Class Prep

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Class Prep

• Bring to Class
• In-Class Exercise
• Paper for Classroom Printer
• Load Files
• M-Files
• Run MATLAB
• switch Current Directory

2
Copy Files

• Copy waves_a.m, waves_b.m from the course folder
  to your directory
• Run MATLAB, set correct Current Directory
• run waves_a, waves_b

3
Week 08-b(11.1-11.2)

• 2-Dimensional PlotsSub-Plots

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Hands-On DEMO Creating a Plot

• The plot function has different forms, depending
  on the input arguments.
• If y is a vector, plot(y) produces a piecewise
  linear graph of the elements of y versus the
  index of the elements of y.
• gtgt y32 55 64 23 88 62 9
• gtgt plot(y)
• If you specify two vectors as arguments,
  plot(x,y) produces a graph of y versus x.
• gtgt x00.12pi ysin(x)
• gtgt figure(2),plot(x,y)

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Hands-On DEMO Adding Title Axis Labels

• xlabel('x 02\pi') Note use of special symbol
  p
• ylabel('Sine of x')
• title('Plot of the Sine Function','FontSize',14)

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To view ALL special symbols available

• \epsilon, \theta, \pi, \uparrow, \newline, etc.
• gtgt doc text
• Then look for text properties in the help index,
  then scroll down to list of symbols (see next
  slide)
• Note that "" will superscript, "_" will
  subscript
• title('(x_1x_2)3(y_1y_2)3')
• yields
• (x1x2)3(y1y2)3

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Plotting Multiple Curves , Same Axes (1 of 2)

• Problem How can you compare several curves?
• Lets start with the following
• We could plot these using

gtgt X 0.0pi/1002pi gtgt Y1 cos(X) gtgt Y2
3cos(X) gtgt Y3 cos(2X) gtgt Y4 sin(X)
gtgt plot(X,Y1) gtgt hold on gtgt plot(X,Y2) gtgt
plot(X,Y3) gtgt plot(X,Y4)
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Plotting Multiple Curves, Same Axes (2 of 2)

• Or we could do
• Or we could do this

gtgt plot(X,Y1,X,Y2,X,Y3,X,Y4)
gtgt Z Y1Y2Y3Y4 gtgt plot(X,Z)
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Hands-On DEMO LineWidth

• gtgt x00.12pi ysin(x)
• LineWidth (in pixels) of a plot can be changed
• gtgt plot(x,y,'r','LineWidth',4)

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The Legend!

• Multiple x-y pair arguments create multiple
  graphs with a single call to plot.
• MATLAB automatically cycles through a predefined
  (but user settable) list of colors to allow
  discrimination between each set of data.
• The legend command provides an easy way to
  identify the individual plots.

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Hands-On DEMO Multiple Data Sets

• gtgt x 00.056 y1 sin(x) y2 sqrt(x)
• gtgt plot(x,y1, x,y2)
• gtgt legend('sin(x)','sqrt(x)')
• This creates a plot with 2 lines and adds a
  2-line legend that describes the lines. See the
  help information on legend for more ways to use
  this function.

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Multiple Data Sets in One Graph
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Labeling with the text command
waves_a.m Plot Bi-chromatic Wave Profile a1
1 a2 1.5 c1 2.0 c2 1.8 time
00.1100 wave1 a1 sin(c1time) wave2 a2
sin(c2time) a1 wave3 wave1
wave2 plot(time,wave1,time,wave2,time,wave3) axis
(0 100 -2 4) xlabel ('time') ylabel ('wave
elevation') title ('Bi-chromatic Wave
Profile') text(42,-1.2, 'wave 1') x, y
position text(42, 2.7, 'wave 2') text(59, 3.6,
'waves 12')
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Highlighting the Plot
COLOR of the Point or Curve
Marker of the Data Points
Plot Line Styles
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Using Lines or Markers or Both

• Plots should follow the following logic
• Lines whenever plotting analytical functions
  like sin(x) where you can compute y for any value
  of x
• Markers whenever plotting discrete experimental
  data or whenever the data are known only
  discretely
• Both connecting markers with straight lines is
  appropriate when you want to show a sequence

gtgt x0.021 gtgt yx.1.5 gtgt yrrandn(size(x)) gt
gt yyy0.1.yr gtgt plot(x,yy,'ro',x,yy)
gtgt x00.021 gtgt yx.1.5 gtgt yrrandn(size(x))
gtgt yyy0.1.yr gtgt plot(x,yy,'rx')
gtgt plot(x,cos(x),'r') gtgt hold on gtgt
plot(x,sin(x),'b--')
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Using Both Markers Lines

• Use lines to show analytical fit through discrete
  data

gtgt x0.021 gtgt yx.1.5 gtgt yrrandn(size(x)) gt
gt yyy0.1.yr gtgt plot(x,yy,'x') gtgt
ppolyfit(x,yy,1) p 1.0159 -0.0927 gtgt
hold on gtgt plot(x,polyval(p,x),'r')
gtgt x00.22.pi gtgt ysin(x) gtgt
yrrandn(size(x)) gtgt plot(x,10.yyr,'ro') gtgt
hold on gtgt plot(x,10.y)
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Hands-On DEMO Plotting Lines and Markers

• In general, use MARKERS for sampled points, and
  LINES for continuous functions
• The statements
• x1 0pi/1002pi
• x2 0pi/102pi
• plot(x1,sin(x1),'r',x2,sin(x2),'bo')
• Plot a red dotted line and places blue o sign
  markers at each "sampled" data point.
• Next slide displays the graph.

