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Plot and compare histograms; pretty by default

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28 Apr 2010 (Updated )

Compares multiple sets of data elegantly. Set bins and axis bounds to be appropriate for the data.

nhist.m
%% description
% function  [theText, rawN, x] = nhist(cellValues, 'parameter', value, ...)
% 
% nhist(x); works just like hist(x) but the resulting plot looks nice.
% 
% t = nhist(Y) bins the elements of Y into equally spaced containers
%            and returns a string with information about the distributions.
%            If Y is a cell array or a structure nhist will make graph the
%            binned (discrete) probability density function of each data
%            set for comparison on the same graph. It will return A cell
%            array or structure which includes a string for each set of
%            data.
% 
% [t, N, X]= nhist(...) also returns the number of items in each bin, N,
%            and the locations of the left edges of each bin. If Y is a
%            cell array or structure then the output is in the same form.
% 
% nhist(Y,'Property', . . . )
% nhist(Y,'PropertyName',PropertyValue, . . . )
% See below for the different parameters.
%__________________________________________________________________________ 
% Summary of what function does:
%  1) Automatically sets the number and range of the bins to be appropriate 
%     for the data.
%  2) Compares multiple sets of data elegantly on one or more plots, with
%     legend or titles. It also graphs the mean and standard deviations.
%     It can also plot the median and mode.
%  3) Outputs text with the usefull statistics for each distribution.
%  4) Allows for changing many more parameters
%
% Highlighted features (see below for details)
% 'separate' to plot each set on its own axis, but with the same bounds
% 'binfactor' change the number of bins used, larger value =more bins
% 'samebins' force all bins to be the same for all plots
% 'legend' add a legend in the graph (default for structs)
% 'noerror' remove the mean and std plot from the graph
% 'median' add the median of the data to the graph
% 'text' return many details about each graph even if not plotted
%  The function is robust to NaN and +-inf data points (with warnings)
% 
%% Optional Properties
% Note: Alternative names to call the properties are listed at the end of each
% entry. 
%__________________________________________________________________________ 
% Histogram and bin settings
%           'binfactor': Effects the number of bins used. A larger number
%                        will mean more bins used. All bins will be some
%                        multiple of the largest bin.
%                        'binfactor','binfactors','factor','f'
%            'samebins': this will make all the bins align with each other
%                        the binwidth will be the mean of all the
%                        recomended bin sizes.
%             'minbins': The minimum number of bins allowed for each graph
%                        default = 10. 'minimumbins'
%             'maxbins': The maximum number of bins allowed for each graph
%                        default = 100. 'maximumbins'
%            'stdtimes': Number of times the standard deviation to set the
%                        horizontal limits of the axis, default is 4.
%                'minx': crop the axis and histogram on the left. 'xmin'
%                'maxx': crop the axis and histogram on the right. 'xmax'
%          'proportion': Plot proportion of total points on the y axis
%                        rather than the totaly number of points or the
%                        probability distribution. Useful for data sets
%                        with small sample sizes. 'p'
%                 'pdf': Plot the pdf on the y axis
%             'numbers': Plot the raw numbers on the graph. 'number'
%              'smooth': Plot a smooth line instead of the step function.
%                 'int': Force it to make bins along integers. If you like
%                        pass 1 or 0 to force int bins, or relax the
%                        restriction if it is imposed automatically.
%                        'integer','discrete','intbins'
%__________________________________________________________________________
% Text related parameters
%     'titles','legend': A cell array with strings to put in the legend or
%                        titles. Also used for text output. 'title'
%           'nolengend': In case you pass a struct, you may force a legend
%                        to disappear. You will have no way to track the
%                        data.
%                'text': Outputs all numbers to text, even ones that are
%                        not plotted, this will include the number of
%                        points, mean, standard deviation, standard error,
%                        median, and approximate mode., 't','alltext'
%       'decimalplaces': Number of decimal places numbers will be output
%                        with, 'decimal', 'precision', 'textprecision'
%             'npoints': this will add (number of points) to the legend or
%                        title automatically for each plot. 'points'
%              'xlabel': Label of the lowest X axis
%              'ylabel': Label of the Y axis, note that the ylabel default
%                        will depend on the type of plot used, it will vary
%                        from 'pdf' (or probability distribution) for
%                        regular plots, 'number' for separate plots (the
%                        number of elements) and 'proportion' for
%                        proportion plots. Setting this parameter will
%                        override the defaults.
%               'fsize': Font size, default 12. 'fontsize'
%            'location': Sets the location of the legend,
%                        example:NorthOutside. 'legendlocation'
%__________________________________________________________________________
% Peripheral elements settings
%                 'box': This will put a nice boxplot above your histogram.
%                        It is a typical box and whiskers plot with a red
%                        line for median, '+' for the mean, a blue box
%                        around the 25% and 75% quartiles and whiskers
%                        bounding 9% and 91%. When comparing multiple plots
%                        the boxplots are colored to match the histogram.
%                        'boxplot','bplot'
%              'median': This will plot a stem plot of the median
%                'mode': This will plot a stem plot of the mode
%                        If both 'mode' and 'median' are passed, the mode
%                        will be plotted with a dashed line.
%              'serror': Will put the mean and 'standard error' bars above
%                        the plot rather than the default standard
%                        deviation. 'serrors','stderror','stderrors','sem'
%
%             'noerror': Will remove the mean and standard deviation error
%                        bars from above the plot. 'noerrors,
%           'linewidth': Sets the width of the lines for all the graphs
%               'color': Sets the colors of the lines.
%                        'qualitative' forces each line to be most
%                             distinguishable, up to 12 different colors.
%                        'sequential' forces the colors into a smooth
%                             spectrum from red to blue.
%                        'colormap' will take the colors from the existing 
%                             colormap, allowing you to choose them freely.
%                        'jet' setting the parameter to an regular colormap
%                             will choose the colors from that map
%                             'jet','gray','summer','cool', etc.
%                        For 'separate' plots color will specify the color of the
%                        bar graphs. You must use the [R G B] standard
%                        color definitions. 
%__________________________________________________________________________
% General Figure Settings
%            'separate': Plot each histogram separately, also use normal
%                        bar plots for the histograms rather than the
%                        stairs function. Data will not be normalized.
%                        'separateplots','plotseparately','normalhist','normal','s'
%              'newfig': Will make a new figure to plot it in. When using
%                        'separateplots' 'newfig' will automatically
%                        change the size of the figure.
%                 'eps': EPS file name of the generated plot to save. It
%                        will automatically print if you pass this
%                        parameter
% 
%% The bin width is defined in the following way
% Disclaimer: this function is specialized to compare data with comparable
% standard deviations and means, but greatly varying numbers of points.
% 
% Scotts Choice used for this function is a theoretically ideal way of
% choosing the number of bins. Of course the theory is general and so not
% rigorous, but I feel it does a good job.
% (bin width) = 3.5*std(data points)/(number of points)^(1/3);
% 
% I did not follow it exactly though, restricting smaller bin sizes to be
% divisible by the larger bin sizes. In this way the different conditions
% can be accurately compared to each other.
% 
% The bin width is further adulterated by user parameter 'binFactor'
% (new bin width) = (old bin width) / (binFactor);
%  it allows the user to make the bins larger or smaller to their tastes.
%  Larger binFactor means more bins. 1 is the default
% 
%Source: http://en.wikipedia.org/wiki/Histogram#Number_of_bins_and_width
% 
%% Default function behaviour
% 
% If you pass it a structure, the field names will become the legend. All
% of the data outputted will be in structure form with the same field
% names. If you pass a cell array, then the output will be in cell form. If
% you pass an array or vector then the data is outputted as a string and
% two arrays.
% 
% standard deviation will be plotted as a default, unless one puts in the
% 'serror' paramter which will plot the standard error = std/sqrt(N)
% 
% There is no maximum or minimum X values.
% minBins=10; The minimum number of bins for the histogram
% maxBins=100;The maximum number of bins for a histogram
% AxisFontSize = 12; 'fsize' the fontsize of everything.
% The number of data points is not displayed
% The lines in the histograms are black
% faceColor = [.7 .7 .7]; The face of the histogram is gray.
% It will plot inside a figure, unless 'newfig' is passed then it will make
% a new figure. It will take over and refit all axes.
% linewidth=2; The width of the lines in the errobars and the histogram
% stdTimes=4; The axes will be cutoff at a maximum of 4 times the standard
% deviation from the mean.
% Different data sets will be plotted with a different number of bins.
%% Acknowledgments
% Thank you to the AP-Lab at Boston University for funding me while I
% developed this function. Thank you to the AP-Lab, Avi and Eli for help
% with designing and testing it and the Mathworks community for comments!
%% Examples
% Cell array example:
% A={randn(1,10^5),randn(10^3,1)+1};
% nhist(A,'legend',{'\mu=0','\mu=1'});
% nhist(A,'legend',{'\mu=0','\mu=1'},'separate');
% 
% A=[randn(1,10^5)+1 randn(1,2*10^5)+5];
% nhist(A,'mode')
% 
% Structure example:
% A.mu_is_Zero=randn(1,10^5); A.mu_is_Two=randn(10^3,1)+2;
% nhist(A);
% nhist(A,'color','summer')
% nhist(A,'color',[.3 .8 .3],'separate')
% nhist(A,'binfactor',4)
% nhist(A,'samebins')
% nhist(A,'median','noerror')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Jonathan Lansey 2010-2013,                                              %
%                   questions to Lansey at gmail.com                      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [theText,rawN, x] = nhist(cellValues, varargin)
%% INITIALIZE PARAMETERS
% Default initialization of the parameters,

stdTimes=4; % the number of times the standard deviation to set the upper end of the axis to be.
binFactor=1.5;
sameBinsFlag=0; % if 1 then all bins will be the same size
proportionFlag=0;
pdfFlag = 0;
numberFlag = 0;
smoothFlag = 0;
intbinsForcedFlag = 0;
intbinsFlag = 0;

