Errorbars on scatter plot

I have 2 scatter plots in one figure and I have calculated errors associated with x and y directions for each point. How can I plot errorbars (both horizontal and vertical) on each point? I would greatly appreciate your help : )

 x1 = [...];   %some data 
errx1 = [...];  % some data

y1 = [...];        % some data
erry1 = [...];     % some data

scatter(x1, y1,170,'k','filled');      % scatter plot with log scale 
set(gca,'FontSize',20,'xscale','log','yscale','log');
hold on
x2 = [...];           % some data
errx2 = [...];         % some data

y2 = [...];             % some data
erry2 = [...];           % some data

scatter(x2, y2,170,'k','filled','s'); 
set(gca,'FontSize',20,'xscale','log','yscale','log') 

Answer 1

[Adam Danz]

Follow this example. If you get stuck, feel free to ask a follow-up question in the comments below.

https://www.mathworks.com/help/matlab/ref/errorbar.html#bvc93io-1 -- If your x and y error are equal

https://www.mathworks.com/help/matlab/ref/errorbar.html#bvc920p-1 -- If your x and y error equal differ.

The error in this function is expressed as a distance from the marker. If your error bar data are expressed as end points rather than a distance, you'll need to convert them to positive distances from the marker.

[Milana Asker]

The errorbar function does not seem to work with my scatter plot.

I use

errorbar(x1,y1,err_x1,err_y1,'o')

[Adam Danz]

Can you provide more detail? What do you mean 'it didn't work'? Did it produce an error or were the results not what you expected? I've used the errorbar function many times with scatter plots so whatever the problem is, I'm sure it's an easy fix. But first I need to understand what's wrong. Also, it would be helpful to have the values (or a sample of the values) of x1, y1, err_x1, and err_y1.

[Milana Asker]

This is my code with the exact values and once I run the code, the graph does not change.

x1 = [     
21.00001824
21.53527947
19.06905992
21.4039635
40.86227126
27.24151417
22.03385789
24.5797018];

err_x1 = [3.626822314
3.719264966
3.358701943
3.696585952
6.718347823
4.592518567
3.759335694
4.161903708];

y1 = [    
38.03480507
26.37515276
24.41236294
40.11468755
44.05238426
32.44167833
25.36387642
27.92989633];

err_y1 = [2.593632226
1.905191835
2.028334226
2.847116982
2.377370617
2.127666334
1.91175608
2.230383052];

errorbar(x1,y1,err_x1,err_y1,'o')

scatter(x1, y1,170,'k','filled');
set(gca,'FontSize',20,'xscale','log','yscale','log');

[Adam Danz]

Two mistakes, easy to fix.

1) your error bars were plotted correctly but when you called 'scatter', it cleared the axes. Solution: use " hold on "

2) plot the horizontal and vertical bars separately.

The code below is the correct way to plot the errorbars. I've formatted them as black with a line width of 2.

scatter(x1, y1,170,'k','filled');
hold on
eb(1) = errorbar(x1,y1,err_x1, 'horizontal', 'LineStyle', 'none');
eb(2) = errorbar(x1,y1,err_y1, 'vertical', 'LineStyle', 'none');
set(eb, 'color', 'k', 'LineWidth', 2)

Alternatively you could plot the errorbars first so they are behind the marker.

[Milana Asker]

Thank you very much : )

Answer 2

[Reza Monadi]

You can use the errorbar but turn off the LineStyle by putting it to 'none':

errorbar(x,y,ye, 'LineStyle','none','Marker','.', 'MarkerSize',10)

[Amir Mohammad Alizadeh]

Smart solution Reza, thanks for sharing!

Answer 3

[Bjorn Gustavsson]

You could use something like this function:

function h = scatter_ellipse(X,Y,C,Cov,varargin)
%SCATTER_ELLIPSE - colored ellipse-plot
%   SCATTER(X,Y,C,Cov) displays colored ellipses at the locations
%   specified by the vectors X and Y (which must be the same size).  
%   
%   C determines the color-hue of the markers. C should be a vector the
%   same length as X and Y, the values in C are linearly mapped
%   to the colors in the current colormap.
%   
%   Cov determines the ellipse-size and shape each marker. Cov
%   should be a 2 x 2 x nP array with the covariances of the
%   C-values at points [X, Y]. For convenience the input arrays X,
%   Y and C will be converted to column arrays with the (:)
%   operation. In order to avoid sorting confusion it is strongly
%   preferable to arrange these input arrays into column (or row)
%   arrays so that the covariance matrices will be used for the
%   correct points [X, Y, C].
%
%   H = SCATTER_ELLIPSE(...) returns handles to the patch objects created.
% 
% Calling: 
%   h = scatter_ellipse(X,Y,C,Cov[,'covclim',clim,'pclr','r','edgecolor','g'])
% Input:
%   X - double array [nP x 1], x-coordinates of points
%   Y - double array [nP x 1], y-coordinates of points
%   C - double array [nP x 1], value of point, linearly mapped
%       between min and max of current colourmap.
%   COV - covariance matrix for each [Xi, Yi]-point, double array
%         [2 x 2 x nP]
% Optional input arguments (property-value pairs):
%   Covclims - scaling of covariance-ellipse-area (CEA) colour between
%              RGB-triplet (smallest area) towards white (larges
%              area) for color of C. Default value [0.1 1], 1 -
%              RGB-tripplet for the smallest CEA, 0.1 -
%              RGB*0.1+0*[1,1,1] for the point with the largest
%              CEA.
%   pclr - plot-colour, standard matlab-color specification, but
%          with 'rgb' function will plot point with RGB-colour
%          corresponding to C.
%   edgecolor - edgecolor of ellipse, defaults to 'none'.
% Output:
%   h - array with graphics handle to covariance ellipses (plotted
%       with fill)
% Example:
%  X = 12*randn(31,1);
%  Y = 12*randn(31,1);
%  for i1 = 1:31,
%    sx = 1+3*rand(1); 
%    sy = 1+3*rand(1);
%    x = sx*randn(41,1);
%    y = sy*randn(41,1) + randn(1)*x;
%    CvM(:,:,i1) = cov([x,y]);
%    C(i1) = mean(x)*mean(y);
%  end
%  clf
%  h = scatter_ellipse(X,Y,...
%                      medfilt1(C),CvM/3,...
%                      'pclr','rgb',...
%                      'Covclim',[0.15 1],...
%                      'edgecolor','none');
% 
% The idea is that points with larger covariance ellipse should get
% reduced graphical weight while points with smaller covariance
% ellipses should be more clearly visible. The RGB-blending towards
% white could be seen as each point have a fixed amount of pigment
% spread out to color the area of the ellipse.


