Basics of MATLAB and Beyond

More documents

Recommendations

Info

$Algoritmos de para calcular la dimensiÃ³n fractal de seÃ±ales 1D La ...$

do very fast operations on the appropriate matrices. matlab’s suite ofutility matrices can also come in handy when vectorising code (see helpelmat).We now look at a slightly more complicated example. Suppose youwant to generate a matrix a ij with elements:⎧⎪⎨a ij =⎪⎩j∑kk=ij ≥ i0 otherwiseThe 5 × 5 version of a is⎛1 1+2 1+2+3 1+2+3+4 1+2+3+4+50 2 2+3 2+3+4 2+3+4+5a =⎜ 0 0 3 3+4 3+4+5⎝ 0 0 0 4 4+50 0 0 0 5⎛1 3 6 10 150 2 5 9 14=⎜ 0 0 3 7 12⎝ 0 0 0 4 90 0 0 0 5⎞⎟⎠⎞⎟⎠A simple loop implementation of this calculation would resemble thefollowing:N = 200;a = zeros(N,N);for i = 1:Nfor j = 1:Nif j>=ia(i,j) = sum(i:j);endendendLet us time this code (call it forloop2):>>t0 = clock;forloop2;etime(clock,t0)ans =2.9241There are may different ways that we could vectorise this calculation,depending on our ingenuity. For now, we note that we can generate thec○ 2000 by CRC Press LLC
first row of a by taking the columnar sum of the triangular matrix s:a(1,:) = sum(s)⎛⎞1 1 1 1 1 ···0 2 2 2 20 0 3 3 3= sum0 0 0 4 4⎜⎝0 0 0 0 5 ⎟⎠....We can generate the second row of a by taking the same columnar sumbut leaving out the first row of s:a(2,:) = sum(s(2:end,:))⎛⎞0 2 2 2 2 ···0 0 3 3 3= sum0 0 0 4 4⎜⎝0 0 0 0 5 ⎟⎠....In general, then, we can generate the ith row of a by taking the columnarsum of s leaving out its first i − 1 rows: a(i,:) = sum(s(i:end,:)).Our final code will consist of putting this statement inside a for loop(this will be a good use of a for loop—see the first paragraph in thissection). Before we do that, though, we still need to generate the utilitymatrix s; here we can use matrix multiplication. The matrix we wantcan be obtained by taking the upper triangular part of the product of acolumn vector and a row vector:⎛⎞ ⎡⎛⎞⎤1 1 1 1 1 ···10 2 2 2 220 0 3 3 330 0 0 4 4= triu4· ( 1 1 1 1 1··· )⎜⎝0 0 0 0 5 ⎟ ⎢⎜⎠ ⎣⎝5 ⎟⎥⎠⎦.... .So here we have the final code to generate the a matrix (for N = 200):N = 200;s = triu((1:N)’*ones(1,N));a = zeros(N,N);for i = 1:N-1a(i,:) = sum(s(i:end,:));enda(N,:) = s(N,:);..c○ 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 36 and 37:
s = 100*spiral(3)s =700 800 900600
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
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 and 106:
[x,y] = meshgrid(1:5,1:3)x =1 2 3 4
Page 107 and 108:
ans(:,:,2) =999And to sum over “p
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
Page 157 and 158: 34.7 Fast DrawingFor fast drawing o
Page 159 and 160: controlled by guide and which are a
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
Page 173 and 174: xt = x([1 9 10 1]);yt = y([1 9 10 1
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 and 186: material dullThe default is materia
Page 187: time taken by this routine to calcu
Page 191 and 192: 38.3 Debuggingmatlab has a suite of
Page 193 and 194: 10: y = linspace(ycentre - L,ycentr
Page 195 and 196: We change variables:p ′ = C + Bx.
Page 197 and 198: Exercise 6 (Page 59)You can generat
Page 199 and 200: 33 ! 36 $ 39 ’ 42 * 45 - 48 034 "
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
show all

Basics of MATLAB and Beyond

Create successful ePaper yourself

Delete template?

Save as template?