% These are used later to set the output parameters right.
structFlag=0;
arrayFlag=0;

minX=[]; % for the axis in case users don't enter anything
maxX=[];
minBins=10;
maxBins=150;
SXLabel = '';
yLabelFlag=0;

EPSFileName = '';
Title = '';
AxisFontSize = 12;
npointsFlag=0;

legendLocation='best';
forceNoLegend=0;
% lineColor = [.49 .49 .49];
lineColor = [0 0 0];
faceColor = [.7 .7 .7];

vertLinesForcedFlag=0;

multicolorFlag=0;
brightnessExponent=1/2;

plotStdFlag = 1; % 1 if either serror or std will be plotted
serrorFlag = 0;
medianFlag = 0;
modeFlag   = 0;
boxplotFlag = 0;
textFlag=0;
decimalPlaces=2;
legendExists=0;
linewidth=2;
newfigFlag=0;

barFactor=1;
normalHist=0;

%% Interpret the user parameters
k = 1;
while k <= length(varargin)
    if ischar(varargin{k})
    switch (lower(varargin{k}))
        case {'legend','titles','title'}
            cellLegend=varargin{k+1};
            legendExists=1;
            k = k + 1;
        case {'location','legendlocation'}
            legendLocation=varargin{k+1};
            k = k + 1;
        case 'nolegend'
            forceNoLegend=1;            
        case 'xlabel'
            SXLabel = varargin{k + 1};
            k = k + 1;
        case 'ylabel'
            SYLabel = varargin{k + 1};
            yLabelFlag=1;
            k = k + 1;
        case {'minx','xmin'}
            minX = varargin{k + 1};
            k = k + 1;
        case {'maxx','xmax'}
            maxX = varargin{k + 1};
            k = k + 1;
        case {'minbins','minimumbins'}
            minBins = varargin{k + 1};
            k = k + 1;
        case {'maxbins','maximumbins'}
            maxBins = varargin{k + 1};
            k = k + 1;
        case 'stdtimes' % the number of times the standard deviation to set the upper end of the axis to be.
            stdTimes = varargin{k + 1};
            k = k + 1;
            if ischar(stdTimes)
                fprintf(['\nstdTimes set to: ' stdTimes]);
                error('stdTimes must be a number')
            end
        case {'binfactor','binfactors','factor','f'}
            binFactor = varargin{k + 1};
            k = k + 1;
            if ischar(binFactor)
                error('binFactor must be a number')
            end
            
        case {'samebins','samebin','same'}
            sameBinsFlag=1;
        case {'proportion','p','fraction','frac','percent'}
            proportionFlag=1;
        case 'pdf'
            pdfFlag=1;
        case {'numbers','number'}
            numberFlag = 1;
        case {'smooth','smoooth'}
            smoothFlag = 1;
            
        case {'int','integer','discrete','intbins','intbin'}
            intbinsForcedFlag = 1;
            intbinsFlag=1;
            
            if k+1<= length(varargin)
                temp = varargin{k + 1};
                if ~ischar(temp) % if its a number then we want to use it.
                    intbinsFlag=temp;
                end
            end
            
        case 'eps'
            EPSFileName = varargin{k + 1};
            k = k + 1;
        case {'fsize','fontsize'}
            AxisFontSize = varargin{k + 1};
            k = k + 1;
        case 'linewidth'
            linewidth = varargin{k + 1};
            k = k + 1;
        case {'color','colors'}
            lineColor=varargin{k+1};
            if ischar(lineColor)
                %             if strcmp(lineColor,'multicolor')
                multicolorFlag = 1;
                %             end 
            else %then lineColor will be redone later
                faceColor = lineColor;
            end
            k = k + 1;
        case {'npoints','points'}
            npointsFlag=1;
        case {'lines','line'}
            vertLinesFlag=1;
            vertLinesForcedFlag=vertLinesForcedFlag+1;
        case {'noline','nolines'}
            vertLinesFlag=0;
            vertLinesForcedFlag=vertLinesForcedFlag+1;
        case { 'decimalplaces','decimal','precision','textprecision'}
            decimalPlaces=varargin{k+1};
            k=k+1;
        case {'newfig','newfigure'}
            newfigFlag=true;
        case {'noerror','noerrors'}
            plotStdFlag = 0;
        case {'serror','serrors','stderror','stderrors','sem'}
            serrorFlag = 1;
        case {'boxplot','bplot','box'} % surprise! undocumented feature.
            boxplotFlag = 1;
            plotStdFlag = 0;
        case {'barwidth','barfactor','errorbarwidth'}
            barFactor = varargin{k+1};
            k = k+1;
        case {'median','medians'}
            medianFlag=1;
        case {'separateplots','separate','plotseparately','normalhist','normal','s'}
            normalHist=1;
        case {'mode','modes'}
            modeFlag = 1;
        case {'text','alltext','t'}
            textFlag=1;
        otherwise
            warning('user entered parameter is not recognized')
            disp('unrecognized term is:'); disp(varargin{k});
    end
    end
    k = k + 1;
end


%%
% intbinsForcedFlag
% intbinsFlag

%% Check if data is an array, not a cell
valueInfo=whos('cellValues');
valueType=valueInfo.class;

switch valueType
    case 'cell' %   There are a few cells there, it will run as usual.
%         normalHist=what you set it to, or zero;
    case 'struct'
        structFlag=1;
        tempValues=cellValues; clear('cellValues');
        if legendExists
            warning(['The legend you entered will be ignored and replaced '...
                'with field names. Use a cell array to pass your own legend, '...
                'or rename the fields']);
        else % set it to Exists,
            if forceNoLegend
                legendExists=0;
            else
                legendExists=1;
            end
        end
        
        forStructLegend=fields(tempValues)';
        for k=1:length(forStructLegend)
            cellValues{k}=tempValues.(forStructLegend{k});
        end
        cellLegend =forStructLegend; % this is for text purposes.
        
    otherwise % Its an array and data needs to be changed to a cell array, for what follows.
        arrayFlag=1;
        cellValues={cellValues};
        normalHist=1;
        
        if legendExists % it is probably passed as a string not a cell
            valueInfo=whos('cellLegend');
            valueType=valueInfo.class;
            if ~strcmp(valueType,'cell')
                cellLegend={cellLegend};
            else
                warning('please pass the legend as the same type as the data');
            end
        end
        
end

%% Check some user-entered parameters for problems
if round(decimalPlaces)~=decimalPlaces 
    warning(['decimalPlaces must be an integer number. You entered ' num2str(decimalPlaces) ' '...
             'the rounded number ' num2str(round(decimalPlaces)) ' will be used instead']);
    decimalPlaces=round(decimalPlaces);
end

if vertLinesForcedFlag>1
    warning(['you cannot specify having and not having vertical lines. ' ...
             'Therefore we will determine it automatically as usual']);
    vertLinesForcedFlag=0;
end         

%% Collect the Data, check some things
num2Plot=length(cellValues);

if legendExists
    if num2Plot~=length(cellLegend)
        warning('legend is not appropriately sized for the data');
        if num2Plot>length(cellLegend)
            for k=length(cellLegend)+1:num2Plot
                cellLegend{k}=['Plot #' num2str(k)];
            end
        end
    end
end

% check for integer, or near integer values (to make integer bins without gaps)

if intbinsFlag
    intbins=ones(1,num2Plot);
else
    intbins=zeros(1,num2Plot);
    if ~intbinsForcedFlag % if its forced, then we want it to stay zero
        for k=1:num2Plot    
            intbins(k) = isdiscrete(cellValues{k});
        end
        if sameBinsFlag % then if one has integers, they all must be plotted along integers.
            intbins = or(intbins,sum(intbins));
        end
    end
end


% This is to collect the means std, and a few other things
for k=1:num2Plot
    if ~isnumeric(cellValues{k})
         error(['You cannot make a histogram of non-numeric data. Plot #' num2str(k) ' non numeric']);
    end
%     infFlag(k)=;

% Changing numbers to doubles makes the 'text' parameter work.
% This also makes it so you can pass it a full matrix, just for fun.
% It is done for each one individually so you can even pass a cell array
% where the individual vectors are differently angled.
    cellValues{k}=double(cellValues{k}(:));

    nanValues = isnan(cellValues{k});
    nnan = sum(nanValues);
% remove NaN values
    if nnan>0
        cellValues{k}=cellValues{k}(~nanValues);
        
        if nnan>1, waswere='were'; else waswere='was';end
        warning(['data set #:' num2str(k) ' has ' num2str(nnan) ' ''NaN'' values which ' waswere ' removed from all analysis and counts\n']);
    end

% Check for and deal with infinite values.
    infValues=isinf(cellValues{k});
    if sum(infValues)%infFlag(k)
        plotStdFlag=0; % the mean of the data makes no sense here.
        if sum(infValues)>1, waswere='were'; else waswere='was';end
        warning(['data set #:' num2str(k) ' has ''inf'' values which ' waswere ' put in the end bin/s. The mean and std will not be displayed\n']);
        
        infV=cellValues{k}(infValues);
        nPosInf=sum(infV>0);
        nNegInf=sum(infV<0);
        cellValues{k}=cellValues{k}(~infValues);
    else
        nPosInf=0;
        nNegInf=0;
    end
    
% Store the values temporarily
    Values=cellValues{k};
% check for imaginary data
    if ~isreal(Values)
        warning('magnitude taken of all imaginary data');
        Values=abs(Values);
        cellValues{k}=Values;
    end
%   check if it is an empty bin
    if isempty(Values)
        isData(k)=false;
        Values=[0 0 0];
        cellValues{k}=Values;
        warning(['data set #:' num2str(k) ' is empty']);
    else
        isData(k)=true;
    end

% Store a few other useful values
    stdV{k}=std(Values); % standard dev of values
    meanV{k}=mean(Values);
    medianV{k}=median(Values);
    numPoints{k}=length(Values); % number of values
    
