/gui * scripts/plot/appearance/__clabel__.m, scripts/plot/appearance/__getlegenddata__.m, scripts/plot/appearance/axis.m, scripts/plot/appearance/box.m, scripts/plot/appearance/caxis.m, scripts/plot/appearance/clabel.m, scripts/plot/appearance/daspect.m, scripts/plot/appearance/diffuse.m, scripts/plot/appearance/grid.m, scripts/plot/appearance/gtext.m, scripts/plot/appearance/hidden.m, scripts/plot/appearance/legend.m, scripts/plot/appearance/orient.m, scripts/plot/appearance/pbaspect.m, scripts/plot/appearance/private/__axis_label__.m, scripts/plot/appearance/private/__axis_limits__.m, scripts/plot/appearance/shading.m, scripts/plot/appearance/specular.m, scripts/plot/appearance/text.m, scripts/plot/appearance/title.m, scripts/plot/appearance/view.m, scripts/plot/appearance/whitebg.m, scripts/plot/appearance/xlabel.m, scripts/plot/appearance/xlim.m, scripts/plot/appearance/ylabel.m, scripts/plot/appearance/ylim.m, scripts/plot/appearance/zlabel.m, scripts/plot/appearance/zlim.m: Moved from scripts/plot to subdir appearance. * scripts/plot/draw/area.m, scripts/plot/draw/bar.m, scripts/plot/draw/barh.m, scripts/plot/draw/colorbar.m, scripts/plot/draw/comet.m, scripts/plot/draw/comet3.m, scripts/plot/draw/compass.m, scripts/plot/draw/contour.m, scripts/plot/draw/contour3.m, scripts/plot/draw/contourc.m, scripts/plot/draw/contourf.m, scripts/plot/draw/cylinder.m, scripts/plot/draw/ellipsoid.m, scripts/plot/draw/errorbar.m, scripts/plot/draw/ezcontour.m, scripts/plot/draw/ezcontourf.m, scripts/plot/draw/ezmesh.m, scripts/plot/draw/ezmeshc.m, scripts/plot/draw/ezplot.m, scripts/plot/draw/ezplot3.m, scripts/plot/draw/ezpolar.m, scripts/plot/draw/ezsurf.m, scripts/plot/draw/ezsurfc.m, scripts/plot/draw/feather.m, scripts/plot/draw/fill.m, scripts/plot/draw/fplot.m, scripts/plot/draw/hist.m, scripts/plot/draw/isocolors.m, scripts/plot/draw/isonormals.m, scripts/plot/draw/isosurface.m, scripts/plot/draw/line.m, scripts/plot/draw/loglog.m, scripts/plot/draw/loglogerr.m, scripts/plot/draw/mesh.m, scripts/plot/draw/meshc.m, scripts/plot/draw/meshz.m, scripts/plot/draw/pareto.m, scripts/plot/draw/patch.m, scripts/plot/draw/pcolor.m, scripts/plot/draw/peaks.m, scripts/plot/draw/pie.m, scripts/plot/draw/pie3.m, scripts/plot/draw/plot.m, scripts/plot/draw/plot3.m, scripts/plot/draw/plotmatrix.m, scripts/plot/draw/plotyy.m, scripts/plot/draw/polar.m, scripts/plot/draw/private/__add_datasource__.m, scripts/plot/draw/private/__bar__.m, scripts/plot/draw/private/__contour__.m, scripts/plot/draw/private/__errcomm__.m, scripts/plot/draw/private/__errplot__.m, scripts/plot/draw/private/__ezplot__.m, scripts/plot/draw/private/__interp_cube__.m, scripts/plot/draw/private/__line__.m, scripts/plot/draw/private/__marching_cube__.m, scripts/plot/draw/private/__patch__.m, scripts/plot/draw/private/__pie__.m, scripts/plot/draw/private/__plt__.m, scripts/plot/draw/private/__quiver__.m, scripts/plot/draw/private/__scatter__.m, scripts/plot/draw/private/__stem__.m, scripts/plot/draw/quiver.m, scripts/plot/draw/quiver3.m, scripts/plot/draw/rectangle.m, scripts/plot/draw/ribbon.m, scripts/plot/draw/rose.m, scripts/plot/draw/scatter.m, scripts/plot/draw/scatter3.m, scripts/plot/draw/semilogx.m, scripts/plot/draw/semilogxerr.m, scripts/plot/draw/semilogy.m, scripts/plot/draw/semilogyerr.m, scripts/plot/draw/shrinkfaces.m, scripts/plot/draw/slice.m, scripts/plot/draw/sombrero.m, scripts/plot/draw/sphere.m, scripts/plot/draw/stairs.m, scripts/plot/draw/stem.m, scripts/plot/draw/stem3.m, scripts/plot/draw/stemleaf.m, scripts/plot/draw/surf.m, scripts/plot/draw/surface.m, scripts/plot/draw/surfc.m, scripts/plot/draw/surfl.m, scripts/plot/draw/surfnorm.m, scripts/plot/draw/tetramesh.m, scripts/plot/draw/trimesh.m, scripts/plot/draw/triplot.m, scripts/plot/draw/trisurf.m, scripts/plot/draw/waterfall.m: