Matlab: Errorlines

The methode:

(German) This post is about plotting errorlines for example for university journals. The methode is to fit a maximal and a minimal line through the y-values an whose error. As shown in the graph it yield a box. The errorlines are connection of the edges diagonal.

The function "[varargout] = errlinefunc(x, y,xerr,yerr, varargin)" plots the error lines in blue. The color can be changed using ('LineColor',[0.5 0.5 0]) for example to orange or the line width ca be changed by ('LineWidth',2). The option 'Fit' plots in greeb ('FitColor') the linear fit through the data set. The option 'Plot' depicts the x and y with corresponding errorbars in black ('PlotColor'). 'Box' shows im black ('BoxColor') the borders of the errorlines. 'Legend' writes a legend with options 'Location','NorthEast' and similare and 'LegendNames',{['1','2','3']} changes the legend.

This operations plots followings:
figure;hold on;box on;
errlinefunc([0;1;2;3;4;5;6],[0;1;2;3;4;4;6],0.1,0.3','Box','Plot','Fit','Legend');

The functions output is a varargout with the min and max slope smax,smin and y-axis cuts rmax,rmin which are used for plotting the error lines.

Here is the function on MathWorks: Download

Soruce code:

function [varargout] = errlinefunc(x, y,xerr,yerr, varargin)
% This is a function to plot a maximal and minimal errorline with given
% errors 'xerr' and 'yerr'. Further options are:
% 'Box' ... Plots a box around min and max errorline (Default: off)
% 'BoxColor',BoxColor ... this changes the color of the box (Default: black)
% 'LineColor',LineColor ... changes color of error lines (Default: blue)
% 'LineWidth',LineWidth ... changes all line widths (Default: 1.5)
% 'Plot' ... Plots input x and y with errorbar xerr and yerr (Default: off)
% 'PlotColor',PlotColor ... changes the color of the plot (Default: black)
% 'MarkerSize',MarkerSize .... changes size of plot marker (Default: 10)
% 'Marker',Marker .... changes marker of the plot (Default: '.')
% 'Fit' ... draws the fit through x and y (Default: off)
% 'FitColor',FitColor ... colors the fit (Default: green)
% 'Legend' ... activates the legend for the chosen plot option
% 'Location',Location ... plots the legend at a certain location (Default:
% NorthWest)
% 'LegendNames',LegendNames ... is a cell array containing the names for
% the legend (Default: {['Data with errorbars','Fit','max error line','min
% error line']})

len=numel(x);
if(xerr==0)
   xerr = zeros([len,1]);
end

if numel(xerr)~=len
   xerr = ones([len,1]).*xerr;
end
if numel(yerr)~=len
   yerr = ones([len,1]).*yerr;
end

ymax=y+yerr;
ymin=y-yerr;

fitmax=fit(x,ymax,'poly1');
fitmin=fit(x,ymin,'poly1');
fitVal=fit(x,y, 'poly1');

%Fit the maximal and the minimal errorlines through the mesured values with
%their deviations.
a=coeffvalues(fitmax);
b=coeffvalues(fitmin);
c=coeffvalues(fitVal);
amax=a(1);
amin=b(1);
bmax=a(2);
bmin=b(2);
% afit=c(1);
% bfit=c(2);

%Declare the 4 corners of the box
xlu=x(1)-xerr(1);
xld=x(1)-xerr(1);
xru=x(len)+xerr(len);
xrd=x(len)+xerr(len);

ylu=amax*xlu+bmax;
yru=amax*xru+bmax;
yld=amin*xld+bmin;
yrd=amin*xrd+bmin;

%Declare the vectors of the corners.
xcorner=[xlu xru xrd xld xlu];
ycorner=[ylu yru yrd yld ylu];
xcrnmax=[xlu xrd];
xcrnmin=[xld xru];
ycrnmax=[ylu yrd];
ycrnmin=[yld yru];

smax=(yru-yld)/(xru-xld);
smin=(yrd-ylu)/(xrd-xlu);
rmax=yld-xld*smax;
rmin=ylu-xlu*smin;

% f1(x)=rmax+x*smax;
% f2(x)=rmin+x*smin;
%Declare the rises and the y-values
% s1=(yrd-ylu)/(xrd-xlu);
% s2=(yru-yld)/(xru-xld);
% y1=ylu-s1*xlu;
% y2=yld-s2*xld;

yneg = yerr;ypos = yerr;
xneg = xerr;xpos = xerr;

