zt

Transcription

1 Prentice-Hall Matlab 6 Mastering Matlab 6 A Comprehensive Tutorial and Reference [ ] D. Hanselman, B.Littlefield Pearson Education

2 Matlab Matlab Matlab Matlab 6 Matlab Matlab Matlab Mastering Matlab 6 A Comprehensive Tutorial and Reference. Copyright 2001 by Prentice Hall,Inc. All rights reserved. No part of the book shall be reproduced or transmitted in any form or by any means,electronic or mechanical,including photocopying,recording or by any information storage retrieval system, without permission from the Publisher.This edition is authorized for sale only in the People s Republic of China(excluding the Special Administrative Region of Hong Kong and Macau). Pearson Education Matlab 6 D. Hanselman, B. Littlefield / ~4000 ISBN /TP

3 Matlab Matlab Matlab Matlab Matlab Matlab M M

4 II Matlab NaNs For...136

5 III 10.2 While If-Else-End Switch-Case Try -Catch M M Matlab ToolBox Feval M M I/O

6 IV Matlab Hermite

7 V IVP ODE BVP PDE plot

8 VI Matlab PostScript get set

9 VII M GUI GUI GUI M GUIDE M Matlab Matlab Matlab Matlab C FORTRAN...454

10 VIII Matlab C FORTRAN Matlab MAT Java Matlab JAVA Java Java Java Java Java Windows ActiveX / Matlab

11 IX A B C D E F G H I J K L Uicontextmenu Uimenu M Uicontrol

12 Matlab Matlab Matlab Matlab Matlab Matlab Matlab Matlab Matlab Toolboxes (Blocksets) Libraries 50 Matlab C Fortran Java PC Matlab Matlab Matlab 6 Matlab 6 Matlab 5.3 mm@eece.maine.edu edu/mm

13 1 1.1 Matlab Matlab Matlab Matlab Matlab GUI Matlab Matlab Matlab Matlab 1.2 Matlab 6 Matlab 6 Matlab 5 Matlab 5 Matlab 6 Command Figure GUI Matlab Matlab 6 Matlab, Matlab Matlab 5 PC UNIX Matlab 6 Matlab 5 PC Matlab 6 Matlab 6 n=100 flop Figure (GUI)

14 2 Matlab 6 Matlab 6 Matlab Matlab 6 Matlab 1.3 Matlab CD CD CD 50M 4500 PDF Matlab CD Matlab / 250M PDF CD 150M HTML Matlab Matlab 6 Matlab Matlab M M Matlab 1 Matlab 2 Matlab 3 Matlab Matlab Matlab Matlab Matlab Matlab Matlab 6 Matlab Matlab Matlab Matlab Matlab Matlab x Matlab edu/mm Matlab.m mm@eece.maine.edu

15 2 Matlab Matlab Matlab Command Matlab >> Command Matlab 2.1 Matlab Mary Mary 4+6+2=12 4*25+6*52+2*99=610 Matlab >> >> 4*25+6*52+2* Matlab Matlab ans answer Matlab >> erasers = 4 erasers = 4 >> pads = 6 pads = 6 >> tape = 2;

16 4 Matlab 6 >> items = erasers + pads + tape items = 12 >> cost = erasers*25 + pads*52 + tape*99 cost = 610 Matlab erasers pads tape Matlab tape Matlab items cost ans Matlab Matlab >> average_cost = cost/items average_cost = average cost Matlab Matlab average_cost Matlab * 3.14 * 6 / \ / 7 or 7 \ ^ 2 ^ Matlab Command Matlab Matlab tape tape Matlab

17 2 5 >> tape tape = 2 Matlab who Matlab >> who Your variables are: ans cost items tape average_cost erasers pads Matlab Matlab Matlab Matlab Matlab Escape EMACS Matlab EMACS Control-U 2.3 Matlab Matlab 31 Howaboutthisvariablename Cost cost CoSt COST how_about_this_variable_name X51483 Matlab a_b_c_d_e Matlab Matlab

18 6 Matlab 6 For end if while function return elseif case otherwise switch continue else try catch global persistent break Matlab Matlab ans beep pi eps inf NaN( )nan i ( )j nargin nargout realmin realmax bitmax varargin vararout /0 0/ tape >> erasers = 4; >> pads = 6; >> tape =2; >> items = erasers + pads + tape items = 12 >>erasers = 6 erasers = 6 >>items items = 12 Mary

19 items Matlab erasers Matlab Matlab Matlab clear >> pi >> pi = 1.23e-4 pi = >> clear pi >> pi pi e-4 clear pi 2.4 Matlab >> erasers erasers = 6 >> items = erasers + pads + tape; >> cost = erasers*25 + pads*52 + tape*99; >> average_cost = cost/items averate_cost = Mary 6 4 items cost Matlab

20 8 Matlab 6 >> tape = 2 % number of rolls of tape purchased tape 2 Matlab >> erasers = 6, pads = 6; tape = 2 erasers = 6 tape = 2 Matlab Matlab >> average_cost = cost/items % command as done earlier average_cost = >>average_cost =cost/ % command with valid continuation items average_cost = >>average_cost = cost % command with valid continuation /items average_cost = >>average_cost = cost/it % command with INvalid continuation ems??? age_cost=cost/items Missing operator,comma,or semi-colon. >> % Comments cannot be continued >> either??? Undefined function or variable 'either'. Matlab Control-C Matlab Ctrl C