Moved from plot/ to subdir draw. * scripts/plot/util/__actual_axis_position__.m, scripts/plot/util/__default_plot_options__.m, scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/__next_line_color__.m, scripts/plot/util/__next_line_style__.m, scripts/plot/util/__plt_get_axis_arg__.m, scripts/plot/util/__pltopt__.m, scripts/plot/util/allchild.m, scripts/plot/util/ancestor.m, scripts/plot/util/axes.m, scripts/plot/util/cla.m, scripts/plot/util/clf.m, scripts/plot/util/close.m, scripts/plot/util/closereq.m, scripts/plot/util/colstyle.m, scripts/plot/util/copyobj.m, scripts/plot/util/figure.m, scripts/plot/util/findall.m, scripts/plot/util/findfigs.m, scripts/plot/util/findobj.m, scripts/plot/util/gca.m, scripts/plot/util/gcbf.m, scripts/plot/util/gcbo.m, scripts/plot/util/gcf.m, scripts/plot/util/gco.m, scripts/plot/util/ginput.m, scripts/plot/util/gnuplot_binary.in, scripts/plot/util/graphics_toolkit.m, scripts/plot/util/hdl2struct.m, scripts/plot/util/hggroup.m, scripts/plot/util/hold.m, scripts/plot/util/isaxes.m, scripts/plot/util/isfigure.m, scripts/plot/util/ishghandle.m, scripts/plot/util/ishold.m, scripts/plot/util/isprop.m, scripts/plot/util/linkprop.m, scripts/plot/util/meshgrid.m, scripts/plot/util/ndgrid.m, scripts/plot/util/newplot.m, scripts/plot/util/print.m, scripts/plot/util/printd.m, scripts/plot/util/private/__add_default_menu__.m, scripts/plot/util/private/__fltk_ginput__.m, scripts/plot/util/private/__fltk_print__.m, scripts/plot/util/private/__ghostscript__.m, scripts/plot/util/private/__gnuplot_get_var__.m, scripts/plot/util/private/__gnuplot_ginput__.m, scripts/plot/util/private/__gnuplot_has_feature__.m, scripts/plot/util/private/__gnuplot_has_terminal__.m, scripts/plot/util/private/__gnuplot_open_stream__.m, scripts/plot/util/private/__gnuplot_print__.m, scripts/plot/util/private/__gnuplot_version__.m, scripts/plot/util/private/__go_draw_axes__.m, scripts/plot/util/private/__go_draw_figure__.m, scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/private/__tight_eps_bbox__.m, scripts/plot/util/refresh.m, scripts/plot/util/refreshdata.m, scripts/plot/util/saveas.m, scripts/plot/util/shg.m, scripts/plot/util/struct2hdl.m, scripts/plot/util/subplot.m: Moved from plot to subdir util. * etc/HACKING: Updated directory structure info. * scripts/Makefile.am, scripts/plot/appearance/module.mk, scripts/plot/draw/module.mk, scripts/plot/util/module.mk: Added new directories to build system.
author Rik <rik@octave.org>
date Fri, 04 Oct 2013 17:09:08 -0700
parents scripts/plot/stemleaf.m@b81b9d079515
children 4f43f87b7c3e 446c46af4b42
line wrap: on
line diff
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/plot/draw/stemleaf.m	Fri Oct 04 17:09:08 2013 -0700
@@ -0,0 +1,596 @@
+## Copyright (C) 2013 Michael D. Godfrey
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or
+## modify it under the terms of the GNU General Public
+## License as published by the Free Software Foundation;
+## either version 3 of the License, or (at your option) any
+## later version.
