1999 BG Mobasseri 1 04/19/23

June 2

GRAPHICS IN MATLAB- PART I

BASIC PLOTTING

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PLOTTING A SINGLE ARRAY

The most basic command that puts a graphic on screen is plot

If y is an array, plot(y) simply plots values of y vs. their array index position

Do this:

– t=[0:0.01:1];

– y=cos(2*pi*t);

– plot(y)

Notice numbers on x-axis. They are not time

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PLOTTING ONE ARRAY AGAINST ANOTHER

If t is one array and y another, plot(t,y) plots y vs. t.

Do this:

– t=[0:0.01:1];

– y=cos(t);

– plot(t,y)

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Try it!

Plotting one array against another generates creative figures

For example, define your x-array as cos(2(pi)t) and y-array as sin(2(pi)t). Then plot y vs.x. Let t run from 0 to 1 as before

Do the same for 2cos(2(pi)t) vs. 4sin(2(pi)t)

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Plots via a matrix

The argument of plot can be a matrix. In this case, each column is plotted separately on the same axis. This is a compact way of plotting several graphs on the same axis

Try

– t=0:pi/16/:2*pi;

– x=[cos(t)’,sin(t)’]

– plot(x)

5 8 9 0

3 5 2 3

6 6 5 4

8 4 6 8

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

each column is plottedseparately vs. position

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Plotting a matrix against another array

Let Y be a matrix and x be the vector of variables , then

– plot(x,Y) plots columns of Y vs. x on the same graph

Try this

– t=0:pi/16:2*pi;

– Y=[cos(t)’,sin(t)’]

– plot(t’,Y)

5 8 9 0

3 5 2 3

6 6 5 4

8 4 6 8

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

each column plottedseparately vs. anotherarray

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Putting multiple plots on the same graph

There are 3 ways to do this. Want to plot 3 data vectors y1,y2 and y3 vs. t

Method 1:

– Y=[y1,y2,y3]

– plot(t,Y) Method 2

– plot(t,y1,t,y2,t,y3) Method 3

– Use hold command

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RC circuit response

Capacitors charge and discharge following an exponential curve. Plot the following 3 voltages on the same graph for 0<t<5.

v1 =1−e−t

v2 =1−e−2t

v3 =1−e−3t

⎧

⎨⎪

⎩⎪

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Try it!

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hold COMMAND

Once hold is turned on, all subsequent plot commands are superimposed on the same axis

hold cycles between on and off.

For example,– plot(t,y1)– hold on– plot(t,y2)– plot(t,y3)– hold off

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Homework #1

Plot y vs. x over the range x=[-2,2]. In addition to your m-file, save your figure and send it to me

y=1

x−0.3( )2 + 0.01+

1x−0.9( )2 + 0.04

−6

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Plotting parametric functions- fplot.

You may want to plot a function, rather than an array of numebrs, against a variable.

Example is plotting cos(x). The command is

fplot(‘cos’,[-pi pi])

Note that the function must be known to MATLAB such as sine and cosinefunction x range

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MULTIPLE PLOTS USING fplot

fplot(‘[sinc(x),sinc(2*x)]’,[-2 2])

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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CONTROLLING LINE TYPES

We can select line styles and colors in a graph

Simply pass a character string to plot

– plot(t,x,’s’)

For example, s=r+, puts red plus(+) marks for every data point.

MATLAB accepts many other choices.

Redo the exponentials using different styles

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Homework #2

Plot the 3 exponentials on slide 8 simultaneously.

– 1. Use red, green and blue solid lines respectively

– 2. Use red plus sign(+), green star(*) and blue dots (.) for each graph

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SPECIALIZED 2D PLOTTING FUNCTIONS

For each item write an m-code to see the plots. Read the example slides

bar - creates a, well, bar graph polar - creates a (plot hist - creates a histogram of data fill - fills the curve with solid colors stairs - similar to bar but without internal

lines

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bar

Usage:

– bar(x,y)

– plot the shape of a normal distribution given by y=exp(-x2) in the range (-2,2).

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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fill

Usage:

– fill(x,y,’b’) where b indicates a blue fill.

– plot the function exp(-t^2), in the range (-2,2)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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polar

Usage:

– polar(theta,rho)

Plot =sin 2θ( )cos 2θ( )

0.1

0.2

0.3

0.4

0.5

30

210

60

240

90

270

120

300

150

330

180 0

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stairs

Usage

– stairs(x,y)

– plot the function exp(-x^2), in the range (-4,4)

-4 -3 -2 -1 0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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ADDING LABELS AND TITLES

There are numerous ways the appearance of a plot can be controlled. The most obvious ones are through

– axis labels

– figure title

– legend

– grid

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LABEL USAGE

axis labels

– xlabel(‘time’)

– ylabel(‘voltage’) Figure title

– title(‘Capacitor voltage’) Legend

– legend(‘first’,’second’,’third’) Grid

– grid - places a grid over the plot

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Try it!

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Homework #3

Over a time range [-3, 3], plot the following 3 functions simultaneously using the matrix method of slide 7

– y=e-4xcos(2*pi*x);