    % initialize to be used later, not a user paramter at all
    modeShift{k}=0;
    
end

if sum(isData)<1
    warning('None of your data is plottable, so nothing was plotted. Please search for more data and try again');
    return;
end


%% FIND THE AXIS BOUNDS
% on each side, left and right
% error the user if they choose retarded bounds (pardon my politically uncorrectness)
if ~isempty(minX) && ~isempty(maxX)
    if maxX<minX
        error(['your max bound: ' num2str(maxX) ' is bigger than your min bound: ' num2str(minX) ' you can''t do that silly']);
    end
end

for k=1:num2Plot
  Values=cellValues{k};
%  warn error if there is only one point of data
  if length(Values)<2 
      warning(['maybe a histogram is not the best method to graph your single number in plot#:' num2str(k)]);
  end
  
% warn the user if they chose a dumb bounds (but not retarded ones)
  if ~isempty(minX)
    if minX>meanV{k}
        warning(['the mean of your data set#' num2str(k) ' is off the chart to the left, '...
                'choose larger bounds or quit messing with the program and let it do '...
                'its job the way it was designed.']);
    end
  end
  if ~isempty(maxX)
    if maxX<meanV{k}
        warning(['the mean of your data set#' num2str(k) ' is off the chart to the right, '...
                'choose larger bounds or quit messing with the program and let it do '...
                'its job the way it was designed.']);
    end
  end
  
%   Note the check stdV{k}>0, just in case the std is zero, we need to set
%   boundaries so that it doesn't crash with 0 bins used. The range of
%   (+1,-1) is totally arbitrary.

% set x MIN values
    if isempty(minX) % user did not specify - then we need to find the minimum x value to use
        if stdV{k}>(10*eps) % just checking there are more than two different points to the data, checking for rounding errors.
            leftEdge = meanV{k}-stdV{k}*stdTimes;
            if leftEdge<min(Values) % if the std is larger than the largest value
                minS(k)=min(Values);
            else % cropp it now on the bottom.
%             cropped!
                minS(k) = leftEdge;
            end
        else % stdV==0, wow, all your data points are equal
            minS(k)=min(Values)-1000*eps; % padd it by 100, seems reasonable
        end
    else % minX is specified so minS is just set stupidly here
        if minX<max(Values)
            minS(k)=minX;
        else % ooh man, even your biggest value is smaller than your min
            minS(k)=min(Values);
            warning(['user parameter minx=' num2str(minX) ' override since it put all your data out of bounds']);
        end
    end
    
% set x MAX values
    if isempty(maxX)
        if stdV{k}>(10*eps) % just checking there are more than two different points to the data
            rightEdge = meanV{k}+stdV{k}*stdTimes;
            if rightEdge>max(Values) % if the suggested border is larger than the largest value
                maxS(k)=max(Values);
            else % crop the graph to cutoff values
                maxS(k)=rightEdge;
            end
        else % stdV==0, wow,
%           Note that minX no longer works in this case.
            maxS(k)=max(Values)+1000*eps; % padd it by 100, seems reasonable
        end
    else % maxX is specified so minS is just set here
        maxS(k)=maxX;    
        if maxX>min(Values)
            maxS(k)=maxX;
        else % ooh man, even your smallest value is bigger than your max
            maxS(k)=max(Values);
            warning(['user parameter maxx=' num2str(maxX) ' override since it put all your data out of bounds']);
        end
    end
    
    if intbins(k)
        maxS(k)=round(maxS(k))+.5;
        minS(k)=round(minS(k))-.5; % subtract 1/2 to make the bin peaks appear on the numbers.
    end
    
end % look over k finished
% This is the range that the x axis will plot at for each one.
% Only set the bounds for things that have data
% isData = logical(isData);
SXRange = [min(minS(isData)) max(maxS(isData))];
% note that later there will be a bit added to maxS of SXRange
% This below is to get estimates for appropriate binsizes
totalRange=diff(SXRange); % if the range is zero, then make it eps instead.

%% deal with the infinity data
% In this case we add the inf values back in as off the charts numbers on
% the appropriate side. In this way the 'cropped' star will be plotted.
for k=1:num2Plot % nNegInf= number of negative infinities removed
    cellValues{k}=[cellValues{k}; repmat(SXRange(1)-100,nNegInf,1); repmat(SXRange(2)+100,nPosInf,1)];    
end


%% FIND OUT IF THERE WERE CROPS DONE

for k=1:num2Plot
    % Set the crop flag
    if min(cellValues{k})<SXRange(1)
        cropped_left{k}=sum(cellValues{k}<SXRange(1));  % flag to plot the star later
    else
        cropped_left{k}=0;
    end
    % Set the crop flag
    if max(cellValues{k})>SXRange(2)
        cropped_right{k}=sum(cellValues{k}>SXRange(2)); % flag to plot the star later
    else
        cropped_right{k}=0;
    end
end

%% DEAL WITH BIN SIZES
% Reccomend a bin width
binWidth=zeros(1,num2Plot);

% Warn users for dumb max/min bin size choices.
if minBins<3,  error('No I refuse to plot this you abuser of functions, the minimum number of bins must be at least 3'); end;
if minBins<10, warning('you are using a very small minimum number of bins, do you even know what a histogram is?'); end;
if minBins>20, warning('you are using a very large minimum number of bins, are you sure you *always need this much precision?'); end;
if maxBins>150,warning('you are using a very high maximum for the number of bins, unless your monitor is in times square you probably won''t need that many bins'); end;
if maxBins<50, warning('you are using a low maximum for the number of bins, are you sure it makes sense to do this?'); end;

% Choose estimate bin widths
for k=1:num2Plot
% This formula "Scott's choice" is described in the introduction above.
% default: binFactor=1;
    binWidth(k)=3.5*stdV{k}/(binFactor*(numPoints{k})^(1/3));
    
  % Instate a mininum and maximum number of bins
    numBins = totalRange/binWidth(k); % Approx number of bins
    if numBins<minBins % if this will imply less than 10 bins
        binWidth(k)=totalRange/(minBins); % set so there are ten bins
    end
    if numBins>maxBins % if there would be more than 75 bins (way too many)
        binWidth(k)=totalRange/maxBins;
    end
    
%   Check if it is intbins, becase then:
    if intbins(k)% binwidth must be an integer, and it must be at least 1
        binWidth(k)=max(round(binWidth(k)),1);
    end
    
    if numBins>=30 && proportionFlag
        warning('it might not make sense to use ''proportion'' here since you have so many bins')
    end
    if numBins>=100 && (proportionFlag || numberFlag)
        warning('it might make sense to use ''pdf'' here since you have so many bins')
    end
    
    nBins(k)=totalRange/binWidth(k);

%   if there is enough space to plot them, then plot vertical lines.
% 30 bins is arbitrarily chosen to be the number after which there are
% vertical lines plotted by default
    if nBins(k)<30
        vertLinesArray(k)=1;
    else
        vertLinesArray(k)=0;
    end
end

% fix the automatic decision if vertical lines were specified by the user
if vertLinesForcedFlag
    vertLinesArray=vertLinesArray*0+vertLinesFlag;
end

% only plot lines if they all can be plotted.
% also creates one flag, so the 'array' does not need to be used.
vertLinesFlag=prod(vertLinesArray); % since they are zeros and 1's, this is an "and" statement

% find the maximum bin width
bigBinWidth=max(binWidth);

%%  resize bins to be multiples of each other - or equal
% sameBinsFlag will make all bin sizes the same.

% Note that in all these conditions the largest histogram bin width
% divides evenly into the smaller bins. This way the data will line up and
% you can easily visually compare the values in different bins
if sameBinsFlag % if 'same' is passed then make them all equal to the average reccomended size
    binWidth=0*binWidth+mean(binWidth); %    
else % the bins will be different if neccesary
    for k=1:num2Plot
%       The 'ceil' rather than 'round' is supposed to make sure that the
%       ratio is at lease 1 (divisor at least 2).
        binWidth(k)=bigBinWidth/ceil(bigBinWidth/binWidth(k));
    end
end


SXRange(2) = SXRange(2)+max(binWidth);
% recalculate totalRange for the axis lims, and histogram calculating.
totalRange=diff(SXRange);


%% CALCULATE THE HISTOGRAM
% 
maxN=0; %for setting they ylim(maxN) command later, find the largest height of a column
for k=1:num2Plot
    Values=cellValues{k};
%  Set the bins
% Note that the range is already expanded by one half, to center columns on numbers
    if intbins(k) 
        SBins{k}=SXRange(1):binWidth(k):SXRange(2);
        % if it is 'samebins' then even if 'intbins' is zero for some of
        % them to start with, it is already enforced that they *all have
        % intbins if at least one of them has it, and there are 'samebins'
    else
        SBins{k}=SXRange(1):binWidth(k):SXRange(2);
    end
    
%  Set it to count all those outside as well.
     binsForHist{k}=SBins{k};
     binsForHist{k}(1)=-inf; binsForHist{k}(end)=inf;
%  Calculate the histograms
     n{k} = histc(Values, binsForHist{k});
     if ~isData(k) % so that the ylim property is not destroyed with maxN being extra large
         if normalHist
             n{k}=n{k}*0+1; % it will plot it from 0 to one,
         else % it needs to be the lowest minimum possible!
             n{k}=n{k}*0+eps;
         end
     else
         n{k}=n{k}';
     end
     
     
%  This here is to complete the right-most value of the histogram.
%      x{k}=[SBins{k} SXRange(2)+binWidth(k)];
       x{k} = SBins{k};
%      n{k}=[n{k} 0];
%  Later we will n`eed to plot a line to complete the left start.