+##
+## Octave is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied
+## warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+## PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public
+## License along with Octave; see the file COPYING. If not,
+## see <http://www.gnu.org/licenses/>.
+
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} stemleaf (@var{x}, @var{caption})
+## @deftypefnx {Function File} {} stemleaf (@var{x}, @var{caption}, @var{stem_sz})
+## @deftypefnx {Function File} {@var{plotstr} =} stemleaf (@dots{})
+## Compute and display a stem and leaf plot of the vector @var{x}.
+##
+## The input @var{x} should be a vector of integers.  Any non-integer values
+## will be converted to integer by @code{@var{x} = fix (@var{x})}.  By default
+## each element of @var{x} will be plotted with the last digit of the element
+## as a leaf value and the remaining digits as the stem.  For example, 123
+## will be plotted with the stem @samp{12} and the leaf @samp{3}.  The second
+## argument, @var{caption}, should be a character array which provides a
+## description of the data.  It is included as a heading for the output.
+##
+## The optional input @var{stem_sz} sets the width of each stem.
+## The stem width is determined by @code{10^(@var{stem_sz} + 1)}.
+## The default stem width is 10.
+##
+## The output of @code{stemleaf} is composed of two parts: a
+## "Fenced Letter Display," followed by the stem-and-leaf plot itself.
+## The Fenced Letter Display is described in @cite{Exploratory Data Analysis}.
+## Briefly, the entries are as shown:
+##
+## @example
+## @group
+##
+##         Fenced Letter Display
+## #% nx|___________________     nx = numel (x)
+## M% mi|       md         |     mi median index, md median
+## H% hi|hl              hu| hs  hi lower hinge index, hl,hu hinges,
+## 1    |x(1)         x(nx)|     hs h_spreadx(1), x(nx) first 
+##            _______            and last data value.
+##      ______|step |_______     step 1.5*h_spread
+##     f|ifl            ifh|     inner fence, lower and higher
+##      |nfl            nfh|     no.\ of data points within fences
+##     F|ofl            ofh|     outer fence, lower and higher
+##      |nFl            nFh|     no.\ of data points outside outer
+##                               fences
+## @end group
+## @end example
+##
+## The stem-and-leaf plot shows on each line the stem value followed by the
+## string made up of the leaf digits.  If the @var{stem_sz} is not 1 the
+## successive leaf values are separated by ",".
+##
+## With no return argument, the plot is immediately displayed.  If an output
+## argument is provided, the plot is returned as an array of strings. 
+##
+## The leaf digits are not sorted.  If sorted leaf values are desired, use
+## @code{@var{xs} = sort (@var{x})} before calling @code{stemleaf (@var{xs})}.
+##
+## The stem and leaf plot and associated displays are described in: 
+## Ch. 3, @cite{Exploratory Data Analysis} by J. W. Tukey, Addison-Wesley, 1977.
+## @seealso{hist, printd}
+## @end deftypefn
+
+## Author: Michael D. Godfrey <michaeldgodfrey@gmail.com>
+## Description: Compute stem and leaf plot
+
+function plotstr = stemleaf (x, caption, stem_sz)
+  ## Compute and display a stem and leaf plot of the vector x.  The x
+  ## vector is converted to integer by x = fix(x).  If an output argument
+  ## is provided, the plot is returned as an array of strings.  The
+  ## first element is the heading followed by an element for each stem.
+  ##
+  ## The default stem step is 10.  If stem_sz is provided the stem
+  ## step is set to: 10^(stem_sz+1).  The x vector should be integers.
+  ## It will be treated so that the last digit is the leaf value and the
+  ## other digits are the stems.
+  ##
+  ## When we first implemented stem and leaf plots in the early 1960's
+  ## there was some discussion about sorting vs. leaving the leaf
+  ## entries in the original order in the data.  We decided in favor of
+  ## sorting the leaves for most purposes.  This is the choice
+  ## implemented in the SNAP/IEDA system that was written at that time.
