Matlab Training Sessions 6,7: Plotting

Course Outline Weeks: 1.Introduction to Matlab and its Interface (Jan ) 2.Fundamentals (Operators) 3.Fundamentals (Flow) 4.Importing Data 5.Functions and M-Files 6.Plotting (2D and 3D) 7.Statistical Tools in Matlab 8.Analysis and Data Structures Course Website:

Week 5 Lecture Outline Plotting Data A.Basics B.Generating data C.2D Plots (Line, Scatter, Bar) D. Plot Features

Basics Matlab has a powerful plotting engine that can generate a wide variety of plots.

Generating Data Matlab does not understand functions, it can only use arrays of numbers. –a=t 2 –b=sin(2*pi*t) –c=e -10*t note: matlab command is exp() –d=cos(4*pi*t) –e=2t 3 -4t 2 +t Generate it numerically over specific range Try and generate a-e over the interval 0:0.01:2 t=0:0.01:10; %make x vector y=t.^2; %now we have the appropriate y % but only over the specified range

Line/Scatter Simplest plot function is plot() Try typing plot(y) –Matlab automatically generates a figure and draws the data and connects its lines –Looks right, but the x axis units are incorrect Type plot(x,y), will look identical but have correct x-axis units Plot(x1,y1,s1,x2,y2,s2, …) many plots in one command Plot(x) where x is a matrix, will result in plotting each column as a separate trace

Line/Scatter Plot a and then plot b –What do you see? –Only b Matlab will replace the current plot with any new one unless you specifically tell it not to To have both plots on one figure use the hold on command To make multiple plots use the figure command plot(t,a) plot(t,b) % Put a and b on one plot plot(t,a); hold on; plot(t,b); % Make two plots plot(t,a); figure; plot(t,b);

Hold On / Hold Off Hold on command only needs to be issued once per figure, thus calling hold on will result in all subsequent plot commands going to one figure unless a new figure command is issued or hold off is used. plot(a); Hold on; plot(b); plot(c); Hold off; Figure; plot(d); plot(a); Hold on; plot(b); plot(c); Hold off; plot(d); plot(a); Hold on; plot(b); plot(c); Figure; plot(d);

Linespec Currently, all the plots were done in the Matlab default color … blue This and many other features can be changed by selecting a different option within the plot command % red line Plot(t,a,’r’); Hold on; % black line Plot(t,b,’k’); % green dots Plot(t,c,’g.’); % cyan x’s Plot(t,d,’cx’) % dashed magenta % line with o’s Plot(t,e,’--om’)

Linespec Now we have added color, line style and markers to the data We can also modify line width, marker edge and fill color and marker size % dashed magenta % line with o’s, … Plot(t,e,’--om’, ‘LineWidth’,3,'MarkerEdgeColor',‘k‘, 'MarkerFaceColor',‘y‘, MarkerSize,9)

Labels, Title and Legend To add labels to the x and y axes, we can use the xlabel and ylabel commands To add a title, use the title command To add a legend, use the legend command plot(t,a,t,b,’r’,t,c,’--om’); %generate all plots in one shot title(‘Random Plots’) xlabel(‘time(ms)’); ylabel(‘f(t)’) legend(‘Function 1’,’Function 2’,’Function 3’);

Quick Assignment 1 Plot a as a thick black line Plot b as a series of red circles. Label each axis, add a title and a legend

Quick Assignment 1 figure plot(t,a,'k','LineWidth',3); hold on; plot(t,b,'ro') xlabel('Time (ms)'); ylabel('f(t)'); legend('t^2','sin(2*pi*t)'); title('Mini Assignment #1')

Axis commands We can alter the displayed range and other parameters of the plot by using the axis command –Axis([xmin xmax ymin ymax]) –Axis equal; –Axis square; Figure; Plot(t,a,’r’); Axis([ ]);

Error Bars In addition to markers, matlab can generate error bars for each datapoint using the errorbar command –errorbar(x,y,e) or errorbar(x,y,ll,lu); –Will generate line plus error bars at y+/-e or (y-ll,y+lu) t2 = 0:1:10; f = t2+(rand(1,length(t2))-0.5); err1 = 0.1*f; err2_l = 0.1*f; err2_u = 0.25*f; errorbar(t2,f,err1); figure; errorbar(t2,f,err2_l, err2_u);

Subplots So far we have only been generating individual plots Matlab can also generate a matrix of plots using the subplot command figure; subplot(2,2,1) plot(t,a); subplot(2,2,2) plot(t,b); subplot(2,2,3) plot(t,c); subplot(2,2,4) plot(t,d);

Quick Assignment 2 Generate a 3x1 array of figures, each with a title Axis range of plots 1 and 2 should be 0 to 1 on x and y Plot 1 should include function a and b (color code) Plot 2 should include c and d (color code) Plot 3 should include f with error bars of your liking