%% Add the number of points used to the legend
    if legendExists
        oldLegend{k}=cellLegend{k};
    else
        oldLegend{k}=['Plot #' num2str(k)];
    end
    
    if npointsFlag
        if legendExists
            cellLegend{k}=[cellLegend{k} ' (' num2str(numPoints{k}) ')'];
        else
            cellLegend{k}=['(' num2str(numPoints{k}) ')'];
            if k==num2Plot % only once they have all been made
                legendExists=1;
            end
        end
    end

end

%% Extra calculations for histogram
rawN=n; % save the rawN before normalization
for k=1:num2Plot
% Normalize, normalize all the data by area
% only do this if they will be plotted together, otherwise leave it be.
  if (~normalHist && ~proportionFlag && ~numberFlag) || pdfFlag
%     n   = (each value)/(width of a bin * total number of points)
%     n   =  n /(Total area under histogram);
      n{k}=n{k}/(binWidth(k)*numPoints{k});
  end % if it is a normalHist - then it will be numbers automatically.

  if proportionFlag
%     n   =  n /(Total number of points);
%     now if you sum all the heights (not the areas) you get one,
      n{k}=n{k}/numPoints{k};
  end

 % Find the maximum for plotting the errorBars
      maxN=max([n{k}(:); maxN]);    
      
%   this calculates the approximate mode, the highest peak here.
%   you need to add the binWidth/2 to get to the center of the bar for
%   the histogram.
    roundedMode{k}=mean(x{k}(n{k}==max(n{k})))+binWidth(k)/2;
end

%% CREATE THE FIGURE
if newfigFlag % determine figure height
    scrsz = get(0,'ScreenSize');
    sizes=[650 850 1000 scrsz(4)-8];
    if num2Plot>=5
        figHeight=sizes(4);
    elseif num2Plot>2
        figHeight=sizes(num2Plot-2);
    end
    if normalHist && num2Plot>2
%         figure('Name', Title,'Position',[4     300     335    figHeight%         ]);
        figure('Position',[4    4     435    figHeight   ]);
    else % no reason to stretch it out so much, use default size
        figure;
    end
%     figure('Name', Title);
    Hx = axes('Box', 'off', 'FontSize', AxisFontSize);
    title(makeTitle(Title));
else % all we need to do is make sure that the old figures holdstate is okay.
    %save the initial hold state of the figure.
    hold_state = ishold;
    if ~hold_state
        if normalHist && num2Plot>1
%           you need to clear the whole figure to use sub-plot
            clf;
        else
            cla; %just in case we have some subploting going on you don't want to ruin that
            axis normal;
            legend('off'); % in case there was a legend up.
%             is there anything else we need to turn off? do it here.
        end
    end
end

hold on;
%% PREPARE THE COLORS
if normalHist %
   if multicolorFlag
%         lineStyleOrder=linspecer(num2Plot,'jet');
        faceStyleOrder=linspecer(num2Plot,lineColor);
        for k=1:num2Plot % make the face colors brighter a bit
            lineStyleOrder{k}=[0 0 0];
            faceStyleOrder{k}=(faceStyleOrder{k}).^(brightnessExponent); % this will make it brighter than the line           
        end
   else % then we need to make all the graphs the same color, gray or not
        for k=1:num2Plot
            lineStyleOrder{k}=[0 0 0];
            faceStyleOrder{k}=faceColor;
        end
   end
else % they will all be in one plot, its simple. there is no faceStyleOrder
    if ischar(lineColor) % then the user must have inputted it! 
%       That means we should use the colormap they gave
        lineStyleOrder=linspecer(num2Plot,lineColor);
    else % just use the default 'jet' colormap.
        lineStyleOrder=linspecer(num2Plot);
    end    
end

%% PLOT THE HISTOGRAM
% reason for this loop:
% Each histogram plot has 2 parts drawn, the legend will look at these
% colors, this just seems like an easy way to make sure that is all plotted
% in the right order - not the most effient but its fast enough as it is.
% it is plotted below the x axis so it will never appear
if normalHist % There will be no legend for the normalHist, therefore this loop is not needed.
% But we might as well run it to set the fontsize here:
    for k=1:num2Plot
        if num2Plot>1
            subplot(num2Plot,1,k);
        end
        hold on;
        plot([0 1],[-1 -1],'color',lineStyleOrder{k},'linewidth',linewidth);
        set(gca,'fontsize',AxisFontSize);
    end
else % do the same thing, but on different subplots
    for k=1:num2Plot
%     Do not put: if isData(k) here because it is important that even
%     places with no data have a reserved color spot on a legend.
%     plot lines below the x axis, they will never show up but will set the
%     legend appropriately.
        plot([0 1],[-1 -1],'color',lineStyleOrder{k},'linewidth',linewidth);
    end
    set(gca,'fontsize',AxisFontSize);
end
if normalHist % plot on separate sub-plots
    for k=1:num2Plot
        if num2Plot>1
            subplot(num2Plot,1,k);
        end
        hold on;
        if isData(k)
%           Note this is basically doing what the 'histc' version of bar does,
%           but with more functionality (there must be some matlab bug which
%           doesn't allow changing the lineColor property of a histc bar graph.)
            if vertLinesFlag % then plot the bars with edges
                bar(x{k}+binWidth(k)/2,n{k}/1,'FaceColor',faceStyleOrder{k},'barwidth',1,'EdgeColor','k','linewidth',1.5)
            else % plot the bars without edges
                bar(x{k}+binWidth(k)/2,n{k}/1,'FaceColor',faceStyleOrder{k},'barwidth',1,'EdgeColor','none')
            end
            
            if ~smoothFlag
                stairs(x{k},n{k},'k','linewidth',linewidth);
                plot([x{k}(1) x{k}(1)],[0 n{k}(1)],'color','k','linewidth',linewidth);
            else % plot it smooth, skip the very edges.
%                 plot(x{k}(1:end-1)+binWidth(k)/2,n{k}(1:end-1),'k','linewidth',linewidth);
                xi = linspace(SXRange(1),SXRange(2),500); yi = pchip(x{k}(1:end-1)+binWidth(k)/2,n{k}(1:end-1),xi);
                plot(xi,yi,'k','linewidth',linewidth);
            end
            
            
        end
    end
else % plot them all on one graph with the stairs function
    for k=1:num2Plot
        if isData(k)
            if ~smoothFlag
                stairs(x{k},n{k},'color',lineStyleOrder{k},'linewidth',linewidth);
                plot([x{k}(1) x{k}(1)],[0 n{k}(1)],'color',lineStyleOrder{k},'linewidth',linewidth);
            else % plot it smooth
                xi = linspace(SXRange(1),SXRange(2),500); yi = pchip(x{k}(1:end-1)+binWidth(k)/2,n{k}(1:end-1),xi);
                plot(xi,yi,'color',lineStyleOrder{k},'linewidth',linewidth);
                if vertLinesFlag % plot those points, otherwise its a wash.
                    plot(x{k}(1:end-1)+binWidth(k)/2,n{k}(1:end-1),'.','color',lineStyleOrder{k},'markersize',15);
                end
            end
        end
    end
end
%% PLOT THE STARS IF CROPPED
% plot a star on the last bin in case the ends are cropped
% This also adds the following text in the caption:
% 'The starred column on the far right represents the bin for all values
% that lie off the edge of the graph.'
%     Note that the star is placed +maxN/20 above the column, this
%     is so that its the same for all data, and relative to the y
%     axis range, not the individual plots. The text starts at the
%     top, so it only needs a very small push to get above it.
if normalHist
    for k=1:num2Plot
        if num2Plot>1
            subplot(num2Plot,1,k);
        end
        if isData(k)
        if cropped_right{k} % if some of the data points lie outside the bins.
            text(x{k}(end-1)+binWidth(k)/10,n{k}(end-1)+max(n{k})/50,'*','fontsize',AxisFontSize,'color',lineStyleOrder{k});
        end
        if cropped_left{k} % if some of the data points lie outside the bins.
            text(x{k}(1)+binWidth(k)/10,n{k}(1)+max(n{k})/30-max(n{k})/50,'*','fontsize',AxisFontSize,'color',lineStyleOrder{k});
        end
        end
    end
else
    for k=1:num2Plot
        if isData(k)
%             stairs(x{k},n{k},'color',lineStyleOrder{k},'linewidth',linewidth);
%             plot([x{k}(1) x{k}(1)],[0 n{k}(1)],'color',lineStyleOrder{k},'linewidth',linewidth);

      %    ADD A STAR IF CROPPED 
            if cropped_right{k} % if some of the data points lie outside the bins.
                text(x{k}(end-1)+binWidth(k)/10,n{k}(end-1)+maxN/50,'*','fontsize',AxisFontSize,'color',lineStyleOrder{k});
            end
            if cropped_left{k} % if some of the data points lie outside the bins.
                text(x{k}(1)+binWidth(k)/10,n{k}(1)+maxN/30-maxN/50,'*','fontsize',AxisFontSize,'color',lineStyleOrder{k});
            end
        end
    end
end