+  ##
+  ## SNAP/IEDA, and particularly its stem and leaf plotting, were further
+  ## developed by Hale Trotter, David Hoagland (at Princeton and MIT),
+  ## and others.
+  ##
+  ## Tukey, in EDA, generally uses unsorted leaves.  In addition, he
+  ## described a wide range of additional display formats.  This
+  ## implementation does not sort the leaves, but if the x vector is
+  ## sorted then the leaves come out sorted.  A simple display format is
+  ## used.
+  ##
+  ## I doubt if providing other options is worthwhile.  The code can
+  ## quite easily be modified to provide specific display results.  Or,
+  ## the returned output string can be edited.  The returned output is an
+  ## array of strings with each row containing a line of the plot
+  ## preceded by the lines of header text as the first row.  This
+  ## facilitates annotation.
+  ##
+  ## Note that the code has some added complexity due to the need to
+  ## distinguish both + and - 0 stems.  The +- stem values are essential
+  ## for all plots which span 0. After dealing with +-0 stems, the added
+  ## complexity of putting +- data values in the correct stem is minor,
+  ## but the sign of 0 leaves must be checked.  And, the cases where the
+  ## stems start or end at +- 0 must also be considered.
+  ##
+  ## The fact that IEEE floating point defines +- 0 helps make this
+  ## easier.
+  ##
+  ## Michael D. Godfrey   January 2013
+
+  ## More could be implemented for better data scaling.  And, of course,
+  ## other options for the kinds of plots described by Tukey could be
+  ## provided.  This may best be left to users.
+
+  if (nargin < 2 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (! isvector (x))
+    error ("stemleaf: X must be a vector");
+  endif
+
+  if (isinteger (x))
+    ## Avoid use of integers because rounding rules do not use fix():
+    ## Example: floor (int32 (-44)/10) == -4, floor (int32 (-46)/10) = -5 !!!
+    x = single (x);
+  elseif (isfloat (x))
+    xint = fix (x);
+    if (any (x != xint))
+      warning ("stemleaf: X truncated to integer values");
+      x = xint;
+    endif
+  else
+    error ("stemleaf: X must be a numeric vector");
+  endif
+
+  if (! ischar (caption))
+    error ("stemleaf: CAPTION must be a character array");
+  endif
+
+  if (nargin == 2)
+    stem_step = 10;
+  else
+    if (isscalar (stem_sz) && stem_sz >= 0 && isreal (stem_sz))
+      stem_sz = fix (stem_sz);
+      stem_step = 10^(stem_sz+1);
+    else
+      error ("stemleaf: STEM_SZ must be a real integer >= 0");
+    endif
+  endif
+
+  ## Note that IEEE 754 states that -+ 0 should compare equal. This has
+  ## led to C sort (and therefore Octave) treating them as equal.  Thus,
+  ## sort([-1 0 -0 1]) yields [-1 0 -0 1], and sort([-1 -0 0 1])
+  ## yields: [-1 -0 0 1].  This means that stem-and-leaf plotting cannot
+  ## rely on sort to order the data as needed for display.
+  ## This also applies to min()/max() so these routines can't be relied
+  ## upon if the max or min is -+ 0.
+
+  ## Compute hinges and fences based on ref: EDA pgs. 33 and 44.
+  ## Note that these outlier estimates are meant to be "distribution free".