Quick Assignment 2 figure subplot(3,1,1) plot(t,a,t,b,'r'); axis([ ]); title('Functions a and b') subplot(3,1,2) plot(t,c,t,d,'m'); axis([ ]); title('Functions c and d') subplot(3,1,3) errorbar(t2,f,err1); title('function f with errorbars')

Bar Graphs So far we have focused on line/scatter plots, the other most common plot type is a bar graph Matlab bar(x,y,width) command will generate a bar graph that is related to the underlying functions where the width of each bar is specified by width (default = 1); Can be used with subplot and all the other features we have discussed so far t3 = 0:1:25; f = sqrt(t3); bar(t3,f);

Histograms Matlab hist(y,m) command will generate a frequency histogram of vector y distributed among m bins Also can use hist(y,x) where x is a vector defining the bin centers –Note you can use histc function if you want to define bin edges instead Can be used with subplot and all the other features we have discussed so far hist(b,10); Figure; Hist(b,[ ]);

Quick Assignment 3 Generate the following data set –It results in multiple noisy repeats of some trial Create mean_x to be the mean of all the trials at each point of x Create std_x to be the standard deviation of all trials at each point of x Add labels and titles t = 0:0.1:1 for(i=1:25) x(i,:) = exp(-10.*t) + 0.5*(rand(1,length(t))-0.5); end

Quick Assignment 3 Make a plot that is to include 2 subplots Plot #1: –Plot each individual trial (25 lines) in thin dotted black lines, tip: remember about how matlab interprets matricies for the plot command. –Plot the mean of the trials with a thick, red, dashed line and error lines surrounding each datapoint that correspond to the standard deviation of each of the points Plot #2: –A histogram that expresses the distribution of the signal at the end of each trial (last sample)

Quick Assignment 3 t = 0:0.1:1 for(i=1:25) x(i,:) = exp(-10.*t) + 0.5*(rand(1,length(t))-0.5); end mean_x = mean(x); std_x = std(x); figure subplot(2,1,1) plot(t,x,'k'); hold on; errorbar(t,mean_x,std_x,'--r','LineWidth', 3); title('Repeats of a Given Task') xlabel('Repeat'); ylabel('Error Rate'); subplot(2,1,2) hist(x(:,11),10) title('Distribution of Endpoint Position'); xlabel('Deviation (mm)') ylabel('Occurances')

Quick Assignment 3

Recap Learned about basic 2D plot functions –plot,bar,hist Dealing with multiple plots and graphs –Hold, figure, subplot Discussed adding features to graphs –Xlabel,title,legend,…

3D Plots Matlab provides a wide range of 3D plot options, we will talk about 3 different plot types. –Mesh, Surf, Contour

Dataset Try [x,y,z] = peaks(25) –Does this work? If not, lets create an arbitrary dataset –x=-10:10; y = -10:10; z=x.^2’*y.^2;

Mesh Connects a series of discrete data points with a mesh –mesh(x,y,z) where X(i) and Y(j) are the intersections of the mesh and Z(i,j) is the height at that intersection –mesh(Z) assumes X and Y are simple 1..N and 1..M

Surf Very similar to mesh, with filled grid

Contour Projection of equal heights of 3D plot onto a 2D plane Use like surf or mesh – contour(x,y,z)

Meshc,surfc Combination surface/mesh and contour plot Use like surf or mesh – meshc(x,y,z)

Plot3 Plots lines and points in space, just like plot but now for an (x,y,z) triple Plot3(x,y,z), each a vector of equal length Use all the same specfiers to generate colors, line-types, etc.

Plot commands Note that almost all 2D plotting commands such as xlabel, ylabel, title will still work in 3D plots 3D plots can be added as subplots just like any other plot type Some other special features and functions exist…

View Changes the view of the current 3D plot –view(az,el) –Az = azimuth (rotation around z-axis) –El = Elevation (rotation around xy-plane) Useful rotations (0,0),(90,0)

Colorbar For the 3D plots, it is useful to add a colorbar to the figure to indicate height. Colorbar(‘vert’) adds a vertical colorbar Colorbar(‘horiz) adds a horizontal colorbar

caxis Allows you to set the range of colors in the plot. Caxis([min max]) will choose the range of colors from the current color map to assign to the plot. Values outside this range will use the min/max available

Colormap Plenty of other controls to personalize the plot –colormap colormap_name sets to new map –Colormap (sets the types of colors that appear in 3D plot). These can be custom of one of several premade –bone Hsv, jet, autumn, vga, summer, … –See help graph3D for more –Use colormapeditor function for graphical selection of color map

Colormap

Next Week Basic Stats / Basic Matlab wrap up

Getting Help Help and Documentation Digital 1.Accessible Help from the Matlab Start Menu 2.Updated online help from the Matlab Mathworks website: 3.Matlab command prompt function lookup 4.Built in Demo’s 5.Websites Hard Copy 3.Books, Guides, Reference The Student Edition of Matlab pub. Mathworks Inc.