%% PLOT the ERROR BARS and MODE
% but only if it was requested
if modeFlag && medianFlag % just a warning here
  warning(['This will make a very messy plot, didn''t your mother '...
           'warn you not to do silly things like this '...
           'Next time please choose either to have mode or the median plotted.']);
    fprintf('The mode is plotted as a dashed line\n');
end

for k=1:num2Plot  
    if isData(k)
%     Note the following varables that were defined much earlier in the code.
%       numPoints
%       stdV{k}=std(Values); % standard dev of values
%       meanV{k}=mean(Values);
%       medianV{k}=median(Values);
%       roundedMode{k}=mean(x{k}(n{k}==max(n{k}))); % finds the maximum of the plot
    if normalHist % separate plots with separate y-axis                
        if num2Plot>1
            subplot(num2Plot,1,k);
        end
        tempMax = max(n{k});
        if modeFlag || medianFlag
            modeShift{k}=.1*max(n{k});
        end            
    else % same plot, same y axis!
        tempMax = maxN;
        if modeFlag || medianFlag
            modeShift{k}=.1*(maxN);
        end
    end
    if medianFlag
        if normalHist % plot with 'MarkerFaceColor'
            stem(medianV{k},(1.1)*tempMax,'color',lineStyleOrder{k},'linewidth',linewidth,'MarkerFaceColor',faceStyleOrder{k});
        else % plot hollow
            stem(medianV{k},(1.1)*tempMax,'color',lineStyleOrder{k},'linewidth',linewidth)
        end
        
    end
%   Plot the Mode
    if modeFlag % then plot the median in the center as a stem plot
%               Note that this mode is rounded . . .
        if medianFlag % plot the mode in a different way
            if normalHist
                stem(roundedMode{k},(1.1)*tempMax,'--','color',lineStyleOrder{k},'linewidth',linewidth,'MarkerFaceColor',faceStyleOrder{k});
            else
                stem(roundedMode{k},(1.1)*tempMax,'--','color',lineStyleOrder{k},'linewidth',linewidth)
            end
            
        else % plot the regular way and there will be no confusion
            if normalHist
                stem(roundedMode{k},(1.1)*tempMax,'color',lineStyleOrder{k},'linewidth',linewidth,'MarkerFaceColor',faceStyleOrder{k})
            else
                stem(roundedMode{k},(1.1)*tempMax,'color',lineStyleOrder{k},'linewidth',linewidth);
            end
        end

    end
%   Plot the standard deviation or standard error
    if plotStdFlag==0 && serrorFlag==1 % just a warning here
        warning('You have can''t have ''noerror'' and eat your ''serror'' too!')
        fprintf('Next time please choose either to have error bars or not have them!\n');
    end
    if (serrorFlag==1) && boxplotFlag == 1 % just a warning here
        warning('You have can''t have your ''serror'' and eat your ''boxplot'' too!')
        fprintf('Next time please choose either to have one or the other only!\n');
        boxplotFlag = 0;
    end
    
    if plotStdFlag % it is important to set the ylim property here so errorb plots the appropriate sized error bars
        if normalHist
            ylim([0 max(n{k})*(1.1+.1)+modeShift{k}]);% add this in case the data is zero
            tempY=tempMax.*1.1+modeShift{k};
        else
            ylim([0 maxN*(1.1+.1*num2Plot)+modeShift{k}]);
            tempY=tempMax*(1+.1*(num2Plot-k+1))+modeShift{k};
        end
        if serrorFlag%==1 % if standard error will be plotted
%           note: that it is plotting it from the top to the bottom! just like the legend is
            errorb(meanV{k},tempY,stdV{k}/sqrt(numPoints{k}),'horizontal','color',lineStyleOrder{k},'barwidth',barFactor,'linewidth',linewidth);
        else % just plot the standard deviation as error
            errorb(meanV{k},tempY,stdV{k},                   'horizontal','color',lineStyleOrder{k},'barwidth',barFactor,'linewidth',linewidth);
        end
        
        if normalHist % plot only the dot in color
            plot(meanV{k},tempY,'.','markersize',25,'color',faceStyleOrder{k});
            plot(meanV{k},tempY,'o','markersize',8,'color',[0 0 0],'linewidth',linewidth);
        else % plot everything in color, this dot and the bars before it
            plot(meanV{k},tempY,'.','markersize',25,'color',lineStyleOrder{k});
        end
    end
%   Plot the boxplot!
    if boxplotFlag % it is important to set the ylim property here so errorb plots the appropriate sized error bars
        if normalHist
            ylim([0 max(n{k})*(1.3+.3)+modeShift{k}]);% add this in case the data is zero
            tempY=tempMax.*1.3+modeShift{k}; % note: 1.3 instead of 1.2 because the boxplot needs a little more room.
        else
            ylim([0 maxN*(1.3+.3*num2Plot)+modeShift{k}]);
            tempY=tempMax*(1+.3*(num2Plot-k+1))+modeShift{k};
        end
        
        if normalHist
            boxplotWidth = max(n{k})*.18; % the highest of & any of the datasets.
        else % do them separately, to each their own width
            boxplotWidth = max([n{:}])*.18; % the highest of & any of the datasets.
        end
        
        if max([numPoints{:}])<400
            pointsOrNo = 'points';
        else
            pointsOrNo = 'nopoints';
        end
        
        if normalHist % plot the thing with all the colors, there is just one of them.
            bplot(cellValues{k},tempY,'barwidth',boxplotWidth,'linewidth',linewidth,'horizontal',pointsOrNo,'specialwidth','histmode');
        else % plot with the color for that data set
            bplot(cellValues{k},tempY,'color',lineStyleOrder{k},'barwidth',boxplotWidth,'linewidth',linewidth,'horizontal',pointsOrNo,'specialwidth','histmode');
        end
        
    end
    end % if isData
end % num2plot loop over
  
%% DEAL WITH FANCY GRAPH THINGS
% note that the legend is already added in the 'plotting' section
% padd the edges of the graphs so the histograms have room to sit in.
axisRange(1)=SXRange(1)-totalRange/30; % just expand it a bit, pleasantry
axisRange(2)=SXRange(2)+totalRange/30;

%% set defaults for the yLabel depending on the type of graph
if yLabelFlag
    % do nothing, the user has input a yLabel
else
    if proportionFlag % override the above defaults for both cases.
        SYLabel = 'proportion';        
    elseif pdfFlag
        SYLabel = 'pdf';
    elseif numberFlag
        SYLabel = 'number';
    else
        if normalHist % then they are not normalized
            SYLabel = 'number';
        else
            SYLabel = 'pdf'; % probability density function
        end
    end
end

if normalHist
    for k=1:num2Plot        
        if num2Plot>1
            subplot(num2Plot,1,k);
        end
%       add a title to each plot, from the legend
        if legendExists
            title(makeTitle(cellLegend{k}),'FontWeight','bold');
        end
%      set axis
        xlim(axisRange);
        if ~plotStdFlag && ~boxplotFlag
%             if the plots std flag happened then it would have been
%             already set
%             ylim([0 max(n{k})*(1.1+.1)+modeShift{k}]);
%         else
            ylim([0 max(n{k})*(1.1)+modeShift{k}]);
        end
%       label y
        ylabel(SYLabel, 'FontSize', AxisFontSize);
    end
%   label x axis only at the end, the bottom subplot
    xlabel(SXLabel, 'FontSize', AxisFontSize);
    
else % all in one plot:
%  set y limits
    if ~plotStdFlag && ~boxplotFlag
%       ylim([0 maxN*(1.1+.1*num2Plot)+modeShift{k}]);
%     else
        ylim([0 maxN*(1.1)+modeShift{k}]);
    end
    % set x limits
    xlim(axisRange);
    % label y and x axis
    ylabel(SYLabel, 'FontSize', AxisFontSize);
    xlabel(SXLabel, 'FontSize', AxisFontSize);
%   Add legend
    if legendExists
        legend(makeTitle(cellLegend),'location',legendLocation);%,'location','SouthOutside');
        legend boxoff;
    end
end

%% Save theText variable with all the special data points plotted
for k=1:num2Plot
    theText{k}=[oldLegend{k} ': '];
    if isData(k)
        if textFlag
            theText{k}=[theText{k} 'number of points=' num2str(numPoints{k},'%.0f') ', '];
            theText{k}=[theText{k} 'mean=' num2str(meanV{k},['%.' num2str(decimalPlaces) 'f']) ', '];
            theText{k}=[theText{k} 'std='  num2str(stdV{k},['%.' num2str(decimalPlaces) 'f']) ', '];
            theText{k}=[theText{k} 'serror='  num2str(stdV{k}/sqrt(numPoints{k}),['%.' num2str(decimalPlaces) 'f']) ', '];
            theText{k}=[theText{k} 'median='  num2str(medianV{k},['%.' num2str(decimalPlaces) 'f']) ', '];
            theText{k}=[theText{k} 'approx mode='  num2str(roundedMode{k},['%.' num2str(decimalPlaces) 'f']) ', '];
        else
            if npointsFlag
                theText{k}=[theText{k} 'number of points=' num2str(numPoints{k},'%.0f') ', '];
            end
            if plotStdFlag
                theText{k}=[theText{k} 'mean='  num2str(meanV{k},['%.' num2str(decimalPlaces) 'f']) ', '];
                if serrorFlag
                    theText{k}=[theText{k} 'standard error='  num2str(stdV{k}/sqrt(numPoints{k}),['%.' num2str(decimalPlaces) 'f']) ', '];
                else %put standard deviation
                    theText{k}=[theText{k} 'std='  num2str(stdV{k},['%.' num2str(decimalPlaces) 'f']) ', '];
                end
            end
            if medianFlag
                theText{k}=[theText{k} 'median='  num2str(medianV{k},['%.' num2str(decimalPlaces) 'f']) ', '];
            end
            if modeFlag
                theText{k}=[theText{k} 'approx mode='  num2str(roundedMode{k},['%.' num2str(decimalPlaces) 'f']) ', '];
            end
        end
        if cropped_left{k} % if some of the data points lie outside the bins.
            theText{k}=[theText{k} num2str(cropped_left{k}) ' points counted in the leftmost bin are less than ' num2str(x{k}(1),['%.' num2str(decimalPlaces) 'f']) ' , '];
        end
        if cropped_right{k} % if some of the data points lie outside the bins.
            theText{k}=[theText{k} num2str(cropped_right{k}) ' points counted in the rightmost bin are greater than ' num2str(x{k}(end-1),['%.' num2str(decimalPlaces) 'f']) ' , '];
        end
    else
        theText{k}=[theText{k} 'Had no data points'];
    end
end

%% set all outputs to structs in case it started that way.
if structFlag % set all output to structures, like it was put in.
    for k=1:num2Plot
        tempText.(forStructLegend{k})=theText{k};
        tempRawN.(forStructLegend{k})=rawN{k};
        tempX.(forStructLegend{k})   =x{k};
    end
    theText=tempText;
    rawN=tempRawN;
    x=tempX;
end

if arrayFlag % you passed an array, you will get an array answer
    theText=theText{1};
    rawN=rawN{1};
    x=x{1};    
end