+
+  nx = numel (x);
+  xs = sort (x);                # Note that sort preserves -0
+  mdidx = fix ((nx + 1)/2);     # median index
+  hlidx = fix ((mdidx + 1)/2);  # lower hinge index
+  huidx = fix (nx + 1 - hlidx); # upper hinge index
+  md = xs(mdidx);               # median
+  hl = xs(hlidx);               # lower hinge
+  hu = xs(huidx);               # upper hinge
+  h_spread = hu - hl;           # h_spread: difference between hinges
+  step = 1.5*h_spread;          # step: 1.5 * h_spread
+  i_fence_l = hl - step;        # inner fences: outside hinges + step
+  o_fence_l = hl - 2*step;      # outer fences: outside hinges + 2*step
+  i_fence_h = hu + step;
+  o_fence_h = hu + 2*step;
+  n_out_l   = sum (x<i_fence_l) - sum (x<o_fence_l);
+  n_out_h   = sum (x>i_fence_h) - sum (x>o_fence_h);
+  n_far_l   = sum (x<o_fence_l);
+  n_far_h   = sum (x>o_fence_h);
+
+  ## display table similar to that on pg. 33
+  plot_out = sprintf ("       Data: %s", caption);
+  plot_out = [plot_out; sprintf(" ")];
+  plot_out = [plot_out; sprintf("         Fenced Letter Display")];
+  plot_out = [plot_out; sprintf(" ")];
+  plot_out = [plot_out; sprintf("     #%3d|___________________", nx)];
+  plot_out = [plot_out; sprintf("     M%3d|       %5d      |", mdidx, md)];
+  plot_out = [plot_out; sprintf("     H%3d|%5d        %5d|   %d", hlidx, hl, hu, h_spread)];
+  plot_out = [plot_out; sprintf("     1   |%5d        %5d|", xs(1), xs(nx))];
+  plot_out = [plot_out; sprintf("               _______")];   
+  plot_out = [plot_out; sprintf("         ______|%5d|_______",step)];
+  plot_out = [plot_out; sprintf("        f|%5d        %5d|", i_fence_l, i_fence_h)];
+  plot_out = [plot_out; sprintf("         |%5d        %5d|  out", n_out_l, n_out_h)];
+  plot_out = [plot_out; sprintf("        F|%5d        %5g|", o_fence_l, o_fence_h)];
+  plot_out = [plot_out; sprintf("         |%5d        %5d|  far",n_far_l,n_far_h)];
+  plot_out = [plot_out; " "];
+
+  ## Determine stem values
+  min_x = min (x);
+  max_x = max (x);
+  if (min_x > 0)      # all stems > 0
+    stems = [fix(min(x)/stem_step) : (fix(max(x)/stem_step)+1)];
+  elseif (max_x < 0)  # all stems < 0
+    stems = [(fix(min_x/stem_step)-1) : fix(max_x/stem_step)];
+  elseif (min_x < 0 && max_x > 0)  # range crosses 0
+    stems = [(fix(min_x/stem_step)-1) : -0, 0 : fix(max_x/stem_step)+1 ];
+  else   # one endpoint is a zero which may be +0 or -0
+    if (min_x == 0)
+      if (any (x == 0 & signbit (x)))
+        min_x = -0;
+      else
+        min_x = +0;
+      endif
+    endif
+    if (max_x == 0)
+      if (any (x == 0 & ! signbit (x)))
+        max_x = +0;
+      else
+        max_x = -0;
+      endif
+    endif
+    stems = [];
+    if (signbit (min_x))
+      stems = [(fix(min_x/stem_step)-1) : -0];
+    endif
+    if (! signbit (max_x))
+      stems = [stems, 0 : fix(max_x/stem_step)+1 ];
+    endif
+  endif
+
+  ## Vectorized version provided by Rik Wehbring (rik@octave.org)
+  ## Determine leaves for each stem:
+  new_line  = 1;
+  for kx = 2: numel (stems)
+
+    stem_sign = signbit (stems(kx));
+    if (stems(kx) <= 0)
+      idx = ((x <= stems(kx)*stem_step) & (x > (stems(kx-1)*stem_step))
+              & (signbit (x) == stem_sign));
+      xlf = abs (x(idx) - stems(kx)*stem_step);
+    else
+      idx = ((x < stems(kx)*stem_step) & (x >= (stems(kx-1)*stem_step))
+              & (signbit (x) == stem_sign));
+      xlf = abs (x(idx) - stems(kx-1)*stem_step);
+    endif
+    ## Convert leaves to a string
+    if (stem_step == 10)
+      lf_str = sprintf ("%d", xlf);
+    else
+      lf_str = "";
+      if (! isempty (xlf))
+        lf_str = sprintf ("%d", xlf(1));
+        if (numel (xlf) > 1)
+          lf_str = [lf_str sprintf(",%d", xlf(2:end))];
+        endif
+      endif
+    endif
+
+    ## Set correct -0
+    if (stems(kx) == 0 && signbit (stems(kx)))
+      line = sprintf ("  -0 | %s",  lf_str);  # -0 stem.
