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## Copyright (C) 2002 Alberto Terruzzi
##
## This program 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 2 of the License, or
## (at your option) any later version.
##
## This program 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 this program; If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{s} =} boxplot (@var{data}, @var{notched}, @
## @var{symbol}, @var{vertical}, @var{maxwhisker}, @dots{})
##
## Produce a box plot.
##
## The box plot is a graphical display that simultaneously describes several
## important features of a data set, such as center, spread, departure from
## symmetry, and identification of observations that lie unusually far from
## the bulk of the data.
##
## @var{data} is a matrix with one column for each data set, or data is a cell
## vector with one cell for each data set.
##
## @var{notched} = 1 produces a notched-box plot. Notches represent a robust
## estimate of the uncertainty about the median.
##
## @var{notched} = 0 (default) produces a rectangular box plot.
##
## @var{notched} in (0,1) produces a notch of the specified depth.
## notched values outside (0,1) are amusing if not exactly practical.
##
## @var{symbol} sets the symbol for the outlier values, default symbol for
## points that lie outside 3 times the interquartile range is 'o',
## default symbol for points between 1.5 and 3 times the interquartile
## range is '+'.
##
## @var{symbol} = '.' points between 1.5 and 3 times the IQR is marked with
## '.' and points outside 3 times IQR with 'o'.
##
## @var{symbol} = ['x','*'] points between 1.5 and 3 times the IQR is marked with
## 'x' and points outside 3 times IQR with '*'.
##
## @var{vertical} = 0 makes the boxes horizontal, by default @var{vertical} = 1.
##
## @var{maxwhisker} defines the length of the whiskers as a function of the IQR
## (default = 1.5). If @var{maxwhisker} = 0 then @code{boxplot} displays all data
## values outside the box using the plotting symbol for points that lie
## outside 3 times the IQR.
##
## Supplemental arguments are concatenated and passed to plot.
##
## The returned matrix @var{s} has one column for each data set as follows:
##
## @multitable @columnfractions .1 .8
## @item 1 @tab Minimum
## @item 2 @tab 1st quartile
## @item 3 @tab 2nd quartile (median)
## @item 4 @tab 3rd quartile
## @item 5 @tab Maximum
## @item 6 @tab Lower confidence limit for median
## @item 7 @tab Upper confidence limit for median
## @end multitable
##
## Example
##
## @example
## title ("Grade 3 heights");
## tics ("x", 1:2, @{"girls"; "boys"@});
## axis ([0,3]);
## boxplot (@{randn(10,1)*5+140, randn(13,1)*8+135@});
## @end example
##
## @end deftypefn
## Author: Alberto Terruzzi <t-albert@libero.it>
## Version: 1.4
## Created: 6 January 2002
## Version: 1.4.1
## Author: Alberto Pose <apose@alu.itba.edu.ar>
## Updated: 3 September 2006
## - Replaced deprecated is_nan_or_na(X) with (isnan(X) | isna(X))
## (now works with this software 2.9.7 and foward)
## Version: 1.4.2
## Author: Pascal Dupuis <Pascal.Dupuis@worldonline.be>
## Updated: 14 October 2011
## - Added support for named arguments
## Version: 1.4.2
## Author: Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## Updated: 01 March 2012
## - Returns structure with handles to plot elements
## - Added example as demo
%# function s = boxplot (data,notched,symbol,vertical,maxwhisker)
function [s hs] = boxplot (data, varargin)
## assign parameter defaults
if (nargin < 1)
print_usage;
endif
%# default values
maxwhisker = 1.5;
vertical = 1;
symbol = ['+', 'o'];
notched = 0;
plot_opts = {};
%# Optional arguments analysis
numarg = nargin - 1;
option_args = ['Notch'; 'Symbol'; 'Vertical'; 'Maxwhisker'];
indopt = 1;
while (numarg)
dummy = varargin{indopt++};
if (!ischar (dummy))
%# old way: positional argument
switch indopt
case 2
notched = dummy;
case 4
vertical = dummy;
case 5
maxwhisker = dummy;
otherwise
error("No positional argument allowed at position %d", --indopt);
endswitch
numarg--; continue;
else
if (3 == indopt && length (dummy) <= 2)
symbol = dummy; numarg--; continue;
else
tt = strmatch(dummy, option_args);
switch (tt)
case 1
notched = varargin{indopt};
case 2
symbol = varargin{indopt};
case 3
vertical = varargin{indopt};
case 4
maxwhisker = varargin{indopt};
otherwise
%# take two args and append them to plot_opts
plot_opts(1, end+1:end+2) = {dummy, varargin{indopt}};
