matlab training sessions 6,7: plotting. course outline weeks: 1.introduction to matlab and its...
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Course Outline
Weeks:
1. Introduction to Matlab and its Interface (Jan 13 2009)
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:
http://www.queensu.ca/neurosci/matlab.php
Week 5 Lecture Outline
Plotting Data
A. Basics
B. Generating data
C. 2D Plots (Line, Scatter, Bar)
D. Plot Features
Generating Data• Matlab does not understand functions, it can
only use arrays of numbers.– a=t2
– b=sin(2*pi*t)– c=e-10*t note: matlab command is exp()– d=cos(4*pi*t)– e=2t3-4t2+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 linePlot(t,a,’r’);Hold on;% black linePlot(t,b,’k’);% green dotsPlot(t,c,’g.’);% cyan x’sPlot(t,d,’cx’)% dashed magenta % line with o’sPlot(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 shottitle(‘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
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Time (ms)
f(t)
Mini Assignment #1
t2
sin(2*pi*t)
Quick Assignment 1
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Time (ms)
f(t)
Mini Assignment #1
t2
sin(2*pi*t)
figureplot(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([-2 2 -2 2]);
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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);
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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);
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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
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1Functions a and b
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Quick Assignment 2
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figuresubplot(3,1,1)plot(t,a,t,b,'r');axis([0 1 0 1]);title('Functions a and b')subplot(3,1,2)plot(t,c,t,d,'m');axis([0 1 0 1]);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);
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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,[-1 -0.75 0 0.25 0.5 0.75 1]);
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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 = 0:0.1:1for(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
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1.4Repeats of a Given Task
Repeat
Err
or R
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Deviation (mm)
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t = 0:0.1:1for(i=1:25) x(i,:) = exp(-10.*t) + 0.5*(rand(1,length(t))-0.5);endmean_x = mean(x);std_x = std(x);figuresubplot(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
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1.4Repeats of a Given Task
Repeat
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Deviation (mm)
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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
Contour• Projection of equal heights of 3D plot onto a
2D plane
• Use like surf or mesh – contour(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
Getting HelpHelp and Documentation
Digital 1. Accessible Help from the Matlab Start Menu
2. Updated online help from the Matlab Mathworks website:
http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html
3. Matlab command prompt function lookup
4. Built in Demo’s
5. Websites
Hard Copy3. Books, Guides, Reference
The Student Edition of Matlab pub. Mathworks Inc.