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|
########################################################################
##
## Copyright (C) 2013-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {} stemleaf (@var{x}, @var{caption})
## @deftypefnx {} {} stemleaf (@var{x}, @var{caption}, @var{stem_sz})
## @deftypefnx {} {@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:
## Chapter 3, @cite{Exploratory Data Analysis} by @nospell{J. W. Tukey},
## Addison-Wesley, 1977.
## @seealso{hist, printd}
## @end deftypefn
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)
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)))
error ("stemleaf: STEM_SZ must be a real integer >= 0");
endif
stem_sz = fix (stem_sz);
stem_step = 10^(stem_sz+1);
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 = fix (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| -81 134|" ,
%! " | 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| -134 81|" ,
%! " | 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| -27 20|" ,
%! " | 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| -35 26|" ,
%! " | 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 <Invalid call> stemleaf ()
%!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)
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