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REPRO-Bench / 42 /replication_package /model_replication /Main nu infinity /binned_plot.m
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function [x_med_out,y_med,y_low,y_high] = binned_plot(x,y,varargin)
% BINNED_PLOT binned scatter plot
%
% BINNED_PLOT(X,Y) splits vector X into bins of aproximately equal size,
% and plots each median against the median of the corresponding Y-values,
% as well as their inter-quartile range. X and Y must have the same
% number of rows or columns.
%
% BINNED_PLOT(X,Y,NUM_BINS) also specifies the (maximum) number of bins.
%
%
% [X_MED,Y_MED,Y_LOW,Y_HIGH] = BINNED_PLOT(...) returns the median of the
% X-bin, the median, lower and upper quartile of the corresponding Y-values
%
% Additional properties can be set as attribute-value pairs:
% - 'y_range' : specifies the width of the Y-band (range 0 .. 0.5;
% e.g., 0.5 plots the range between maxima and minima);
% default: 0.25
% - 'y_mean_std' : plot means and standard deviations instead of medians
% and quartiles ['on','off']
% - 'style' : plotting style (same options as in plot command)
% - 'density' : transparency corresponds to the number of points in
% the shaded area ['on','off']
% - 'transparency' : transparency of filled range (for non-density plots)
% - 'transparency_min': minimum transparency of filled range (for density plots)
% - 'transparency_max': maximum transparency of filled range (for density plots)
%
%
% Example:
% x=0:0.1:20;
% y=[sin(x); cos(x)] + randn(2,201);
% binned_plot(x,y)
%
% Stefan Schroedl
% 04/07/2008
optargin = size(varargin,2);
stdargin = nargin - optargin;
if (stdargin<2)
error('at least two arguments required')
end
% defaults for optional arguments
num_bins = [];
y_range = [];
style = [];
y_mean_std = 0;
transparency = 0.1;
transparency_max = 0.6;
transparency_min = 0.1;
density_transparency = 0;
% parse optional arguments
i=1;
while (i <= optargin)
if (i==1 && isnumeric(varargin{i}))
num_bins = varargin{i}; % interpret as number of bins
i = i + 1;
elseif (strcmp(varargin{i},'style') && i < optargin)
style = varargin{i+1};
i = i + 2;
elseif (strcmp(varargin{i},'y_range') && i < optargin)
y_range = varargin{i+1};
i = i + 2;
elseif (strcmp(varargin{i},'transparency') && i < optargin)
transparency = varargin{i+1};
i = i + 2;
elseif (strcmp(varargin{i},'transparency_max') && i < optargin)
transparency_max = varargin{i+1};
i = i + 2;
elseif (strcmp(varargin{i},'transparency_min') && i < optargin)
transparency_min = varargin{i+1};
i = i + 2;
elseif (strcmp(varargin{i},'y_mean_std') && i < optargin)
if (strcmp(varargin{i+1},'on'))
y_mean_std = 1;
elseif (strcmp(varargin{i+1},'off'))
y_mean_std = 0;
else
error('unrecognized option for y_mean_std, should be [on/off]');
end
i = i + 2;
elseif (strcmp(varargin{i},'density') && i < optargin)
if (strcmp(varargin{i+1},'on'))
density_transparency = 1;
elseif (strcmp(varargin{i+1},'off'))
density_transparency = 0;
else
error('unrecognized option for density, should be [on/off]');
end
i = i + 2;
elseif (ischar(varargin{i}))
error('unrecognized attribute: %s', varargin{i});
else
error('at most three arguments expected');
end
end
if (transparency_min >= transparency_max)
error('transparency_min should be smaller than transparency_max');
end
% determine input matrix sizes
[nx,mx] = size(x);
[ny,my] = size(y);
if nx > 1 && mx > 1
error('first argument must be a vector');
end
% adjust matrices to be column vectors
if mx>1
% transpose
x = x(:);
nx = mx;
mx = 1;
end
if my == nx
% transpose
y = y';
[ny,my] = size(y);
else
if ny ~= nx
error('first and second arguments must have either same number of rows or columns');
end
end
if isempty(num_bins)
num_bins = max( min(length(x),3), floor(sqrt(length(x)-1))-1); % default heuristic for number of bins
else if ~isnumeric(num_bins)
