# Plotting

Matlab has excellent support for data visualization and graphics with over 70 types of plots currently available. We won't be able to go into all of them here, nor will we need to, as they all operate in very similar ways. In fact, by understanding how Matlab plotting works in general, we'll be able to see most plot types as simple variations of each other. Fundamentally, they all use the same basic constructs. Rather than explain all this in detail, we will just give some useful examples; it should be pretty clear what is going on from context.

## Contents

## Scatter plots for 2D Data

Here we show how to plot some random 2d data.

rand('twister',0); % seed the random number generator X = 5*rand(100,1); y = rand*X + rand(100,1); % generate some synthetic data f1 = figure; % create a blank figure p1 = plot(X,y,'.'); % plot X vs y X1 = X;

We have told Matlab to plot the data in X vs the data in y and to display a blue solid dot for each data point. There are many different types of marker and line styles available. For a complete list type **doc linespec**. Lets make a few changes.

clf(f1); % clear the figure p2 = plot(X,y,'o','MarkerEdgeColor','k',... % plot larger red circles with black edges 'MarkerFaceColor','r',... 'MarkerSize',8);

## Title and axis labels

We can specify the axis range and labels as follows.

axis([-1,6,-1,5]); xlabel('x'); ylabel('y');title('this is the title');

## Plotting curves

Plotting functions (curves) is very similar to the data plotting we just performed. We evaluate the function at every point along its domain and plot the resulting x,y pairs, connecting consecutive dots. Here we plot two functions on the same set of axes. The **hold on** command tells Matlab to superimpose all the plots onto the same figure, rather than overwriting previous plots.

f = @(x) x.^2; % create a function of x, namely f(x) = x.^2 g = @(x) 5*sin(x)+5; % create a second function of x, g(x) = 5*sin(x) + 5 res = 0.001; % resolution of the plot domain = -pi:res:pi; % the domain of x, (i.e. points at which to evaluate f,g) f2 = figure; % open a new figure p3 = plot(domain,f(domain)); % plot f, w.r.t. x over its domain hold on; % tell Matlab to add future plots to the same set of axes p4 = plot(domain,g(domain)); % plot the second function.

Not bad for a first attempt but there are a lot of improvements we could make. Lets try again but this time, we will plot each function in its own color, change the line widths and types, the tick marks, the range of the axes, the background color, the font size, and add labels, a title, and a legend. We'll keep the functions and domain the same. Let us also add error bars to one of the functions denoting one standard deviation of the dependent variable.

f3 = figure('Color',[1,1,1]); hold on; % new figure with a white background p5 = plot(domain,f(domain),'--r','LineWidth',3); % plot a thick dashed red line p6 = plot(domain,g(domain),'-b','LineWidth',3); % plot a thick solid blue line subdomain = domain(1:400:end); % we will plot error bars at every 400th point oneSTD = std(g(domain)); % standard deviation of g(domain) oneSTD = oneSTD*ones(size(subdomain)); % make correct size, as needed by errorbar p7 = errorbar(subdomain,g(subdomain),oneSTD); % plot the error bars title('example figure','FontSize',12); % add a title xlabel('distance','FontSize',12); % label the horizontal axis ylabel('height','FontSize',12); % label the vertical axis axis([-3,3,-5,15]); % set the axis range grid on; % add grid lines legend('f', 'g');

## Subplots

We often want to plot multiple subfigures within a larger one. We can write **subplot(nr,nc,i)** to make an nr * nc plot. This command selects the i'th such subplot, numbered from left to right, top to bottom. Kevin Murphy's subplot2 function is sometime more convenient: you write **subplot2(nr,nc,i,j)** to select the subplot in row i, column j. Drea Thomas' suptitle function can be used to provide a title for all the plots. Below we give an example.

figure; for i=1:6 subplot(2,3,i); hist(rand(1,100),10); title(sprintf('subplot %d', i)); end suptitle('master title')

## Handles and Customization

Figure generation in Matlab is object oriented. Figures are top level objects and contain other objects such as axes and annotations. Axes further contain sub-objects such as plots and labels, which are often built up from smaller objects too. All of these objects have attributes that can be retrieved and, (for the most part) changed, using the *get()* and *set()* commands. The first parameter to these functions is a handle to an object. We can obtain such handles when we create the objects as in *fig = figure*.