% output the slope s and the x axis cut t from f(x)=r+x*s; where max
% describes the upper errorline
varargout{1} = smax;
varargout{2} = smin;
varargout{3} = rmax;
varargout{4} = rmin;

if max(strcmp(varargin,'LineWidth'))
    idx = 1 + find(strcmp(varargin,'LineWidth'));
    LineWidth = varargin{1,idx};
else
    LineWidth = 1.5;
end
      
      
hold on;
legCount = 1;
myLegend = gobjects(1,1);
myLegNames{1,legCount} = cell(1,1);
% depicts mimal and maximal error line
if max(strcmp(varargin,'LineColor'))
    idx = 1 + find(strcmp(varargin,'LineColor'));
    LineColor = varargin{1,idx};
else
    LineColor = [0 0.4 0.7];
end


% show the plot with errorbars
if max(strcmp(varargin,'Plot'))
    if max(strcmp(varargin,'Marker'))
        idx = 1 + find(strcmp(varargin,'Marker'));
        Marker = varargin{1,idx};
    else
        Marker = '.';
    end
  
    if max(strcmp(varargin,'MarkerSize'))
        idx = 1 + find(strcmp(varargin,'MarkerSize'));
        MarkerSize = varargin{1,idx};
    else
        MarkerSize = 10;
    end
  
    if max(strcmp(varargin,'PlotColor'))
        idx = 1 + find(strcmp(varargin,'PlotColor'));
        PlotColor = varargin{1,idx};
    else
        PlotColor = [0 0 0];
    end
  
    hError = errorbar(x,y,yneg,ypos,xneg,xpos,'.','Color',PlotColor,...
        'LineWidth',LineWidth*0.7);
    plot(x,y,Marker,'Color',PlotColor,...
        'LineWidth',LineWidth,'MarkerSize',MarkerSize);
    myLegend(legCount) = hError;
    myLegNames{1,legCount} = 'Data with errorbars';
    legCount = legCount + 1;
end

% draw the fit through x and y
if max(strcmp(varargin,'Fit'))
    if max(strcmp(varargin,'FitColor'))
        idx = 1 + find(strcmp(varargin,'FitColor'));
        FitColor = varargin{1,idx};
    else
        FitColor = [0.2 0.7 0.2];
    end
  
    hFit = plot(fitVal);
    set(hFit,'LineWidth',LineWidth','Color',FitColor);
    myLegend(1,legCount) = hFit;
    myLegNames{1,legCount} = ['Fit: ',num2str(round(c(1),2)),'*x+',...
        num2str(round(c(2),2))];
    legCount = legCount + 1;
end

hErrLineMax = line(xcrnmax,ycrnmax,'Color',LineColor,'LineWidth',LineWidth);
hErrLineMin = line(xcrnmin,ycrnmin,'Color',LineColor,'LineWidth',LineWidth);
myLegend(legCount) = hErrLineMax;
myLegNames{1,legCount} = ['max error line: ',num2str(round(smax,2)),'*x+',...
        num2str(round(rmax,2))];
legCount = legCount + 1;
myLegend(legCount) = hErrLineMin;
myLegNames{1,legCount} = ['min error line: ',num2str(round(smin,2)),'*x+',...
        num2str(round(rmin,2))];

% depict the box of the errorlines
if max(strcmp(varargin,'Box'))
    if max(strcmp(varargin,'BoxColor'))
        idx = 1 + find(strcmp(varargin,'BoxColor'));
        BoxColor = varargin{1,idx};
    else
        BoxColor = [0 0 0];
    end
    plot(xcorner,ycorner,'--','Color',BoxColor,'LineWidth',LineWidth*0.7);
end

% add a legend
if max(strcmp(varargin,'Legend'))
  
    if max(strcmp(varargin,'Location'))
        idx = 1 + find(strcmp(varargin,'Location'));
        Location = varargin{1,idx};
    else
        Location = 'NorthWest';
    end
  
    if max(strcmp(varargin,'LegendNames'))
        idx = 1 + find(strcmp(varargin,'LegendNames'));
        LegendNames = varargin{1,idx};
    else
        LegendNames = myLegNames;
    end
    legend(myLegend,LegendNames,'Location',Location);
end


end