Basics of MATLAB and Beyond

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29.2 Operations with Multidimensional ArraysMany matrix operators work with multidimensional arrays. For example,the columnar sum of our 3 × 3 × 2 matrix, a, is>> aa(:,:,1) =1 2 34 5 67 8 9a(:,:,2) =3 3 33 3 33 3 3>> sum(a)ans(:,:,1) =12 15 18ans(:,:,2) =9 9 9If you look carefully, you will see that the result of the sum is a 1 × 3 × 2matrix:>> size(sum(a))ans =1 3 2This is not the same as a 3 × 2 matrix. If you want the result to bea3× 2 matrix, you can use the squeeze function, which gets rid ofsingleton dimensions:>> squeeze(sum(a))ans =12 915 918 9matlab does not do an automatic squeeze whenever the result has singletondimensions because there are times when you need the singletondimension to add more data.If you want to sum over other dimensions than the rows, you give asecond parameter to the sum function specifying the dimension you wantto sum over. For example, to sum over columns:>> sum(a,2)ans(:,:,1) =61524c○ 2000 by CRC Press LLC
ans(:,:,2) =999And to sum over “pages”:>> sum(a,3)ans =4 5 67 8 910 11 12Note that sum(a) is equal to sum(a,1). The sum over “pages” gives a3 × 3 matrix, which is the same as a 3 × 3 × 1 matrix.The sum function and other functions that operate on vectors, likemean, diff, max, and so on, work as you might expect them to for multidimensionalarrays. By default they usually operate on the first nonsingletondimension of the array. Many functions that operate on twodimensionalmatrices do not have such straightforward multidimensionalextensions. For example, if we try to take the transpose of our matrix:>> a’??? Error using = = > ’Transpose on ND array is not defined.The transpose operation (exchanging rows and columns) makes no sensehere because it is insufficiently specified. (If you want to rearrange amultidimensional array’s dimensional ordering, use the permute function;in our example, try permute(a,[2 1 3])). Another example isthe eigenvalue operator eig, which has no mathematical meaning formultidimensional arrays. In fact, none of the functions that appear ifyou type help matfun has a reasonable meaning for multidimensionalmatrices. Nor do the matrix operators *, ^, \ or /.29.3 RGB ImagesIntroduction to RGB ImagesRGB images in matlab are M ×N ×3 matrices consisting of red, green,and blue intensity maps. When such a three-dimensional matrix is usedas an input to the image command, matlab adds the red, green, andblue intensities to give the right colours on the screen. To illustrate theidea, our first example reproduces three overlapped discs of red, green,and blue light to give yellow, cyan, magenta, and white overlaps. Wegenerate matrices of (x, y) points covering the plane from −2 to2:[x,y] = meshgrid(linspace(-2,2,200));c○ 2000 by CRC Press LLC
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BASICS OFMATLAB®and Beyondc○ 200
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Library of Congress Cataloging-in-P
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typing pwd (print working directory
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ContentsIBasics of MATLAB1 First St
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20 Time-Frequency Analysis21 Line A
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39Answers to Exercises (Part I)40 A
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Set → Getting Started with MATLAB
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1.5 The Colon OperatorTo generate a
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matlab will recall the last command
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a = zeros(2,3)a =0 0 00 0 0>> b = o
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[a a(a)]ans =1 2 3 1 4 74 5 6 2 5 8
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a + bans =11 3344 6677 993.8 Transp
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4.2 Adding PlotsWhen you issue a pl
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x = [[1 2 3 4]’ [2 3 4 5]’ [3 4
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4.7 AxesSo far we have allowed matl
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v =1122>> v*uans =1 2 0 11 2 0 12 4
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max returns a vector containing the
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s = 100*spiral(3)s =700 800 900600
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We can plot the surface z as a func
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The contour function plots the cont
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m = gray(8);colormap(m)imagesc(1:10
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hold onplot3(x(ind),y(ind),z(ind),
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z = 5*ones(3,3)z =5 5 55 5 55 5 5>>
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contour(x,y,z,30);You may have noti
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variables that are local to themsel
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SwitchThe basic form of a switch st
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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
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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
Page 86 and 87: str =you’re the one>> str = ’
Page 88 and 89: strrep(str,’go’,’am’)ans =I
Page 90 and 91: ans =3.14159e+100Some additional te
Page 92 and 93: eval(str)v =1 2 3 4 5The eval(str)
Page 94 and 95: Inline objects, like every other ma
Page 96 and 97: a(1,1) = {[1 2 3]}a =[1x3double]or>
Page 98 and 99: t = {’help’ spiral(3) ; eye(2)
Page 101 and 102: meteo.Temperatureans =24ans =19.000
Page 103 and 104: 3 >> a = [1 2 ;4 5 6;7 8 9]a =1 2 3
Page 105: [x,y] = meshgrid(1:5,1:3)x =1 2 3 4
Page 109 and 110: An Application of RGB ImagesTo see
Page 111 and 112: You can see that over the 8 time st
Page 113 and 114: name>> staff(2,1,2).name(5:9)ans =B
Page 115 and 116: q =7 8 96 1 25 4 3>> save saved_dat
Page 117 and 118: fid = fopen(’asc.dat’);The fope
Page 119 and 120: display and the enclosed area is th
Page 121 and 122: MarkerEdgeColor = auto(and so on)In
Page 123 and 124: text(-.7,f(-.7),’f(X)’)But we h
Page 125 and 126: plt(x,f(x/2),’--’)Let us try ca
Page 127 and 128: Example: findobjThe findobj command
Page 129 and 130: 3. Add the property you want to set
Page 131 and 132: is numbered from top to bottom. The
Page 133 and 134: axis ijUsually images like this do
Page 135 and 136: 32.2 Tick Marks and Labelsmatlab’
Page 137 and 138: clfaxes(’pos’,[.2 .1 .7 .4])x =
Page 139 and 140: property to [0 top] in the call to
Page 141 and 142: object’s HorizontalAlignment and
Page 143 and 144: the required symbols. The m-file ti
Page 145 and 146: 1. Use graphical elements that serv
Page 147 and 148: uicontrol(’Callback’,’ezplot(
Page 149 and 150: uicontrol(’Pos’,[110 280 60 19]
Page 151 and 152: ’String’,’0.5’,’Style’,
Page 153 and 154: function exradio(action)if nargin =
Page 155 and 156: 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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