+    elseif (stems(kx) < 0)
+      line = sprintf ("%4d | %s", stems(kx), lf_str);
+    elseif (stems(kx) > 0)
+      line = sprintf ("%4d | %s", stems(kx-1), lf_str);
+    else
+      line = "";
+    endif
+
+    if (! isempty (lf_str) || stems(kx) == 0 || stems(kx-1) == 0)
+      plot_out = [plot_out; line];
+      new_line = 1;
+    else
+      if (new_line == 1) 
+        plot_out = [plot_out; "     :"];  # just print one : if no leaves
+        new_line = 0;
+      endif
+    endif
+
+  endfor    # kx = 2: numel (stems)
+
+  if (nargout == 0)
+    disp (plot_out);
+  else
+    plotstr = plot_out;
+  endif
+
+endfunction
+
+
+%!demo
+%! %% Unsorted plot:
+%! x = [-22 12 -28 52  39 -2 12 10 11 11 42 38 44 18 44];
+%! stemleaf (x, 'Unsorted plot');
+
+%!demo
+%! %% Sorted leaves:
+%! x = [-22 12 -28 52  39 -2 12 10 11 11 42 38 44 18 44];
+%! y = sort (x);
+%! stemleaf (y, 'Sorted leaves');
+
+%!demo
+%! %% Sorted leaves (large dataset):
+%! x = [-22 12 -28 52  39 -2 12 10 11 11 42 38 44 18 44 37 113 124 37 48     ...
+%!      127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119   ...
+%!      58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 ...
+%!      121 58 114 126 53 114 96 25 109 7 31 141 46 -13 71 43 117 116 27 7   ...
+%!      68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40    ...
+%!      119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114   ...
+%!      34 133 45 120 30 127 31 116 146 21 23 30 10 20 21 30 0 100 110 1 20  ...
+%!      0];
+%! y = sort (x);
+%! stemleaf (y, 'Sorted leaves (large dataset)');
+
+%!demo
+%! %% Gaussian leaves:
+%! x = fix (30 * randn (300,1));
+%! stemleaf (x, 'Gaussian leaves');
+
+%!test
+%! ## test minus to plus
+%! x = [-22 12 -28 52  39 -2 12 10 11 11 42 38 44 18 44 37 113 124 37 48 127   ...
+%!      36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109  ...
+%!      23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58   ...
+%!      114 126 53 114 96 25 109 7 31 141 46 -13 71 43 117 116 27 7 68 40 31   ...
+%!      115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 ...
+%!      122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30  ...
+%!      127 31 116 146 21 23 30 10 20 21 30 0 100 110 1 20 0];
+%! x = sort (x);
+%! rexp = char (
+%! "       Data: test minus to plus"    ,
+%! " "                                  ,
+%! "         Fenced Letter Display"     ,
+%! " "                                  ,
+%! "     #138|___________________"      ,     
+%! "     M 69|          52      |"      ,     
+%! "     H 35|   30          116|   86" ,
+%! "     1   |  -28          146|"      ,
+%! "               _______"             ,
+%! "         ______|  129|_______"      ,
+%! "        f|  -99          245|"      ,     
+%! "         |    0            0|  out" ,
+%! "        F| -228          374|"      ,
+%! "         |    0            0|  far" ,
+%! " "                                  ,
+%! "  -2 | 82"                          ,
+%! "  -1 | 3"                           ,
+%! "  -0 | 2"                           ,
+%! "   0 | 00177"                       ,
+%! "   1 | 00112288"                    ,
+%! "   2 | 001133577777899"             ,
+%! "   3 | 000111123456777889"          ,
+%! "   4 | 00122233344456788"           ,
+%! "   5 | 223788"                      ,
+%! "   6 | 138"                         ,
+%! "   7 | 11"                          ,
+%! "     : "                            ,
+%! "   9 | 69"                          ,
+%! "  10 | 04555567999"                 ,
+%! "  11 | 0133344455566667777899"      ,
+%! "  12 | 0011223444555677788"         ,
+%! "  13 | 1239"                        ,
+%! "  14 | 16"                          );
+%! r = stemleaf (x, "test minus to plus", 0);
+%! assert (r, rexp);
+
+%!test
+%! ## positive values above 0
+%! x = [5 22 12 28 52 39 12 11 11 42 38 44 18 44];
+%! rexp = char (
+%! "       Data: positive values above 0",
+%! " "                                   ,
+%! "         Fenced Letter Display"      ,
+%! " "                                   ,
+%! "     # 14|___________________"       ,     