After the fact, we can obtain the handle to the current figure by using the *gcf()* command or to the current set of axes by using the *gca()* command. We can see a list of all of the attributes of an object by typing **get(handle)** at the command prompt.

figure(f3); get(gca)

ActivePositionProperty = outerposition ALim = [0 1] ALimMode = auto AmbientLightColor = [1 1 1] Box = off CameraPosition = [0 5 17.3205] CameraPositionMode = auto CameraTarget = [0 5 0] CameraTargetMode = auto CameraUpVector = [0 1 0] CameraUpVectorMode = auto CameraViewAngle = [6.60861] CameraViewAngleMode = auto CLim = [0 1] CLimMode = auto Color = [1 1 1] CurrentPoint = [ (2 by 3) double array] ColorOrder = [ (7 by 3) double array] DataAspectRatio = [3 10 1] DataAspectRatioMode = auto DrawMode = normal FontAngle = normal FontName = Helvetica FontSize = [10] FontUnits = points FontWeight = normal GridLineStyle = : Layer = bottom LineStyleOrder = - LineWidth = [0.5] MinorGridLineStyle = : NextPlot = add OuterPosition = [0 0 1 1] PlotBoxAspectRatio = [1 1 1] PlotBoxAspectRatioMode = auto Projection = orthographic Position = [0.13 0.11 0.775 0.815] TickLength = [0.01 0.025] TickDir = in TickDirMode = auto TightInset = [0.0821429 0.097619 0.00892857 0.0595238] Title = [712] Units = normalized View = [0 90] XColor = [0 0 0] XDir = normal XGrid = on XLabel = [713] XAxisLocation = bottom XLim = [-3 3] XLimMode = manual XMinorGrid = off XMinorTick = off XScale = linear XTick = [ (1 by 7) double array] XTickLabel = -3 -2 -1 0 1 2 3 XTickLabelMode = auto XTickMode = auto YColor = [0 0 0] YDir = normal YGrid = on YLabel = [714] YAxisLocation = left YLim = [-5 15] YLimMode = manual YMinorGrid = off YMinorTick = off YScale = linear YTick = [-5 0 5 10 15] YTickLabel = -5 0 5 10 15 YTickLabelMode = auto YTickMode = auto ZColor = [0 0 0] ZDir = normal ZGrid = on ZLabel = [715] ZLim = [-1 1] ZLimMode = auto ZMinorGrid = off ZMinorTick = off ZScale = linear ZTick = [-1 0 1] ZTickLabel = ZTickLabelMode = auto ZTickMode = auto BeingDeleted = off ButtonDownFcn = Children = [ (3 by 1) double array] Clipping = on CreateFcn = DeleteFcn = BusyAction = queue HandleVisibility = on HitTest = on Interruptible = on Parent = [3] Selected = off SelectionHighlight = on Tag = Type = axes UIContextMenu = [] UserData = [] Visible = on

We can access specific properties using **get(handle,'property')**

```
get(gca,'xtick')
```

ans = -3 -2 -1 0 1 2 3

The command **set(handle)** lists not only the attributes but also valid potential values.

set(gca)