db error('third argument num_bins must be numeric');
end
end
if isempty(y_range)
y_range = 0.25; % default: quartile
end
if isempty(style)
style = ''; % no style specified
end
% determine colors and markers
colors = repmat('b',1,my);
noColSpec = cell(1,my);
for i=1:my
[colors(i),noColSpec{i}] = getColorSpec(style,i);
end
% x quantiles
qvals = 0:(1/num_bins):(1-1/num_bins);
x_quant = quantile(x,[qvals 1]);
% remove identical bins
x_quant = sort(unique(x_quant));
% due to interpolation, some bins can still be empty
x_quant2 = x_quant;
x_quant = x_quant(1);
count_bin = length(find(x>x_quant2(1)));
for i=2:length(x_quant2)
count_bin2 = length(find(x>x_quant2(i)));
if count_bin2 ~= count_bin
x_quant = [x_quant x_quant2(i)];
end
count_bin = count_bin2;
end
% preallocate outputs
x_med = zeros(length(x_quant)-1,1);
y_med = zeros(length(x_quant)-1,my);
y_low = zeros(length(x_quant)-1,my);
y_high = zeros(length(x_quant)-1,my);
% desired y range
for i = 1:length(x_quant)-1
idx = x >= x_quant(i) & (x < x_quant(i+1));
if (~y_mean_std)
q = quantile(y(idx,:),[0.5-y_range 0.5 0.5 + y_range]);
% hack for quantile output dim
if my == 1
q = q';
end
y_low(i,:) = q(1,:);
y_med(i,:) = q(2,:);
y_high(i,:) = q(3,:);
x_med(i) = median(x(idx));
else
% use mean and std dev
m = mean(y(idx,:));
s = std(y(idx,:));
y_med(i,:) = m;
y_low(i,:) = m-s;
y_high(i,:) = m+s;
x_med(i) = mean(x(idx));
end
end
if (nargout == 0)
hold_mode = ishold;
x_min = x_quant(1);
x_max = x_quant(end);
for i=1:my
inner_spec = strcat(colors(i), noColSpec{i});
if(~density_transparency)
% fill between quartiles
xpoints=[x_min; x_med; x_max; x_max; flipud(x_med); x_min ];
ypoints=[y_high([ 1 1:end end],i); flipud(y_low([1 1:end end],i)) ];
fillhandle=fill(xpoints,ypoints,colors(i));
set(fillhandle,'EdgeColor',colors(i),'FaceAlpha',transparency,'EdgeAlpha',transparency); %set transparency
else
% precompute trapezoids, areas
xpoints = zeros(4,length(x_med)+1);
ypoints = zeros(4,length(x_med)+1);
area_fill = zeros(1,length(x_med)+1);
xpoints(:,1) = [x_min; x_med(1); x_med(1); x_min];
ypoints(:,1) = [y_high(1,i); y_high(1,i); y_low(1,i); y_low(1,i)];
area_fill(1) = (xpoints(2,1)-xpoints(1,1))*(ypoints(1,1)-ypoints(4,1)+ypoints(2,1)-ypoints(3,1))/2;
for j=1:(length(x_med)-1)
xpoints(:,j+1) = [x_med(j); x_med(j+1); x_med(j+1); x_med(j)];
ypoints(:,j+1) = [y_high(j,i); y_high(j+1,i); y_low(j+1,i); y_low(j,i)];
area_fill(j+1) = (xpoints(2,j+1)-xpoints(1,j+1))*(ypoints(1,j+1)-ypoints(4,j+1)+ypoints(2,j+1)-ypoints(3,j+1))/2;
end
xpoints(:,end) = [x_med(end); x_max; x_max; x_med(end)];
ypoints(:,end) = [y_high(end,i); y_high(end,i); y_low(end,i); y_low(end,i)];
area_fill(end) = (xpoints(2,end)-xpoints(1,end))*(ypoints(1,end)-ypoints(4,end)+ypoints(2,end)-ypoints(3,end))/2;
area_max = max(area_fill);
area_min = min(area_fill);
area_range = area_max - area_min;
if (area_range == 0)
area_range = 1;
end
transparency_range = transparency_max - transparency_min;
% scale transparency according to density (i.e., inversely
% proportional to trapezoid area)
transp_mod = transparency_max - (area_fill - area_min) .* transparency_range ./ area_range;
for j=1:(length(x_med)+1)
fillhandle=fill(xpoints(:,j),ypoints(:,j),colors(i),'LineStyle','none');
hold on;
set(fillhandle,'EdgeColor',colors(i),'FaceAlpha',transp_mod(j),'EdgeAlpha',transp_mod(j)); % set transparency
end
end
% plot median line
hold on;
plot(x_med,y_med(:,i),inner_spec);
end
% restore old hold mode
if hold_mode == 0
hold off;
end
else
x_med_out = x_med;
end
% auxiliary function to retrieve color specification (if any) and remainder
function [color,noColSpec] = getColorSpec(s,i)
colors = 'bgrcmykw';
color=colors(mod(i-1,8) + 1); % default color cycle
noColSpec = '-'; % default line style
if (~isempty(s))
idx=ismember(s,colors);
if any(~idx)
noColSpec=s(~idx);
end
if any(idx)
color=s(idx(1));
end
end