%  Copyright © Bjorn Gustavsson 20190410, [e-mail]
%  This is free software, licensed under GNU GPL version 2 or later

dOPS.Covclim = [0.1 1];
dOPS.pclr  = 'rgb';
dOPS.edgecolor  = 'none';

for i1 = 1:2:numel(varargin)
  curr_option = varargin{i1};
  switch lower(varargin{i1})
   case 'covclim'
    dOPS.Covclim = varargin{i1+1};
   case 'pclr'
    dOPS.pclr = varargin{i1+1};
   case 'edgecolor'
    dOPS.edgecolor = varargin{i1+1};
   otherwise
  end

end
dOPS.Covclim(2) = max(0,min(1,dOPS.Covclim(2)));
dOPS.Covclim(1) = max(0,min(1,dOPS.Covclim(1)));

X = X(:);
Y = Y(:);
C = C(:);

Cmap = colormap;
nCmap = size(Cmap,1);


for i3 = numel(X):-1:1,
  [Xe(i3,:),Ye(i3,:),Aellipse(i3)] = ellipse_xy(Cov(:,:,i3));
end

[Aellipse,iS] = sort(Aellipse);
Xe = Xe(iS,:);
Ye = Ye(iS,:);
X = X(iS);
Y = Y(iS);
C = C(iS);

if max(C) ~= min(C)
  rgbCp = interp1(linspace(0,1,nCmap),...
                 Cmap,...
                 (C-min(C))/(max(C)-min(C)),...
                 'pchip');
else
  rgbCp = repmat(Cmap(end,:),size(C));
end

AeMax = max(Aellipse);
Aemin = min(Aellipse);

Covclim = dOPS.Covclim;
for i1 = numel(X):-1:1,
  resaturation = Covclim(2) - (Aellipse(i1)-Aemin)/(AeMax-Aemin)*diff(Covclim);
  rgbC(i1,:) = rgbCp(i1,:)*resaturation + ...
                   [1 1 1]*(1-resaturation);
end

hold_state = get(gca,'nextplot');
hold on
for i1 = numel(X):-1:1;

  h(i1) = fill(X(i1)+Xe(i1,:),Y(i1)+Ye(i1,:),rgbC(i1,:));
  if strcmp(dOPS.pclr,'rgb')
    plot(X(i1),Y(i1),'.','color',rgbCp(i1,:))
  else
    plot(X(i1),Y(i1),'.','color',dOPS.pclr)
  end
end

set(h,'edgecolor',dOPS.edgecolor)

set(gca,'nextplot',hold_state);

function [x,y,Aellipse] = ellipse_xy(C)

p = linspace(0,2*pi,361); % one-degree steps around 2*pi

[eigvec,lambda] = eig(C); % Eigenvalues and eigen-vectors
xy = [cos(p'),sin(p')] * sqrt(lambda) * eigvec'; % Transformation
x = xy(:,1);
y = xy(:,2);
Aellipse = pi*prod(diag(eigval));

HTH

[Milana Asker]

Thank you a lot for your answer. Unfortunately, this code seems a bit complicated to me and I would like you to elaborate on it a bit more if it is not too hard for you? ; )

p.s. like where do I put my values for x- and y-coordinates and error values?

[Bjorn Gustavsson]

You put your x-coordinates into X, and your y-coordinates into Y. Since you used scatter with constant size (170), you can set C to something constant:

C = 170*ones(size(X));

Then you need to put your errorx1 and errory1 into a stack of covariance-matrices with the same number of levels as number of points in x and y:

for i3 = numel(X):-1:1
  CovM(:,:,i3) = [errorx1(i3)^2,0;0,errory1(i3)^2];
end

That shold give you a single-hued scatter-plot with whitening corresponding to the size of your error-ellipse:

scatter_ellipse(X,Y,C,CovM)

HTH