ActivePositionProperty: [ position | {outerposition} ] ALim ALimMode: [ {auto} | manual ] AmbientLightColor Box: [ on | {off} ] CameraPosition CameraPositionMode: [ {auto} | manual ] CameraTarget CameraTargetMode: [ {auto} | manual ] CameraUpVector CameraUpVectorMode: [ {auto} | manual ] CameraViewAngle CameraViewAngleMode: [ {auto} | manual ] CLim CLimMode: [ {auto} | manual ] Color ColorOrder DataAspectRatio DataAspectRatioMode: [ {auto} | manual ] DrawMode: [ {normal} | fast ] FontAngle: [ {normal} | italic | oblique ] FontName FontSize FontUnits: [ inches | centimeters | normalized | {points} | pixels ] FontWeight: [ light | {normal} | demi | bold ] GridLineStyle: [ - | -- | {:} | -. | none ] Layer: [ top | {bottom} ] LineStyleOrder LineWidth MinorGridLineStyle: [ - | -- | {:} | -. | none ] NextPlot: [ new | add | {replace} | replacechildren ] OuterPosition PlotBoxAspectRatio PlotBoxAspectRatioMode: [ {auto} | manual ] Projection: [ {orthographic} | perspective ] Position TickLength TickDir: [ {in} | out ] TickDirMode: [ {auto} | manual ] Title Units: [ inches | centimeters | {normalized} | points | pixels | characters ] View XColor XDir: [ {normal} | reverse ] XGrid: [ on | {off} ] XLabel XAxisLocation: [ top | {bottom} ] XLim XLimMode: [ {auto} | manual ] XMinorGrid: [ on | {off} ] XMinorTick: [ on | {off} ] XScale: [ {linear} | log ] XTick XTickLabel XTickLabelMode: [ {auto} | manual ] XTickMode: [ {auto} | manual ] YColor YDir: [ {normal} | reverse ] YGrid: [ on | {off} ] YLabel YAxisLocation: [ {left} | right ] YLim YLimMode: [ {auto} | manual ] YMinorGrid: [ on | {off} ] YMinorTick: [ on | {off} ] YScale: [ {linear} | log ] YTick YTickLabel YTickLabelMode: [ {auto} | manual ] YTickMode: [ {auto} | manual ] ZColor ZDir: [ {normal} | reverse ] ZGrid: [ on | {off} ] ZLabel ZLim ZLimMode: [ {auto} | manual ] ZMinorGrid: [ on | {off} ] ZMinorTick: [ on | {off} ] ZScale: [ {linear} | log ] ZTick ZTickLabel ZTickLabelMode: [ {auto} | manual ] ZTickMode: [ {auto} | manual ] ButtonDownFcn: string -or- function handle -or- cell array Children Clipping: [ {on} | off ] CreateFcn: string -or- function handle -or- cell array DeleteFcn: string -or- function handle -or- cell array BusyAction: [ {queue} | cancel ] HandleVisibility: [ {on} | callback | off ] HitTest: [ {on} | off ] Interruptible: [ {on} | off ] Parent Selected: [ on | off ] SelectionHighlight: [ {on} | off ] Tag UIContextMenu UserData Visible: [ {on} | off ]

We can test if a variable is a valid handle or not with the *ishandle()* method. Figure handles are actually just integer values starting at 1 that have been registered with the root graphics object.

Below, we use the *set()* method to change a number of axes attributes. Multiple attributes can be changed in one command, (or in multiple commands if you prefer) and the name of the attribute always precedes its new value.

figure(f3); set(gca,'box' ,'on' ... % draw a box around the figure ,'LineWidth', 2 ... % increase the line width ,'FontSize' ,12 ... % increase the font size ,'XTick' ,[-3,0,3]... % only these x-ticks ,'YTick' ,[0,5,10]); % only these y-ticks Xequal = domain(abs(f(domain) - g(domain)) < 2*res); % find where the two graphs meet p8 = plot(Xequal,f(Xequal),'o','MarkerFaceColor','g'... % plot green circles there ,'MarkerEdgeColor','k'... % black border around circles ,'LineWidth' , 2 ... % thicken black border ,'MarkerSize' ,10); % increase the circle size legend([p5,p6,p8],{'f(x) = x^2','g(x) = 5*sin(x)+5','f(x) == g(x)'},'Location','NorthWest'); % Prevent close commands from closing this figure. We will use it again later. %set(f3,'HandleVisibility','off');

As you can see, most plotting commands, such as *legend()* above, have many possible parameters and parameterizations. It would be redundant to go into them all here; type **doc legend** ,for example, to see more information on the legend command.

There are Matlab functions designed to make function plotting easier such as *fplot()* , *ezplot()* , *ezsurf()* , *ezmesh()* , *ezcontour()* , etc... While these can be useful for quick and dirty figures, they can make customization more difficult and so we recommend using, and learning to use, *plot()* instead. All of these functions take function handles as arguements and the ez*** functions auto set the axes limits for you.

The *loglog()* , *semilogx()* , and *semilogy()* functions are useful for plotting on logarithmic scales. However we can achieve the exact same effect by plotting with *plot()* and calling **set(gca,'XScale','log')** and/or **set(gca,'YScale','log')** . We can reverse the direction of an axis with **set(gca,'YDir','reverse')** or **set(gca,'XDir','reverse')** and move an axis with **set(gca,'YAxisLocation','right')** or **set(gca,'XAxisLocation','top')** . Recall that we can find the names of these properties with **get(gca)** or the valid values with say **set(gca,'YDir')** .