%% print figure    
  % Save the figure to a EPS file
  if ~strcmp(EPSFileName, ''), print('-depsc', EPSFileName); end
  
%% return the hold state of the figure to the way it was
if ~newfigFlag % otherwise hold_state will not be saved
    if ~hold_state
        hold off;
    end
end
end

% This will tell if the data is an integer or not.
% first it will check if matlab says they are integers, but even so, they
% might be integers stored as doubles!
function L = isdiscrete(x,varargin) % L stands for logical
minError=eps*100; % the minimum average difference from integers they can be.
L=0; % double until proven integer
if ~isempty(varargin)
    minError=varargin{1};
end 
if isinteger(x)||islogical(x) % your done, duh, its an int.
    L=1;
    return; 
else
    if sum(abs(x-round(x)))/length(x)<minError
        L=1;
    end
end

end



%% function errorb(x,y,varargin) to plot nice healthy error bars
% It is possible to plot nice error bars on top of a bar plot with Matlab's
% built in errorbar function by setting tons of different parameters to be
% various things.
% This function plots what I would consider to be nice error bars as the
% default, with no modifications necessary.
% It also plots, only the error bars, and in black. There are some very
% useful abilities that this function has over the matlab one, see below:
% 
%% Basics (same as matlab's errobar)
% errorb(Y,E) plots Y and draws an error bar at each element of Y. The
% error bar is a distance of E(i) above and below the curve so that each
% bar is symmetric and 2*E(i) long.
% If Y and E are a matrices, errob groups the bars produced by the elements
% in each row and plots the error bars in their appropriate place above the
% bars.
% 
% errorb(X,Y,E) plots Y versus X with
% symmetric error bars 2*E(i) long. X, Y, E must
% be the same size. When they are vectors, each error bar is a distance of E(i) above
% and below the point defined by (X(i),Y(i)).
% 
% errorb(X,Y,'Parameter','Value',...) see below
% 
%% Optional Parameters
%    horizontal: will plot the error bars horizontally rather than vertically
%    top: plot only the top half of the error bars (or right half for horizontal)
%    barwidth: the width of the little hats on the bars (default scales with the data!)
%              barwidth is a scale factor not an absolute value.
%    linewidth: the width of the lines the bars are made of (default is 2)
%    points: will plot the points as well, in the same colors.
%    color: specify a particular color for all the bars to be (default is black, this can be anything like 'blue' or [.5 .5 .5])
%    multicolor: will plot all the bars a different color (thanks to my linespecer function)
%                colormap: in the case that multicolor is specified, one
%                           may also specify a particular colormap to
%                           choose the colors from.
%% Examples
% y=rand(1,5)+1; e=rand(1,5)/4;
% hold off; bar(y,'facecolor',[.8 .8 .8]); hold on;
% errorb(y,e);
% 
% defining x and y
% x=linspace(0,2*pi,8); y=sin(x); e=rand(1,8)/4;
% hold off; plot(x,y,'k','linewidth',2); hold on;
% errorb(x,y,e) 
% 
% group plot:
% values=abs(rand(2,3))+1; errors=rand(2,3)/1.5+0;
% errorb(values,errors,'top');
%% Acknowledgments
% Thank you to the AP-Lab at Boston University for funding me while I
% developed these functions. Thank you to the AP-Lab, Avi and Eli for help
% with designing and testing them.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Jonathan Lansey Jan 2009,     questions to Lansey at gmail.com          %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function errorb(x,y,varargin)
%% first things first
%save the initial hold state of the figure.
hold_state = ishold;
if ~hold_state
    cla;
end


%% If you are plotting errobars on Matlabs grouped bar plot
if size(x,1)>1 && size(x,2)>1 % if you need to do a group plot
% Plot bars
    num2Plot=size(x,2);
    e=y; y=x;
	handles.bars = bar(x, 'edgecolor','k', 'linewidth', 2);
	hold on
	for i = 1:num2Plot
		x =get(get(handles.bars(i),'children'), 'xdata');
		x = mean(x([1 3],:)); 
%       Now the recursive call!
		errorb(x,y(:,i), e(:,i),'barwidth',1/(num2Plot),varargin{:}); %errorb(x,y(:,i), e(:,i),'barwidth',1/(4*num2Plot),varargin{:});
    end
    if ~hold_state
        hold off;
    end
    return; % no need to see the rest of the function
else
    x=x(:)';
    y=y(:)';
    num2Plot=length(x);
end
%% Check if X and Y were passed or just X

if ~isempty(varargin)
    if ischar(varargin{1})
        justOneInputFlag=1;
        e=y; y=x; x=1:num2Plot;
    else
        justOneInputFlag=0;
        e=varargin{1}(:)';
    end
else % not text arguments, not even separate 'x' argument
    e=y; y=x; x=1:length(e);
    justOneInputFlag=0;
end

hold on; % axis is already cleared if hold was off
%% Check that your vectors are the proper length
if num2Plot~=length(e) || num2Plot~=length(y)
    error('your data must be vectors of all the same length')
end

%% Check that the errors are all positive
signCheck=min(0,min(e(:)));
if signCheck<0
    error('your error values must be greater than zero')
end

%% In case you don't specify color:
color2Plot = [ 0 0 0];
% set all the colors for each plot to be the same one. if you like black
for kk=1:num2Plot
    lineStyleOrder{kk}=color2Plot;
end

%% Initialize some things before accepting user parameters
horizontalFlag=0;
topFlag=0;
pointsFlag=0;
barFactor=1;
linewidth=2;
colormapper=colorm;
% colormapper='jet';

multicolorFlag=0;

%% User entered parameters
%  if there is just one input, then start at 1,
%  but if X and Y were passed then we need to start at 2
k = 1 + 1 - justOneInputFlag; %
% 
while k <= length(varargin) && ischar(varargin{k})
    switch (lower(varargin{k}))
      case 'horizontal'
        horizontalFlag=1;
        if justOneInputFlag % need to switch x and y now
            x=y; y=1:num2Plot; % e is the same
        end
      case 'color' %  '': can be 'ampOnly', 'heat'
        color2Plot = varargin{k + 1};
%       set all the colors for each plot to be the same one
        for kk=1:num2Plot
            lineStyleOrder{kk}=color2Plot;
        end
        k = k + 1;
      case 'linewidth' %  '': can be 'ampOnly', 'heat'
        linewidth = varargin{k + 1};
        k = k + 1;
      case 'barwidth' %  '': can be 'ampOnly', 'heat'
        barFactor = varargin{k + 1};
%         barWidthFlag=1;
        k = k + 1;
      case 'points'
        pointsFlag=1;
      case {'multicolor','mcolor'}
          multicolorFlag=1;
      case 'colormap' % used only if multicolor
        colormapper = varargin{k+1};
        k = k + 1;
      case 'top'
          topFlag=1;
      otherwise
        warning('Dude, you put in the wrong argument');
%         p_ematError(3, 'displayRose: Error, your parameter was not recognized');
    end
    k = k + 1;
end

if multicolorFlag
    lineStyleOrder=linspecer(num2Plot,colormapper);
end

%% Set the bar's width if not set earlier
if num2Plot==1
%   defaultBarFactor=how much of the screen the default bar will take up if
%   there is only one number to work with.
    defaultBarFactor=20;
    p=axis;
    if horizontalFlag
        barWidth=barFactor*(p(4)-p(3))/defaultBarFactor;
    else
        barWidth=barFactor*(p(2)-p(1))/defaultBarFactor;
    end
else % is more than one datum
    if horizontalFlag
        barWidth=barFactor*(y(2)-y(1))/4;
    else
        barWidth=barFactor*(x(2)-x(1))/4;
    end
end

%% Plot the bars
for k=1:num2Plot
    if horizontalFlag
        ex=e(k);
        esy=barWidth/2;
%       the main line
        if ~topFlag || x(k)>=0  %also plot the bottom half.
            plot([x(k)+ex x(k)],[y(k) y(k)],'color',lineStyleOrder{k},'linewidth',linewidth);
    %       the hat     
            plot([x(k)+ex x(k)+ex],[y(k)+esy y(k)-esy],'color',lineStyleOrder{k},'linewidth',linewidth);
        end
        if ~topFlag || x(k)<0  %also plot the bottom half.
            plot([x(k) x(k)-ex],[y(k) y(k)],'color',lineStyleOrder{k},'linewidth',linewidth);
            plot([x(k)-ex x(k)-ex],[y(k)+esy y(k)-esy],'color',lineStyleOrder{k},'linewidth',linewidth);
            %rest?
        end
    else %plot then vertically
        ey=e(k);
        esx=barWidth/2;
%         the main line
        if ~topFlag || y(k)>=0 %also plot the bottom half.
            plot([x(k) x(k)],[y(k)+ey y(k)],'color',lineStyleOrder{k},'linewidth',linewidth);
    %       the hat
            plot([x(k)+esx x(k)-esx],[y(k)+ey y(k)+ey],'color',lineStyleOrder{k},'linewidth',linewidth);
        end
        if ~topFlag || y(k)<0 %also plot the bottom half.
            plot([x(k) x(k)],[y(k) y(k)-ey],'color',lineStyleOrder{k},'linewidth',linewidth);
            plot([x(k)+esx x(k)-esx],[y(k)-ey y(k)-ey],'color',lineStyleOrder{k},'linewidth',linewidth);
        end
    end
end
%
%% plot the points, very simple

if pointsFlag
    for k=1:num2Plot
        plot(x(k),y(k),'o','markersize',8,'color',lineStyleOrder{k},'MarkerFaceColor',lineStyleOrder{k});
    end
end

drawnow;
% return the hold state of the figure
if ~hold_state
    hold off;
end

end


%% lineStyles=linspecer(N)
% This function creates a cell array of N, [R B G] color matricies
% These can be used to plot lots of lines with distinguishable and nice
% looking colors. The colors are largely taken from
% http://colorbrewer2.org and Cynthia Brewer, Mark Harrower and The Pennsylvania State University
% plotting lines of varying colors.
% 
% lineStyles = linspecer(N);  makes n colors for you to use like:
%                                         plot(x,y,'color',linestyles{ii});
% lineStyles = linspecer(N,'qualitative'); forces the colors to all be distinguishable
% lineStyles = linspecer(N,'sequential'); forces the colors to vary along a spectrum 
% lineStyles = linspecer(N,colormap); picks the colors according to your favorite colormap, like 'jet'
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Written Jonathan Lansey March 2009, updated 2013  Lansey at gmail.com %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%

function lineStyles=linspecer(N,varargin)

