Basics of MATLAB and Beyond

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s = 100*spiral(3)s =700 800 900600 100 200500 400 300>> ind = find(s>400)ind =12347>> s(ind)ans =700600500800900>> s(s>400)ans =700600500800900After introducing graphics of functions of two variables in the next section,we will see how the find command can be used to do the threedimensionalequivalent of the plot shown on page 23, where the domainof a curve satisfying a logical test was extracted.7 Graphics of Functions of Two Variables7.1 Basic PlotsA matlab surface is defined by the z coordinates associated with a setof (x, y) coordinates. For example, suppose we have the set of (x, y)coordinates:(x, y) =⎛⎜⎝1, 1 2, 1 3, 1 4, 11, 2 2, 2 3, 2 4, 21, 3 2, 3 3, 3 4, 31, 4 2, 4 3, 4 4, 4The points can be plotted as (x, y) pairs:⎞⎟⎠ .c○ 2000 by CRC Press LLC
The (x, y) pairs can be split into two matrices:⎛⎞ ⎛1 2 3 4x = ⎜ 1 2 3 4⎟⎝ 1 2 3 4 ⎠ ; y = ⎜⎝1 2 3 41 1 1 12 2 2 23 3 3 34 4 4 4⎞⎟⎠ .The matrix x varies along its columns and y varies down its rows. Wedefine the surface z:z = √ x 2 + y 2 ;which is the distance of each (x, y) point from the origin (0, 0). Tocalculate z in matlab for the x and y matrices given above, we beginby using the meshgrid function, which generates the required x and ymatrices:>> [x,y] = meshgrid(1:4)x =1 2 3 41 2 3 41 2 3 41 2 3 4y =1 1 1 12 2 2 23 3 3 34 4 4 4Now we simply convert our distance equation to matlab notation; z =√x2 + y 2 becomes:>> z = sqrt(x.^2 + y.^2)z =1.4142 2.2361 3.1623 4.12312.2361 2.8284 3.6056 4.47213.1623 3.6056 4.2426 5.00004.1231 4.4721 5.0000 5.6569c○ 2000 by CRC Press LLC
Page 2 and 3: BASICS OFMATLAB®and Beyondc○ 200
Page 4 and 5: Library of Congress Cataloging-in-P
Page 6 and 7: typing pwd (print working directory
Page 8 and 9: ContentsIBasics of MATLAB1 First St
Page 10 and 11: 20 Time-Frequency Analysis21 Line A
Page 12 and 13: 39Answers to Exercises (Part I)40 A
Page 14 and 15: Set → Getting Started with MATLAB
Page 16 and 17: 1.5 The Colon OperatorTo generate a
Page 18 and 19: matlab will recall the last command
Page 20 and 21: a = zeros(2,3)a =0 0 00 0 0>> b = o
Page 22 and 23: [a a(a)]ans =1 2 3 1 4 74 5 6 2 5 8
Page 24 and 25: a + bans =11 3344 6677 993.8 Transp
Page 26 and 27: 4.2 Adding PlotsWhen you issue a pl
Page 28 and 29: x = [[1 2 3 4]’ [2 3 4 5]’ [3 4
Page 30 and 31: 4.7 AxesSo far we have allowed matl
Page 32 and 33: v =1122>> v*uans =1 2 0 11 2 0 12 4
Page 34 and 35: max returns a vector containing the
Page 38 and 39: We can plot the surface z as a func
Page 40 and 41: The contour function plots the cont
Page 42 and 43: m = gray(8);colormap(m)imagesc(1:10
Page 44 and 45: hold onplot3(x(ind),y(ind),z(ind),
Page 46 and 47: z = 5*ones(3,3)z =5 5 55 5 55 5 5>>
Page 48 and 49: contour(x,y,z,30);You may have noti
Page 50 and 51: variables that are local to themsel
Page 52 and 53: SwitchThe basic form of a switch st
Page 54 and 55: i =i =123136Vectorised Codematlab i
Page 56 and 57: 9.1 MATLAB FormatTo save all the va
Page 58 and 59: 11 StartupEach time you start matla
Page 60 and 61: Where p i is the population for yea
Page 62 and 63: NaNs by leaving them off the plot.
