external/other/qq_plot.m
function h = qq_plot(varargin)
%  Quantile-quantile plot with patch option
%
%   QQ_PLOT(Y) displays a quantile-quantile plot of the sample quantiles of
%   Y versus theoretical quantiles from a normal distribution. If the
%   distribution of Y is normal, the plot will be close to linear.
% 
%   QQ_PLOT(X,Y) displays a quantile-quantile plot of two samples. If the
%   samples come from the same distribution, the plot will be linear.
% 
%   The inputs X and Y should be numeric and have an equal number of
%   elements; every element is treated as a member of the sample.
% 
%   The plot displays the sample data with the plot symbol 'x'.
%   Superimposed on the plot is a dashed straight line connecting the first
%   and third quartiles.
% 
%   QQ_PLOT(...,MODE) allows the appearance of the plot to be configured.
%   With MODE='line' (default), the plot appears as described above. With
%   MODE='patch', the data are plotted as a patch object, with the area
%   bound by the x-distribution and the linear fit shaded grey. With
%   mode='both' the two appearances are combined.
%   
%   QQ_PLOT(...,MODE,METHOD) and QQ_PLOT(...,[],METHOD) allows the method
%   for calculating the quartiles, used for the fit line, to be specified.
%   The default is 'R-8'. Type 'help quantile2' for more information. The
%   latter form of the function call uses the default mode.
% 
%   H = QQ_PLOT(...) returns a two- or three-element vector of handles to
%   the plotted object. The nature of the handles depends upon the mode. In
%   all cases, the first handle is to the sample data, the second handle is
%   to the fit line. With MODE='patch' or MODE='both', there is third
%   handle to the patch object.
% 
%   Example
% 
%      % Display Q-Q plots for the rand and randn functions
%      figure
%      subplot(2,1,1)
%      qq_plot(rand(20),'patch')
%      subplot(2,1,2)
%      h = qq_plot(randn(20),'patch');
%      set(h(3),'FaceColor','r') % change fill color

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% LICENSE FILE:
% -----------------------------------------------------------------------
% Copyright (c) 2015, Christopher Hummersone
% All rights reserved.
% 
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are
% met:
% 
%     * Redistributions of source code must retain the above copyright
%       notice, this list of conditions and the following disclaimer.
%     * Redistributions in binary form must reproduce the above copyright
%       notice, this list of conditions and the following disclaimer in
%       the documentation and/or other materials provided with the distribution
% 
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
% POSSIBILITY OF SUCH DAMAGE.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ==========================================================
% Last changed:     $Date: 2015-05-20 16:28:56 +0100 (Wed, 20 May 2015) $
% Last committed:   $Revision: 380 $
% Last changed by:  $Author: ch0022 $
% ==========================================================

    %% determine X and Y

    IXn = cellfun(@(x) isnumeric(x) & ~isempty(x),varargin);

    switch sum(IXn)
        case 0
            error('No input data specified')
        case 1
            % compare to normal distrbution
            Y = get_input_sample(varargin,IXn);
            p = (.5:length(Y))/length(Y);
            X = sqrt(2)*erfinv(2*p - 1);
            x_label = 'Standard normal quantiles';
            y_label = 'Sample quantiles';
        case 2
            % compare to input data distribution
            Y = get_input_sample(varargin,find(IXn,1,'last'));
            X = get_input_sample(varargin,find(IXn,1,'first'));
            assert(isequal(size(X),size(Y)),'Input data must be the same size')
            x_label = 'X quantiles';
            y_label = 'Y quantiles';
        otherwise
            error('Unknown input specified')
    end

    %% determine mode and method

    % find inputs
    IXc = cellfun(@(x) ischar(x) | isempty(x),varargin);
    switch sum(IXc)
        case 0
            mode = [];
            method = [];
        case 1
            mode = varargin{IXc};
            method = [];
        case 2
            mode = varargin{find(IXc,1,'first')};
            method = varargin{find(IXc,1,'last')};
        otherwise
            error('Unknown string specified')
    end

    % defaults
    if isempty(mode)
        mode = 'line';
    end
    if isempty(method)
        method = 'R-8';
    end

    %% calculate fit to first and third quartile

    % quartiles
    q1x = quantile2(X,.25,[],method);
    q3x = quantile2(X,.75,[],method);
    q1y = quantile2(Y,.25,[],method);
    q3y = quantile2(Y,.75,[],method);

    % slope
    slope = (q3y-q1y)./(q3x-q1x);
    centerx = (q1x+q3x)/2;
    centery = (q1y+q3y)/2;

    % fit
    maxx = max(X);
    minx = min(X);
    maxy = centery + slope.*(maxx - centerx);
    miny = centery - slope.*(centerx - minx);

    % lines
    X_fit = linspace(minx,maxx,length(X));
    Y_fit = linspace(miny,maxy,length(X));

    %% plot data

    hold on

    if strcmpi(mode,'patch') || strcmpi(mode,'both')
        Hp = patch([X fliplr(X_fit)],[Y fliplr(Y_fit)],[0.5 0.5 0.5]);
        set(Hp,'edgecolor','none')
    else
        Hp = NaN;
    end

    switch lower(mode)
        case 'line'
            linestyle = 'xk';
        case 'patch'
            linestyle = '-k';
        case 'both'
            linestyle = 'xk';
        otherwise
            error('Unknown mode specified')
    end

    H = plot(X,Y,linestyle,X_fit,Y_fit,'--k');

    hold off

    % axis labels
    xlabel(x_label)
    ylabel(y_label)

    box on; axis tight
    set(gca,'layer','top')

    % return handle
    if nargout>0
        h = H;
        if isobject(Hp) || ishandle(Hp)
            h = [h; Hp];
        end
    end

end

function Z = get_input_sample(z,IX)
%GET_INPUT_SAMPLE get sample, order, and convert to vector
    Z = z{IX};
    Z = sort(Z(:))';
end