% interperet varagin
qualFlag = 0;

if ~isempty(varargin)>0 % you set a parameter?
    switch lower(varargin{1})
        case {'qualitative','qua'}
            if N>12 % go home, you just can't get this.
                warning('qualitiative is not possible for greater than 12 items, please reconsider');
            else
                if N>9
                    warning(['Default may be nicer for ' num2str(N) ' for clearer colors use: whitebg(''black''); ']);
                end
            end
            qualFlag = 1;
        case {'sequential','seq'}
            lineStyles = cmap2linspecer(colorm(N));
            return;
        case 'colormap'
                A = colormap;
                if size(A,1)<N
                    warning('your colormap needs more values, there will be duplicate colors');
                end
                values=round(linspace(1,size(A,1),N)); % pick evenly space points along the colormap;
                C = A(values,:); % pick only the colors we want
                lineStyles = cmap2linspecer(C);
                return;
        otherwise
            if exist(varargin{1}) % this is an existing colormap specification. We'll just use that.
                C = eval([varargin{1} '(' num2str(N) ')']);
                lineStyles = cmap2linspecer(C);
                return;
            else
                warning(['parameter ''' varargin{1} ''' not recognized']);
            end
    end
end      
      
% predefine some colormpas
set3 = colorBrew2mat({[141, 211, 199];[ 255, 237, 111];[ 190, 186, 218];[ 251, 128, 114];[ 128, 177, 211];[ 253, 180, 98];[ 179, 222, 105];[ 188, 128, 189];[ 217, 217, 217];[ 252, 205, 229];[ 204, 235, 197];[ 255, 255, 179]}');
set1JL = brighten(colorBrew2mat({[228, 26, 28];[ 55, 126, 184];[ 77, 175, 74];[ 255, 127, 0];[ 255, 237, 111]*.95;[ 166, 86, 40];[ 247, 129, 191];[ 153, 153, 153];[ 152, 78, 163]}'));
% set1JL = set1JL);
set1 = brighten(colorBrew2mat({[ 55, 126, 184]*.95;[228, 26, 28];[ 77, 175, 74];[ 152, 78, 163];[ 255, 127, 0]}),.8);
% 
%
if N<=0
    lineStyles={};
    return;
end
switch N
    case 1
        lineStyles = { [  55, 126, 184]/255};
    case {2, 3, 4, 5 }
        lineStyles = set1(1:N);
    case {6 , 7, 8, 9}
        lineStyles = set1JL(1:N);
    case {10, 11, 12}
        if qualFlag % force qualitative graphs
            lineStyles = set3(1:N);
        else % 10 is a good number to start with the sequential ones.
            lineStyles = cmap2linspecer(colorm(N));
        end
        
otherwise % any old case where I need a quick job done.
    
    lineStyles = cmap2linspecer(colorm(N));
    
end

end
% extra functions
function varIn = colorBrew2mat(varIn)
for ii=1:length(varIn) % just divide by 255
    varIn{ii}=varIn{ii}/255;
end        
end

function varIn = brighten(varIn,varargin) % increase the brightness

if isempty(varargin), frac = .9; else, frac = varargin{1}; end

for ii=1:length(varIn)
    varIn{ii}=varIn{ii}*frac+(1-frac);
end        
end

function vOut = cmap2linspecer(vIn) % changes the format from a double array to a cell array with the right format
vOut = cell(1,size(vIn,1));
for ii=1:size(vIn,1)
    vOut{ii} = vIn(ii,:);
end
end
%%
% colorm returns a colormap which is really good for creating informative
% heatmap style figures.
% No particular color stands out and it doesn't do too badly for colorblind people either.
% It works by interpolating the data from the
% 'spectral' setting on http://colorbrewer2.org/ set to 11 colors
% 
% It is modified a little to make the brightest yellow a little less bright.
% 
% Jonathan Lansey 2013
% % % % % % % % % % % % % % % % 
% % Example:
% x=rand(15);figure;imagesc(x);figure;imagesc(x);colormap(colorm);
% % % 
function cmap = colorm(varargin)
n = 100;
if ~isempty(varargin)
    n = varargin{1};
end

if n==1
    cmap =  [0.2005    0.5593    0.7380];
    return;
end
if n==2
     cmap =  [0.2005    0.5593    0.7380;
              0.9684    0.4799    0.2723];
          return;
end

frac=.95; % Slight modification from colorbrewer here to make the yellows in the center just a bit darker
cmapp = [158, 1, 66; 213, 62, 79; 244, 109, 67; 253, 174, 97; 254, 224, 139; 255*frac, 255*frac, 191*frac; 230, 245, 152; 171, 221, 164; 102, 194, 165; 50, 136, 189; 94, 79, 162];
x = linspace(1,n,size(cmapp,1));
xi = 1:n;
for ii=1:3
    cmap(:,ii) = pchip(x,cmapp(:,ii),xi);
end
cmap = flipud(cmap/255);
end
%%

function t2 = makeTitle(t1)
t2 = strrep(t1, '_', ' ');
end

%%
% This function can be found here:
% http://www.mathworks.com/matlabcentral/fileexchange/42470-box-and-whiskers-plot-without-statistics-toolbox
% 
% function forLegend = bplot(X,varargin)
% This function will create a nice boxplot from a set of data. You don't
% need any toolboxes.
% 
%     bplot(D) will create a boxplot of data D, no fuss.
% 
% T = bplot(D)  If X is a matrix, there is one box per column; if X is a
%               vector, there is just one box. On each box, the central
%               mark is the median, the edges of the box are the 25th and
%               75th percentiles
%               array 'T' for a legend. You can add the legend as legend(T)
% 
% T = bplot(D,x) will plot the boxplot of data D above the 'x' value x
% 
% T = bplot(D,y,'horiz') will plot a horizontal boxplot at the 'y' value of y
% 
% T = bplot(...,'Property', . . . )
% T = bplot(...,'PropertyName',PropertyValue, . . . )
% 
%   SINGLE PARAMETERS:
% 
%          'horizontal': Display the boxplot along the horizontal axis. The
%                        default is to display the boxplot vertically.
%                        'horiz'
%            'outliers': Displays the outliers as dots. The default
%                        settings are to display the dots only if you do
%                        not pass it a position and only if the number of
%                        points are less than 400.
%                        'points','dots'%
%          'nooutliers': Does NOT display the outliers as dots. The default
%                        settings are to display the dots only if you do
%                        not pass it a position and only if the number of
%                        points are less than 400.
%                        'nopoints','nodots'
%                 'std': Set the whiskers to be the meanstandard deviation
%                        The legend information will be updated
%                        'standard'
%              'nomean': Don't plot the mean 'plus' symbol '+'
%            'nolegend': Force the elements to display without any legend
%                        annotation.
% PARAMETER PAIRS
%                 'box': Set the percentage of points that the boxes span.
%                        Default is the first and third quartile. Choose
%                        only the lower number in %, for example: 25.
%                        'boxes','boxedge'
%             'whisker': Set the percentage of points that the whiskers
%                        span. Default is the 9% and 91%. Choose only the
%                        lower number in %, for example: 9. 
%                        'whiskers','whiskeredge'
%           'linewidth': Set the width of all the lines.
%               'color': Change the color of all the lines. If you use this
%                        feature then the legend returns an empty matrix.
%                        'colors'
%               'width': Set the width of the boxplot rectangle. For a
%                        horizontal plot this parameter sets the height.
%                        Default width is .8 for vertical plots and for
%                        horizontal plots the height is 1.5/20 of the y axis
%                        the  bars.
%                        'barwidth'
% 
%% Jitter feature 
% The boxplot has a cool jitter feature which will help you view each
% outlier separately even if two have identical values. It jitters the
% points around the other axis so that you can see exactly how many are
% there.
% 
% % Examples: 
% bplot(randn(30,3),'outliers')
% bplot(randn(30,3),'color','black');
% ----
% X = round(randn(30,4)*5)/5; % random, with some duplicates
% T = bplot(X,'points');
% legend(T,'location','eastoutside');
% 
%% development notes:
% This function was developed to be part of a larger histogram function
% which can be found at this location:
% http://www.mathworks.com/matlabcentral/fileexchange/27388-plot-and-compare-histograms-pretty-by-default
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Jonathan Lansey 2013,                                                   %
%                   questions to Lansey at gmail.com                      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%
function forLegend = bplot(x,varargin)
%% save the initial hold state of the figure.
hold_state = ishold;
if ~hold_state
    clf;
end
%%
if size(x,1)>1 && size(x,2)>1 % great, you want to plot a bunch.
    if isempty(varargin)
        forLegend = bplot(x(:,1),1);
        for ii=2:size(x,2)
            hold on;
            bplot(x(:,ii),ii,'nolegend');
        end
    else
        if ~ischar(varargin{1})
            warning('You can''t specify a location for multiple guys, this will probably crash');
        end
        forLegend = bplot(x(:,1),1,varargin{:});
        for ii=2:size(x,2)
            hold on;
            bplot(x(:,ii),ii,'nolegend',varargin{:});

        end
    end
    if ~hold_state
        hold off;
    end
    return;
end

%%
if ~isempty(varargin)
    if ischar(varargin{1})
        justOneInputFlag=1;
        y=1;
    else
        justOneInputFlag=0;
        y=varargin{1};
    end
else % not text arguments, not even separate 'x' argument
    y=1;
    justOneInputFlag=1;
end
%% check that there is at least some data
if isempty(x)
    warning('you asked for no data, so no data is what you plot.');
    return;
end
%%
if length(y)>1
    warning('The location can only be a scalar, it has been set to ''1''');
    y=1;
end
%% serialize and remove NaNs
x=x(:);
x = x(~isnan(x));