Page 64 and 65: clfpolar(t,gdb)In this case you mus
Page 66 and 67: -0.5000-0.3750-0.2500-0.125000.1250
Page 68 and 69: the periodograms of the blocks, and
Page 70 and 71: plot(y(1:1000))axis([0 1000 -5 5])z
Page 72 and 73: comet(x,y)(You can get a three-dime
Page 74 and 75: By clicking within the panner box a
Page 76 and 77: x = linspace(-1,1,8192);Fs = 1000;y
Page 78 and 79: 23.3 Graphical Object Hierarchymatl
Page 80 and 81: Now we need to get the handles of a
Page 82 and 83: Beyond the BasicsPreludeThis part o
Page 84 and 85: clfgplot(A,[x y])axis off(Try zoomi
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str =you’re the one>> str = ’
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strrep(str,’go’,’am’)ans =I
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ans =3.14159e+100Some additional te
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eval(str)v =1 2 3 4 5The eval(str)
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Inline objects, like every other ma
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a(1,1) = {[1 2 3]}a =[1x3double]or>
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t = {’help’ spiral(3) ; eye(2)
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meteo.Temperatureans =24ans =19.000
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3 >> a = [1 2 ;4 5 6;7 8 9]a =1 2 3
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[x,y] = meshgrid(1:5,1:3)x =1 2 3 4
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ans(:,:,2) =999And to sum over “p
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An Application of RGB ImagesTo see
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You can see that over the 8 time st
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name>> staff(2,1,2).name(5:9)ans =B
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q =7 8 96 1 25 4 3>> save saved_dat
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fid = fopen(’asc.dat’);The fope
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display and the enclosed area is th
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MarkerEdgeColor = auto(and so on)In
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text(-.7,f(-.7),’f(X)’)But we h
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plt(x,f(x/2),’--’)Let us try ca
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Example: findobjThe findobj command
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3. Add the property you want to set
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is numbered from top to bottom. The
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axis ijUsually images like this do
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32.2 Tick Marks and Labelsmatlab’
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clfaxes(’pos’,[.2 .1 .7 .4])x =
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property to [0 top] in the call to
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object’s HorizontalAlignment and
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the required symbols. The m-file ti
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1. Use graphical elements that serv
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uicontrol(’Callback’,’ezplot(
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uicontrol(’Pos’,[110 280 60 19]
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’String’,’0.5’,’Style’,
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function exradio(action)if nargin =
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fail. One place to put variables th
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34.7 Fast DrawingFor fast drawing o
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controlled by guide and which are a
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InvertHardcopy: [ {on} | off ]Paper
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Another option is to use an image f
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yur is the y coordinate of the uppe
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\end{center}\caption{This is the fi
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x 294x1 ...y 294x1 ...z 294x1 ...Gr
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diagram. Such a triangular grid can
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xt = x([1 9 10 1]);yt = y([1 9 10 1
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x = [0 0 .5 0.5 .5 1 11 .5 .5 .5];y
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fac2 = [1 2 61 6 31 4 61 6 5];The r
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t = linspace(0,2*pi,20);x = cos(t);
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N = 20;dt = 2*pi/N;t = 0:dt:(N-1)*d
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colouring of the sphere itself. To
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material dullThe default is materia
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time taken by this routine to calcu
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first row of a by taking the column
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38.3 Debuggingmatlab has a suite of
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10: y = linspace(ycentre - L,ycentr
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We change variables:p ′ = C + Bx.
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Exercise 6 (Page 59)You can generat
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33 ! 36 $ 39 ’ 42 * 45 - 48 034 "
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R = 1; N = 200;[x,y] = meshgrid(lin
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(The plot might take a few seconds
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% Reproduce the layers at the diffe
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