Basics of MATLAB and Beyond

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To get the following result Iused trial and error to get the right valuesfor the surface reflectance properties:clfh = surf(x,y,z);set(h,’facecolor’,[.5 .5 .5],...’edgecol’,’none’)hl = light(’pos’,[1000,0,0]);axis equalaxis offview(-20,0)set(h,’specularstrength’,0)set(h,’ambientstrength’,1)set(h,’diffusestrength’,10)set(h,’backfacelighting’,’unlit’)38 MATLAB Programming38.1 Vectorising CodeIonce heard Cleve Moler say, “The for loop gets a bad rap.” Oneof the clearest ways to see the truth of this statement will be in thissection on speeding up matlab routines by vectorising code. We will beeliminating for loops and replacing them with operations on vectors ormatrices. Yet, do not think that you must then eliminate all for loopsfrom your matlab code. When for loops are used appropriately theyare still very fast, efficient, and convenient. With this proviso, let uslook at an example.matlab’s diff function takes the difference between successive pairsof elements in a vector, and writes them to another vector. Suppose youwant to carry out a similar operation, except now you want to computethe sum of successive pairs instead of the difference. In mathematicalnotation, you would write the formula:b i = a i + a i+1 , i =1, 2,...N − 1.where a is the input vector of length N, and b is the output vector ofpairwise sums. The following piece of matlab code would do the job:N = length(a);b = zeros(1,N - 1);for i = 1:N-1b(i) = a(i) + a(i + 1);endThis code, or at least the line inside the for loop, has the advantageof resembling the mathematical notation quite closely. We measure thec○ 2000 by CRC Press LLC
time taken by this routine to calculate the pairwise sum of a 100,000-element vector (the code is saved in the m-file forloop1 and we useetime to measure the execution time):>>t0 = clock;forloop1;etime(clock,t0)ans =5.3545A little over five seconds. Now we try to do it another way. Here isa diagram of what we want to do, with the elements we want to sumwritten out as indices of the respective vectors:(a1 2 3 4 ... N − 2 N − 1)(+ a(= b2 3 4 5 ... N − 1 N1 2 3 4 ... N − 2 N − 1))Writing the operation in this way allows us to see how we can use vectorsof indices to do the summation. The top line of the sum can be writtenin matlab notation as a(1:N-1), and the second line can be writtenas a(2:N). The pairwise sum vector b therefore can be calculated inmatlab with the following code:b = a(1:end-1) + a(2:end);We have used the special index end to refer to the final element of thevector. This time there is no advantage in pre-allocating the b vectoras we did before the for loop above. With regular use, the vectorisedmatlab representation will seem to resemble the mathematical representationjust as closely as the for loop. The time taken by this codeist0 = clock;b = a(1:end-1) + a(2:end);etime(clock,t0)ans =2.2400The vectorised version runs a little more than twice as fast as thefor loop implementation.Looping over matrix or vector subscripts can often be replacedby such matrix operations. Appropriate matrices can be generatedusing subscripting, as here, or by rearranging the input matrices usingreshape, the transpose operator, or other matrix manipulations. matlab’scolumnar operations sum, diff, prod, etc. can then be used toc○ 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
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9.1 MATLAB FormatTo save all the va
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11 StartupEach time you start matla
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Where p i is the population for yea
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NaNs by leaving them off the plot.
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clfpolar(t,gdb)In this case you mus
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-0.5000-0.3750-0.2500-0.125000.1250
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the periodograms of the blocks, and
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plot(y(1:1000))axis([0 1000 -5 5])z
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comet(x,y)(You can get a three-dime
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By clicking within the panner box a
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x = linspace(-1,1,8192);Fs = 1000;y
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23.3 Graphical Object Hierarchymatl
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Now we need to get the handles of a
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Beyond the BasicsPreludeThis part o
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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
Page 135 and 136: 32.2 Tick Marks and Labelsmatlab’
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Page 145 and 146: 1. Use graphical elements that serv
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Page 149 and 150: uicontrol(’Pos’,[110 280 60 19]
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Page 153 and 154: function exradio(action)if nargin =
Page 155 and 156: fail. One place to put variables th
Page 157 and 158: 34.7 Fast DrawingFor fast drawing o
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Page 161 and 162: InvertHardcopy: [ {on} | off ]Paper
Page 163 and 164: Another option is to use an image f
Page 165 and 166: yur is the y coordinate of the uppe
Page 167 and 168: \end{center}\caption{This is the fi
Page 169 and 170: x 294x1 ...y 294x1 ...z 294x1 ...Gr
Page 171 and 172: diagram. Such a triangular grid can
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Page 175 and 176: x = [0 0 .5 0.5 .5 1 11 .5 .5 .5];y
Page 177 and 178: fac2 = [1 2 61 6 31 4 61 6 5];The r
Page 179 and 180: t = linspace(0,2*pi,20);x = cos(t);
Page 181 and 182: N = 20;dt = 2*pi/N;t = 0:dt:(N-1)*d
Page 183 and 184: colouring of the sphere itself. To
Page 185: material dullThe default is materia
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Page 191 and 192: 38.3 Debuggingmatlab has a suite of
Page 193 and 194: 10: y = linspace(ycentre - L,ycentr
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Page 197 and 198: Exercise 6 (Page 59)You can generat
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Page 201 and 202: R = 1; N = 200;[x,y] = meshgrid(lin
Page 203 and 204: (The plot might take a few seconds
Page 205: % Reproduce the layers at the diffe
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