endswitch
endif
indopt++; numarg -= 2;
endif
endwhile
if (1 == length (symbol)) symbol(2) = symbol(1); endif
if (1 == notched) notched = 0.25; endif
a = 1-notched;
## figure out how many data sets we have
if (iscell (data))
nc = length (data);
else
if (isvector (data)) data = data(:); endif
nc = columns (data);
endif
## compute statistics
## s will contain
## 1,5 min and max
## 2,3,4 1st, 2nd and 3rd quartile
## 6,7 lower and upper confidence intervals for median
s = zeros (7,nc);
box = zeros (1,nc);
whisker_x = ones (2,1)*[1:nc,1:nc];
whisker_y = zeros (2,2*nc);
outliers_x = [];
outliers_y = [];
outliers2_x = [];
outliers2_y = [];
for indi = (1:nc)
## Get the next data set from the array or cell array
if (iscell (data))
col = data{indi}(:);
else
col = data(:, indi);
endif
## Skip missing data
col(isnan (col) | isna (col)) = [];
## Remember the data length
nd = length (col);
box(indi) = nd;
if (nd > 1)
## min,max and quartiles
s(1:5, indi) = statistics (col)(1:5);
## confidence interval for the median
est = 1.57*(s(4, indi)-s(2, indi))/sqrt (nd);
s(6, indi) = max ([s(3, indi)-est, s(2, indi)]);
s(7, indi) = min ([s(3, indi)+est, s(4, indi)]);
## whiskers out to the last point within the desired inter-quartile range
IQR = maxwhisker*(s(4, indi)-s(2, indi));
whisker_y(:, indi) = [min(col(col >= s(2, indi)-IQR)); s(2, indi)];
whisker_y(:,nc+indi) = [max(col(col <= s(4, indi)+IQR)); s(4, indi)];
## outliers beyond 1 and 2 inter-quartile ranges
outliers = col((col < s(2, indi)-IQR & col >= s(2, indi)-2*IQR) | (col > s(4, indi)+IQR & col <= s(4, indi)+2*IQR));
outliers2 = col(col < s(2, indi)-2*IQR | col > s(4, indi)+2*IQR);
outliers_x = [outliers_x; indi*ones(size(outliers))];
outliers_y = [outliers_y; outliers];
outliers2_x = [outliers2_x; indi*ones(size(outliers2))];
outliers2_y = [outliers2_y; outliers2];
elseif (1 == nd)
## all statistics collapse to the value of the point
s(:, indi) = col;
## single point data sets are plotted as outliers.
outliers_x = [outliers_x; indi];
outliers_y = [outliers_y; col];
else
## no statistics if no points
s(:, indi) = NaN;
end
end
## Note which boxes don't have enough stats
chop = find (box <= 1);
## Draw a box around the quartiles, with width proportional to the number of
## items in the box. Draw notches if desired.
box *= 0.4/max (box);
quartile_x = ones (11,1)*[1:nc] + [-a;-1;-1;1;1;a;1;1;-1;-1;-a]*box;
quartile_y = s([3,7,4,4,7,3,6,2,2,6,3],:);
## Draw a line through the median
median_x = ones (2,1)*[1:nc] + [-a;+a]*box;
median_y = s([3,3],:);
## Chop all boxes which don't have enough stats
quartile_x(:, chop) = [];
quartile_y(:, chop) = [];
whisker_x(:,[chop, chop+nc]) = [];
whisker_y(:,[chop, chop+nc]) = [];
median_x(:, chop) = [];
median_y(:, chop) = [];
## Add caps to the remaining whiskers
cap_x = whisker_x;
cap_x(1, :) -= 0.05;
cap_x(2, :) += 0.05;
cap_y = whisker_y([1, 1], :);
#quartile_x,quartile_y
#whisker_x,whisker_y
#median_x,median_y
#cap_x,cap_y
## Do the plot
if (vertical)
if (isempty (plot_opts))
h = plot (quartile_x, quartile_y, "b;;",
whisker_x, whisker_y, "b;;",
cap_x, cap_y, "b;;",
median_x, median_y, "r;;",
outliers_x, outliers_y, [symbol(1), "r;;"],
outliers2_x, outliers2_y, [symbol(2), "r;;"]);
else
h = plot (quartile_x, quartile_y, "b;;",
whisker_x, whisker_y, "b;;",
cap_x, cap_y, "b;;",
median_x, median_y, "r;;",
outliers_x, outliers_y, [symbol(1), "r;;"],
outliers2_x, outliers2_y, [symbol(2), "r;;"], plot_opts{:});
endif
else
if (isempty (plot_opts))
h = plot (quartile_y, quartile_x, "b;;",
whisker_y, whisker_x, "b;;",
cap_y, cap_x, "b;;",
median_y, median_x, "r;;",
outliers_y, outliers_x, [symbol(1), "r;;"],
outliers2_y, outliers2_x, [symbol(2), "r;;"]);
else
h = plot (quartile_y, quartile_x, "b;;",
whisker_y, whisker_x, "b;;",
cap_y, cap_x, "b;;",
median_y, median_x, "r;;",
outliers_y, outliers_x, [symbol(1), "r;;"],
outliers2_y, outliers2_x, [symbol(2), "r;;"], plot_opts{:});
endif
endif
% Distribute handles
nq = 1:size(quartile_x,2);
hs.box = h(nq);
nw = nq(end) + [1:2*size(whisker_x,2)];
hs.whisker = h(nw);
nm = nw(end)+ [1:size(median_x,2)];
hs.median = h(nm);
no = nm(end) + [1:size(outliers_y,2)];
hs.outliers = h(no);
no2 = no(end) + [1:size(outliers2_y,2)];
hs.outliers2 = h(no2);
endfunction
#!demo
#! title ("Grade 3 heights");
#! tics ("x", 1:2, @{"girls"; "boys"@});
#! axis ([0,3]);
#! boxplot (@{randn(10,1)*5+140, randn(13,1)*8+135@});