+%! "     M  7|          22      |"       ,     
+%! "     H  4|   12           42|   30"  ,
+%! "     1   |    5           52|"       ,
+%! "               _______"              ,
+%! "         ______|   45|_______"       ,
+%! "        f|  -33           87|"       ,     
+%! "         |    0            0|  out"  ,
+%! "        F|  -78          132|"       ,
+%! "         |    0            0|  far"  ,
+%! " "                                   ,
+%! "   0 | 5"                            ,
+%! "   1 | 22118"                        ,
+%! "   2 | 28"                           ,
+%! "   3 | 98"                           ,
+%! "   4 | 244"                          ,
+%! "   5 | 2"                            );
+%! r = stemleaf (x, "positive values above 0");
+%! assert (r, rexp);
+
+%!test
+%! ## negative values below 0
+%! x = [5 22 12 28 52 39 12 11 11 42 38 44 18 44];
+%! x = -x;
+%! rexp = char (
+%! "       Data: negative values below 0",
+%! " "                                   ,
+%! "         Fenced Letter Display"      ,
+%! " "                                   ,
+%! "     # 14|___________________"       ,     
+%! "     M  7|         -28      |"       ,     
+%! "     H  4|  -42          -12|   30"  ,
+%! "     1   |  -52           -5|"       ,
+%! "               _______"              ,
+%! "         ______|   45|_______"       ,
+%! "        f|  -87           33|"       ,     
+%! "         |    0            0|  out"  ,
+%! "        F| -132           78|"       ,
+%! "         |    0            0|  far"  ,
+%! " "                                   ,
+%! "  -5 | 2"                            ,
+%! "  -4 | 244"                          ,
+%! "  -3 | 98"                           ,
+%! "  -2 | 28"                           ,
+%! "  -1 | 22118"                        ,
+%! "  -0 | 5"                            );
+%! r = stemleaf (x, "negative values below 0");
+%! assert (r, rexp);
+
+%!test
+%! ## positive values from 0
+%! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44];
+%! rexp = char (
+%! "       Data: positive values from 0",
+%! " "                                  ,
+%! "         Fenced Letter Display"     ,
+%! " "                                  ,
+%! "     # 15|___________________"      ,     
+%! "     M  8|          22      |"      ,     
+%! "     H  4|   11           42|   31" ,
+%! "     1   |    0           52|"      ,
+%! "               _______"             ,
+%! "         ______|   46|_______"      ,
+%! "        f|  -35           88|"      ,     
+%! "         |    0            0|  out" ,
+%! "        F|  -82          135|"      ,
+%! "         |    0            0|  far" ,
+%! " "                                  ,
+%! "   0 | 20"                          ,
+%! "   1 | 22118"                       ,
+%! "   2 | 28"                          ,
+%! "   3 | 98"                          ,
+%! "   4 | 244"                         ,
+%! "   5 | 2"                           );
+%! r = stemleaf (x, "positive values from 0");
+%! assert (r, rexp);
+
+%!test
+%! ## negative values from 0
+%! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44];
+%! x = -x;
+%! rexp = char (
+%! "       Data: negative values from 0",
+%! " "                                  ,
+%! "         Fenced Letter Display"     ,
+%! " "                                  ,
+%! "     # 15|___________________"      ,     
+%! "     M  8|         -22      |"      ,     
+%! "     H  4|  -42          -11|   31" ,
+%! "     1   |  -52            0|"      ,
+%! "               _______"             ,
+%! "         ______|   46|_______"      ,
+%! "        f|  -88           35|"      ,     
+%! "         |    0            0|  out" ,
+%! "        F| -135           82|"      ,
+%! "         |    0            0|  far" ,
+%! " "                                  ,
+%! "  -5 | 2"                           ,
+%! "  -4 | 244"                         ,
+%! "  -3 | 98"                          ,
+%! "  -2 | 28"                          ,
+%! "  -1 | 22118"                       ,
+%! "  -0 | 20"                          );
+%! r = stemleaf (x, "negative values from 0");
+%! assert (r, rexp);
+
+%!test