## Tickmarks

We can change the tick marks and their labels as follows on the axes. For example,

figure(f1); xs = linspace(min(X1), max(X1), 5); set(gca, 'xtick', xs, 'xticklabel', {'a','b','c','d'}) % gca = get current axis

When we have long strings for the tick marks, we can use xticklabelrot, which prints them at an angle to save space.

figure(f1); xticklabelRot({'foo','bar',22,'apple','long string'}, 45)

Warning: You may need to manually reset the XLABEL vertical position

## Histograms

Histograms are one of the most useful plots for 1d data, and for probability mass functions. Below we display a histogram of a hypothetical class grade distribution.

figure; grades = fix(normrnd(70,10,100,1)); hist(grades); % plot the histogram xlabel('percent'); ylabel('count'); title('grade distribution'); set(gca,'XLim',[0,100],'YGrid','on'); % gca = get current axis set(gca,'YMinorTick','on');

Here we organize marks into bins representing letter grades. We use the extremely quick *histc()* function to count the number of data points that fall between specified edges. Once we have obtained the counts, we can visualize them with the *bar()* function.

figure; bins = [0,50,55,60,64,68,72,76,80,85,90,inf]; % The bins letters = {'F','D','C-','C','C+','B-','B','B+','A-','A','A+'}; % The labels counts = histc(grades,bins); % count grades bar(counts(1:end-1)); % plot counts set(gca,'XTickLabel',letters,'Ygrid','on'); % set tick labels xlabel('grade'); ylabel('count'); title('grade distribution'); set(gca,'YMinorTick','on')

## Plotting 1d probability density functions

As an example of some other functions, we make a fancy plot of the Gaussian pdf in which we shade the tails using an *area()* plot, and add a few vertical bars using the *stem()* command.

figure; domain = -4:0.01:4; plot(domain,normpdf(domain),'-r','LineWidth',3); hold on % We shade two regions with the area command L = fix(length(domain))/3; R = 2*fix(length(domain))/3; area(domain(1:L),normpdf(domain(1:L))); area(domain(R:end),normpdf(domain(R:end))); % Now add gratuitous vertical lines stem([-0.7,0.1,0.4],normpdf([-0.7,0.1,0.4]),'LineWidth',2); axis([-4,4,0,0.5]); set(gca,'XMinorTick','on'); set(gca,'YMinorTick','on');

## Plotting images

The *imagesc()* function can be used to view an image. (If you have the image processing toolbox, you can use **imshow** instead.)

load mandrill % built-in image figure; imagesc(X); % display it axis image % window dimensions appropriate for an imag map = colormap(gray); % a possible color scheme. axis off

## Heatmaps and Hinton diagrams

We can also use *imagesc* to make **heatmaps** of a 2d matrix.

```
figure;
rand('twister',1);
X = randn(10,10);
imagesc(X);
colorbar
```

Often it is preferable to use hintonDiagram (named after Geoff Hinton, who used this type of display to plot the weight matrix of a neural network), where the size of the square represents the magnitude, and the color represents the polarity (red = positive, green = negative).

figure; hintonDiagram(X)

## Saving and Printing

We can print figures and save them as any major graphics type from the file drop down menu of a figure window. Also here is the 'export setup' option which opens a window where the default figure resolution and size settings can be set. Newer versions of Matlab also let you automatically increase the line widths and font sizes of the figures you are exporting. To save or print programatically, we can use the *print()* function. Type **doc print** for more details.

%figure(gcf); %print -djpeg test.jpg %print(gcf, '-djpeg', 'test.jpg'); % equivalent, useful if filename is a variable

If you find that there is too much white space surrounding the exported figure, (a particular problem when exporting to pdf) try changing the figure's paper size before exporting, with the following commands.

%pos = get(gcf,'Position'); %set(gcf,'PaperSize',pos(3:4)); %set(gcf,'PaperPositionMode','auto');

Matt Dunham has written a handy function pdfcrop that automatically ensures the paper size is set equal to the figure size, so that pdf files have a tight border.

%pdfcrop(gcf); %print(gcf, '-dpdf', 'test.pdf');

Another very useful function is exportfig which will automatically make your fonts larger, etc, before saving to a file for use in a publication.

## PlaceFigures

When many figures are generated at once, they will often overlap each other. You can manually drag them around, but Matt Dunham's placeFigures function automatically places the figures on the screen for you in a way that allows you to see them all simultaneously. Simply call *placeFigures* after generating the figures. You can specify the layout manually with say *placeFigures('nrows',2,'ncols',4)* , create new blank figures with the 'newfigs' option and display figures on a second monitor with the 'monitor' option. See the function documentation for more information. (Note that by automatically creating this web page with *publish*, the layout of the figures looks somewhat different than on the screen.)

%close all %for i=1:10 % figure; imagesc(rand(10,10)); %end placeFigures

ans = 173.0133 3.0000 6.0000 9.0000 2.0000 1.0000 7.0000 10.0000 4.0000 5.0000 8.0000 -1.0000