%% Initialize some things before accepting user parameters
horizontalFlag=0;
barFactor=1; % 
linewidth=2;
forceNoLegend=0; % will any legend items be allowed in.
stdFlag = 0;
meanFlag = 1;
specialWidthFlag = 0; % this flag will determine whether the bar width is 
%                       automatically set as a proportion of the axis width

toScale = 0; % this flag is to scale the jitter function in case the 
%              histogram function is calling it

if justOneInputFlag
    if length(x)<400
        outlierFlag = 1;
    else
        outlierFlag = 0;
    end
    
else
    outlierFlag = 0;
end
widthFlag =0;

boxColor = [0.0005    0.3593    0.7380];
wisColor = [0 0 0]+.3;
meanColor = [0.9684    0.2799    0.0723];

percentileNum = 25; % for the main quantiles
percentileNum2 = 9; % for the whisker ends

%% interpret user paramters
k = 1 + 1 - justOneInputFlag;
while k <= length(varargin)
    if ischar(varargin{k})
    switch (lower(varargin{k}))
        case 'nolegend'
            forceNoLegend=1;
        case {'box','boxes','boxedge'}
            percentileNum = varargin{k + 1};
            k = k + 1;
        case {'wisker','wiskers','whisker','whiskers','whiskeredge'}
            percentileNum2 = varargin{k + 1};
            k = k + 1;
        case {'std','standard'}
            stdFlag = 1;
        case 'linewidth'
            linewidth = varargin{k + 1};
            k = k + 1;
        case {'color','colors'}
            boxColor = varargin{k+1};
            wisColor = varargin{k+1};
            meanColor = varargin{k+1};
            forceNoLegend=1;
            k = k + 1;
        case {'points','dots','outliers'} % display those outliers
            outlierFlag = 1;
        case {'nopoints','nodots','nooutliers'} % display those outliers
            outlierFlag = 0;
        case {'horizontal','horiz'}
            horizontalFlag = 1;
        case {'width','barwidth'}
            barWidth = varargin{k+1};
            widthFlag = 1;
            k = k+1;
        case {'specialwidth','proportionalwidth','width2'}
            specialWidthFlag = 1;
            widthFlag = 1;
        case {'nomean'}
            meanFlag=0;
        case {'toscale','histmode','hist'}
            toScale = 1; % scale away folks!
        otherwise
            warning('user entered parameter is not recognized')
            disp('unrecognized term is:'); disp(varargin{k});
    end
    end
    k = k + 1;
end

%%
meanX = mean(x);
medianX = median(x);
defaultBarFactor=1.5/20;
p=axis;
if ~widthFlag % if the user didn't specify a specific width of the bar.
    if specialWidthFlag
        barWidth=barFactor*(p(4)-p(3))*defaultBarFactor;
    else
        barWidth = .8;
    %     barWidth = barFactor*(p(2)-p(1))*defaultBarFactor/5;
    end
end
%% calculate the necessary values for the sizes of the box and whiskers
boxEdge = prctile(x,[percentileNum 100-percentileNum]);
IQR=max(diff(boxEdge),eps);  % in case IQR is zero, make it eps
if stdFlag
    stdX = std(x);
    wisEdge = [meanX-stdX meanX+stdX];
else
    wisEdge = prctile(x,[percentileNum2  100-percentileNum2]);
end

%% display all the elements for the box plot

hReg=[];
hReg2 = [];

if horizontalFlag
    hReg2(end+1) = rectangle('Position',[boxEdge(1),y-barWidth/2,IQR,barWidth],'linewidth',linewidth,'EdgeColor',boxColor);

    hold on;
    hReg2(end+1) = plot([medianX medianX],[y-barWidth/2 y+barWidth/2],'color',meanColor,'linewidth',linewidth);
    if meanFlag
        hReg2(end+1) = plot(meanX,y,'+','color',meanColor,'linewidth',linewidth,'markersize',10);
    end
    hReg2(end+1) = plot([boxEdge(1) boxEdge(2)],[y-barWidth/2 y-barWidth/2],'linewidth',linewidth,'color',boxColor);

    hReg(end+1) = plot([wisEdge(1) boxEdge(1)],[y y],'--','linewidth',linewidth,'color',wisColor);
    hReg(end+1) = plot([boxEdge(2) wisEdge(2)],[y y],'--','linewidth',linewidth,'color',wisColor);
    hReg2(end+1) = plot([wisEdge(1) wisEdge(1)],[y-barWidth/3 y+barWidth/3],'-','linewidth',linewidth,'color',wisColor);
    hReg(end+1) = plot([wisEdge(2) wisEdge(2)],[y-barWidth/3 y+barWidth/3],'-','linewidth',linewidth,'color',wisColor);
else %
    hReg2(end+1) = rectangle('Position',[y-barWidth/2,boxEdge(1),barWidth,IQR],'linewidth',linewidth,'EdgeColor',boxColor);
    hold on;
    
    hReg2(end+1) = plot([y-barWidth/2 y+barWidth/2],[medianX medianX],'color',meanColor,'linewidth',linewidth);
    if meanFlag
        hReg2(end+1) = plot(y,meanX,'+','linewidth',linewidth,'color',meanColor,'markersize',10);
    end
    hReg2(end+1) = plot([y-barWidth/2 y-barWidth/2],[boxEdge(1) boxEdge(2)],'linewidth',linewidth,'color',boxColor);

    hReg(end+1) = plot([y y],[wisEdge(1) boxEdge(1)],'--','linewidth',linewidth,'color',wisColor);
    hReg(end+1) = plot([y y],[boxEdge(2) wisEdge(2)],'--','linewidth',linewidth,'color',wisColor);
    hReg2(end+1) = plot([y-barWidth/3 y+barWidth/3],[wisEdge(1) wisEdge(1)],'-','linewidth',linewidth,'color',wisColor);
    hReg(end+1) = plot([y-barWidth/3 y+barWidth/3],[wisEdge(2) wisEdge(2)],'-','linewidth',linewidth,'color',wisColor);

end

%% add the points to the graph
% Note that the spread of points should depend on the width of the bars and
% the total number of points that need to be spread.
if outlierFlag % but only if you want to
    I = (x<wisEdge(1))+(x>wisEdge(2));
    I=logical(I);
    xx=x(I);
    yy=I*0+y;
    yy=yy(I);
    
    if ~isempty(yy)
        yy = jitter(xx,yy,toScale);

        maxPointHeight = 2.5;
        yy = (yy-y)*4+y;
        yy = (yy-y)*(barWidth/maxPointHeight)/max([yy-y; barWidth/maxPointHeight])+y;

        if ~isempty(xx)
            if horizontalFlag
                hReg2(6) = plot(xx,yy,'o','linewidth',linewidth,'color',wisColor);
            else
                 hReg2(6) = plot(yy,xx,'o','linewidth',linewidth,'color',wisColor);
            end
        end
    end
end
%% Remove the legend entries 
% remove extras for all the items.
for ii=1:length(hReg)
    set(get(get(hReg(ii),'Annotation'),'LegendInformation'),'IconDisplayStyle','off'); % Exclude line from legend
end

% remove all remenants of legends
if forceNoLegend
    for ii=1:length(hReg2)
        set(get(get(hReg2(ii),'Annotation'),'LegendInformation'),'IconDisplayStyle','off'); % Exclude line from legend
    end
end
%% set the axis
% The axis is only messed with if you didn't pass a position value (because
% I figured you just wanted to make a quick plot without worry about much

if justOneInputFlag
    if horizontalFlag
        padxfac = .1;
        padyfac = 2;
    else
        padxfac = 2;
        padyfac = .1;
    end
    
    axis tight;
    p = axis;
    padx = (p(2)-p(1))*padxfac; pady = (p(4)-p(3))*padyfac;
    axis(p+[-padx padx -pady pady]);
end
%% Set the legend
if stdFlag
    whiskerText = '\mu  \sigma';
else
    whiskerText = [num2str(percentileNum2) '%-' num2str(100-percentileNum2) '%'];
end
if meanFlag
    forLegend={'Median','\mu',[num2str(percentileNum) '%-' num2str(100-percentileNum) '%'],whiskerText,'outliers'};
else
    forLegend={'Median',[num2str(percentileNum) '%-' num2str(100-percentileNum) '%'],whiskerText,'outliers'};
end

%% return the hold state
% just being polite and putting the hold state back to the way it was.
if ~hold_state
    hold off;
end
% end main bplot function over
end

%% jitter function
% in case two point appear at the same value, the jitter function will make
% them appear slightly separated from each other so you can see the real
% number of points at a given location.
function yy =jitter(xx,yy,toScale)
if toScale
    tempY=yy(1);
else
    tempY=1;
end

for ii=unique(xx)';
    I = xx==(ii);
    fI = find(I)';
    push = -(length(fI)-1)/2; % so it will be centered if there is only one.
    for jj=fI
        yy(jj)=yy(jj)+tempY/50*(push);
        push = push+1;
    end
end
end

%% This is the function for calculating the quantiles for the bplot.
function yi = prctile(X,p)
x=X(:);
if length(x)~=length(X)
    error('please pass a vector only');
end
n = length(x);
x = sort(x);
Y = 100*(.5 :1:n-.5)/n;
x=[min(x); x; max(x)];
Y = [0 Y 100];
yi = interp1(Y,x,p);

end

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