+%! ## both +0 and -0 present
+%! x = [-9 -7 -0 0 -0];
+%! rexp = char (
+%! "       Data: both +0 and -0 present",
+%! " "                                  ,
+%! "         Fenced Letter Display"     ,
+%! " "                                  ,
+%! "     #  5|___________________"      ,     
+%! "     M  3|           0      |"      ,     
+%! "     H  2|   -7            0|   7"  ,
+%! "     1   |   -9            0|"      ,
+%! "               _______"             ,
+%! "         ______|   10|_______"      ,
+%! "        f|  -17           10|"      ,     
+%! "         |    0            0|  out" ,
+%! "        F|  -28           21|"      ,
+%! "         |    0            0|  far" ,
+%! " "                                  ,
+%! "  -0 | 9700"                        ,
+%! "   0 | 0"                           );
+%! r = stemleaf (x, "both +0 and -0 present");
+%! assert (r, rexp);
+
+%!test
+%! ## both <= 0 and -0 present
+%! x = [-9 -7 0 -0];
+%! rexp = char (
+%! "       Data: both <= 0 and -0 present",
+%! " "                                    ,
+%! "         Fenced Letter Display"       ,
+%! " "                                    ,
+%! "     #  4|___________________"        ,     
+%! "     M  2|          -7      |"        ,     
+%! "     H  1|   -9            0|   9"    ,
+%! "     1   |   -9            0|"        ,
+%! "               _______"               ,
+%! "         ______|   13|_______"        ,
+%! "        f|  -22           13|"        ,     
+%! "         |    0            0|  out"   ,
+%! "        F|  -36           27|"        ,
+%! "         |    0            0|  far"   ,
+%! " "                                    ,
+%! "  -0 | 970"                           ,
+%! "   0 | 0"                             );
+%! r = stemleaf (x, "both <= 0 and -0 present");
+%! assert (r, rexp);
+
+%!test
+%! ##   Example from EDA: Chevrolet Prices pg. 30
+%! x = [150 250 688 695 795 795 895 895 895 ...
+%!      1099 1166 1333 1499 1693 1699 1775 1995];
+%! rexp = char (
+%! "       Data: Chevrolet Prices EDA pg.30",
+%! " "                                      ,
+%! "         Fenced Letter Display"         ,
+%! " "                                      ,
+%! "     # 17|___________________"          ,          
+%! "     M  9|         895      |"          ,
+%! "     H  5|  795         1499|   704"    ,
+%! "     1   |  150         1995|"          ,
+%! "               _______"                 ,
+%! "         ______| 1056|_______"          ,
+%! "        f| -261         2555|"          ,
+%! "         |    0            0|  out"     ,
+%! "        F|-1317         3611|"          ,
+%! "         |    0            0|  far"     ,
+%! " "                                      ,
+%! "   1 | 50"                              ,
+%! "   2 | 50"                              ,
+%! "     :"                                 ,
+%! "   6 | 88,95"                           ,
+%! "   7 | 95,95"                           ,
+%! "   8 | 95,95,95"                        ,
+%! "     :"                                 ,
+%! "  10 | 99"                              ,
+%! "  11 | 66"                              ,
+%! "     :"                                 ,
+%! "  13 | 33"                              ,
+%! "  14 | 99"                              ,
+%! "     :"                                 ,
+%! "  16 | 93,99"                           ,
+%! "  17 | 75"                              ,
+%! "     :"                                 ,
+%! "  19 | 95"                              );
+%! r = stemleaf (x, "Chevrolet Prices EDA pg.30", 1);
+%! assert (r, rexp);
+
+## Test input validation
+%!error stemleaf ()
+%!error stemleaf (1, 2, 3, 4)
+%!error <X must be a vector> stemleaf (ones (2,2), "")
+%!warning <X truncated to integer values> tmp = stemleaf ([0 0.5 1],"");
+%!error <X must be a numeric vector> stemleaf ("Hello World", "data")
+%!error <CAPTION must be a character array> stemleaf (1, 2)
+%!error <STEM_SZ must be a real integer> stemleaf (1, "", ones (2,2))
+%!error <STEM_SZ must be a real integer> stemleaf (1, "", -1)
+%!error <STEM_SZ must be a real integer> stemleaf (1, "", 1+i)
+