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Plotting Lines and Markers, Example
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Hands-On DEMO What NOT To Do

• Using previous values for x, y1, y2
• gtgt x 00.056 y1 sin(x) y2 sqrt(x)
• gtgt plot(x,y1,'', x,y2, '')
• Note that we are plotting a continuous function
  (sqrt) as individual points (using ).
• Not Good! Notice how the plus-signs run
  together...

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Setting Axis Limits

• By default, MATLAB finds the maxima and minima of
  the data to choose the axis limits to span this
  range.
• The axis command enables you to specify your own
  limits
• axis(xmin xmax ymin ymax)
• axis(xmin xmax ymin ymax zmin zmax)
• (needed for ex8b)
• Use the command
• axis auto
• to re-enable MATLAB's automatic limit selection.

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Summary of Basic Plot Commands

• axis(xmin, xmax, ymin, ymax) sets axis limit
  values (note use of )
• axis off turns off display of axes (plot
  unchanged)
• axis on turns on display of axes
• grid on/off turns on/off display of a grid
• text(x,y,'string') - places horizontal text
  starting at (x,y)
• line(x,y) adds line specified by x y vectors

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Specialized 2D Plots

• There are a number of other specialized 2D plots
• area(x,y) builds a stacked area plot
• pie() creates a pie chart (with options)
• bar(x,y) creates a vertical bar chart (with many
  options)
• stairs(x,y) similar to bar() but shows only
  outline
• errorbar(x,y,e) plots x vs y with error bars
  defined by e
• scatter(x,y) creates a scatter plot with options
  for markers
• And many others (explore these yourself you may
  find a good use in a later course)

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Hands-On DEMO Bar, Pie Charts

• gtgt y3 7 2 9 1
• gtgt figure(1), bar(y)
• gtgt title('Bar Chart','FontSize',14)
• gtgt figure(2), pie(y)
• gtgt title('Pie Chart','FontSize',14)

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subplot Command

• There are times when it is better to create
  several smaller plots arranged in some kind of
  grid subplot(m,n,k) does this
• mrows, ncolumns in the grid
• kcurrent focus (numbered row-wise)
• Lets define a 2x3 subplot grid for
  subplot(2,3,1) with the focus on the first plot.

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MATLAB SubPlots
subplot ( m, n, p ) breaks the figure window
into m by n small figures, select the p-th figure
for the current plot
subplot (3, 2, 1) plot (t,wv1) subplot (3,
2, 2) plot (t,wv2) subplot (3, 2, 4) plot
(t, wv1wv2) subplot (3, 2, 6) plot (t,
wv1-wv2)
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2
3
4
5
6
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x00.110 y1sin(pix) y2sin(0.5pix)
y3y1y2 z1cos(pix) z2cos(0.5pix)
z3z1-z2 subplot(3,2,1) H1plot(x,y1,'b')
set(H1,'LineWidth',2) subplot(3,2,2)
H2plot(x,z1,'b') set(H2,'LineWidth',2)
subplot(3,2,3) H3plot(x,y2,'m')
set(H3,'LineWidth',2) subplot(3,2,4)
H4plot(x,z2,'m') set(H4,'LineWidth',2)
subplot(3,2,5) H5plot(x,y3,'r')
set(H5,'LineWidth',2) subplot(3,2,6)
H6plot(x,z3,'r') set(H6,'LineWidth',2)
Multiple Plots,Same Figure
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Labeling SubPlots
waves_b.m Plot Bi-chromatic Wave Profile
Display the results in three subplots close all
closes the graphics window a1 1 a2 1.5
c1 2.0 c2 1.8 time 00.1100 wave1 a1
sin(c1time) wave2 a2 sin(c2time) wave3
wave1 wave2 subplot(3,1,1) top
figure plot(time,wave1,'m') axis(0 100 -3 3)
ylabel('wave 1') subplot(3,1,2) middle
figure plot(time,wave2,'g') axis(0 100 -3 3)
ylabel('wave 2') subplot(3,1,3) bottom
figure plot(time,wave3,'r') axis(0 100 -3
3) xlabel('x') ylabel('waves 12')
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Example of Log Plots

• Using a log scale can reveal large dynamic ranges

gtgt xlinspace(.1,10,1000) gtgt damp0.05 gtgt
y1./sqrt((1-x.2).2 (2.damp.x).2) gtgt
plot(x,y) gtgt semilogx(x,y) gtgt loglog(x,y)
Describes the behavior of vibrating systems
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Hands-On DEMO SubPlots using Log Scale

• Plot polynomial function y 2x2 7x 9

Generate the polynomial x linspace (0, 10,
100) y 2x.2 7x 9 plotting the
polynomial subplot (2,2,1), plot (x,y) title
('Polynomial, linear/linear scale') ylabel
('y'), grid on subplot (2,2,2), semilogx
(x,y) title ('Polynomial, log/linear
scale') ylabel ('y'), grid on subplot (2,2,3),
semilogy (x,y) title ('Polynomial, linear/log
scale') xlabel('x'), ylabel ('y'), grid on
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Results on Log Linear Scales
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In-Class Exercise 8b 2-D Plots

• Write a script to produce
• Title in 14-point
• Line red, width2
• Don't forget legend!
• To Print directly from Figure
• File Menu ? Print

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END