dynare/matlab/+gsa/boxplot.m

function sout = boxplot (data,notched,symbol,vertical,maxwhisker)
% sout = boxplot (data,notched,symbol,vertical,maxwhisker)
% Creates a box plot

% Copyright © 2010-2023 Dynare Team
%
% This file is part of Dynare.
%
% Dynare 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.
%
% Dynare 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 Dynare.  If not, see <https://www.gnu.org/licenses/>.

if nargin < 5 || isempty(maxwhisker), maxwhisker = 1.5; end
if nargin < 4 || isempty(vertical), vertical = 1; end
if nargin < 3 || isempty(symbol), symbol = ['+','o']; end
if nargin < 2 || isempty(notched), notched = 0; end

if length(symbol)==1, symbol(2)=symbol(1); end

if notched==1, notched=0.25; end
a=1-notched;

% % figure out how many data sets we have
if iscell(data)
    nc = length(data);
else
    %   if isvector(data), data = data(:); end
    nc = size(data,2);
end

% 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 i=1:nc
    %   Get the next data set from the array or cell array
    if iscell(data)
        col = data{i}(:);
    else
        col = data(:,i);
    end
    %   Skip missing data
    % % % % % % %   col(isnan(col) | isna (col)) = [];
    col(isnan(col)) = [];

    %   Remember the data length
    nd = length(col);
    box(i) = nd;
    if (nd > 1)
        % min,max and quartiles
        s(1,i)=min(col);
        s(5,i)=max(col);
        s(2,i)=myprctilecol(col,25);
        s(3,i)=myprctilecol(col,50);
        s(4,i)=myprctilecol(col,75);

        % confidence interval for the median
        est = 1.57*(s(4,i)-s(2,i))/sqrt(nd);
        s(6,i) = max([s(3,i)-est, s(2,i)]);
        s(7,i) = min([s(3,i)+est, s(4,i)]);
        % whiskers out to the last point within the desired inter-quartile range
        IQR = maxwhisker*(s(4,i)-s(2,i));
        whisker_y(:,i) = [min(col(col >= s(2,i)-IQR)); s(2,i)];
        whisker_y(:,nc+i) = [max(col(col <= s(4,i)+IQR)); s(4,i)];
        % outliers beyond 1 and 2 inter-quartile ranges
        outliers = col((col < s(2,i)-IQR & col >= s(2,i)-2*IQR) | (col > s(4,i)+IQR & col <= s(4,i)+2*IQR));
        outliers2 = col(col < s(2,i)-2*IQR | col > s(4,i)+2*IQR);
        outliers_x = [outliers_x; i*ones(size(outliers))];
        outliers_y = [outliers_y; outliers];
        outliers2_x = [outliers2_x; i*ones(size(outliers2))];
        outliers2_y = [outliers2_y; outliers2];
    elseif (nd == 1)
        % all statistics collapse to the value of the point
        s(:,i) = col;
        % single point data sets are plotted as outliers.
        outliers_x = [outliers_x; i];
        outliers_y = [outliers_y; col];
    else
        % no statistics if no points
        s(:,i) = 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 = box*0.23/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,:) =cap_x(1,:)- 0.05;
cap_x(2,:) =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
mm=min(min(data));
MM=max(max(data));
if isnan(mm)
    mm=0; 
    MM=0; 
end

if vertical
    plot (quartile_x, quartile_y, 'b',  ...
          whisker_x, whisker_y, 'b--',   ...
          cap_x, cap_y, 'k',   ...
          median_x, median_y, 'r',  ...
          outliers_x, outliers_y, [symbol(1),'r'],   ...
          outliers2_x, outliers2_y, [symbol(2),'r']);
    set(gca,'XTick',1:nc);
    set(gca, 'XLim', [0.5, nc+0.5]);
    set(gca, 'YLim', [mm-(MM-mm)*0.05-eps, MM+(MM-mm)*0.05+eps]);
end

if nargout
    sout=s;
end

function y = myprctilecol(x,p)

xx = sort(x);
[m,n] = size(x);

if m==1 | n==1
    m = max(m,n);
    if m == 1
        y = x*ones(length(p),1);
        return
    end
    n = 1;
    q = 100*(0.5:m - 0.5)./m;
    xx = [min(x); xx(:); max(x)];
else
    q = 100*(0.5:m - 0.5)./m;
    xx = [min(x); xx; max(x)];
end

q = [0 q 100];
y = interp1(q,xx,p);