21 Matlab Matlab >> c1 = 1-2i % the appended i signifies the imaginary part c1 = i >> c1 = 1-2j % j also works c1 = i; >> c2=3*(2-sqrt(-1)*3) c2 = i >> c3 = sqrt(-2) c3 = i >> c4 = 6+sin(.5)*i c4 = i >>c5 = 6+sin(.5)*j c5 = i Matlab i=j= 1 i j sin(.5)i sin(.5)j Matlab i j Matlab >> c6 = (c1+c2)/c3 % from the above data c6 = i >> c6r = real(c6) c6r = >> c6i = imag(c6) c6i = >>check_it_out = i^2 % sqrt(-1) squared must be 1! check_it_out = -1 Matlab 0 real imag

22 10 Matlab 6 M θ =Me j = a + bj M a + bj 2 2 M= a + b =tan -1 (b /a ) a =M cos( ) b= M sin( ) Matlab real imag abs angle >> c1 c1 = i >>mag_c1 = abs(c1) % magnitude mag_c1 = >> angle_c1 = angle(c1) % angle in radians angle_c1 = >> deg_c1 = angle_c1*180/pi % angle in degrees deg_c1 = >> real_c1 = real(c1) % real part real_c1 = 1 >> imag_c1 = imag(c1) % imaginary part imag_c1 = -2 Matlab abs Matlab angle Matlab 2.6 Matlab Matlab >> format long % tell MATLAB to display more precision >> realmax e+308 Matlab

23 2 11 >> realmin e-308 >> eps e-016 Matlab >> e-017 >> >> Matlab Matlab >> sin(0) 0 >> sin(pi) e sin( ) 0 eps Matlab >> bitmax

24 12 Matlab e Matlab >> x = sqrt(2)/2 x = >> y = asin(x) y = >> y_deg = y*180/pi y_deg = / 2 Matlab >> y = sqrt(3^2 + 4^2) % show right triangle relationship y = 5 >> y = rem(23,4) % remainder function, 23/4 has a remainder of 3 y = 3 >> x = 2.6, y1 = fix(x), y2 = floor(x),y3 = ceil(x), y4 = round(x) x = y1 = 2 y2 = 2 y3 = 3 y4 = 3 acos acosh acot acoth

25 2 13 acsc acsch asec asech asin asinh atan atan2 atanh cos cosh cot coth csc csch sec sech sin sinh tan tanh ^ exp ln log lg log10 10 lb log2 2 pow2 2 sqrt nextpow2 P 2 P N abs angle conj

26 14 Matlab 6 imag real unwrap isreal true cplxpair complex fix 0 floor ceil round mod rem sign cart2sph cartpol pol2cart sph2cart factor isprime true primes gcd lcm rat rats perms nchoosek N K

27 2 15 airy Airy besselj bessely besselh besseli besselk beta beta betainc beta betaln beta ellipj Jacobi ellipke erf erfc erfcx erfinv expint gamma gamma gammainc gamma gammaln gamma legendre Legendre cross dot

28 3 Matlab Matlab Matlab Matlab Matlab Matlab Matlab Matlab Matlab Matlab View 3.1 Matlab Matlab 1 Command 2 Command History 3 Launch Pad (4)Current Directory 5 Help 6 Workspace 7 Array Editor 8 Editor/Debugger / Command Command History Launch Pad Current Directory Help Workspace Array Editor Editor/Debugger Matlab Command Matlab Matlab Matlab Matlab 3.2 Matlab Matlab Command Command Command Matlab

29 3 Matlab 17 Matlab Workspace Command who >> who Your variables are: angle_c1 c4 cost pads ans c5 deg_c1 real_c1 average_cost c6 erasers tape c1 c6i imag_c1 c2 c6r items c3 check_it_out mag_c1 Matlab whos >> whos Name Size Bytes Class angle_c double array ans double array average_cost double array c double array(complex) c double array(complex) c double array(complex) c double array(complex) c double array(complex) c double array(complex) c6i double array c6r double array check_it_out double array cost double array deg_c double array erasers double array imag_c double array items double array mag_c double array pads double array real_c double array tape double array Grand total is 21 elements using 216 bytes Matlab Workspace Matlab workspace Matlab View Workspace Workspace clear Matlab >> clear real_c1 imag_c1 c*

30 18 Matlab 6 >> who Your variables are: angle_c1 deg_c1 mag_c1 ans erasers pads average_cost items tape real_c1 imag_c1 c help helpwin clear >> help clear CLEAR Clear variables and functions from memory. CLEAR removes all variables from the workspace. CLEAR VARIABLES does the same thing. CLEAR GLOBAL removes all global variables. CLEAR FUNCTIONS removes all compiled M- and MEX-functions. CLEAR ALL removes all variables, globals, functions, and MEX links. CLEAR ALL at the command prompt also removes the Java packages import list. CLEAR IMPORT removes the Java packages import list at the command prompt. It cannot be used in a function. CLEAR CLASSES is the same as CLEAR ALL except that class definitions are also cleared. If any objects exist outside the workspace(say in userdata or persistent in a locked m-file) a warning will be issued and the class definition will not be cleared. CLEAR CLASSES must be used if the number or names of fields in a class are changed. CLEAR VAR1 VAR2... clears the variables specified. The wild card character'*' can be used to clear variables that match a pattern.for instance, CLEAR X* clears all the variables in the current workspace that start with X. If X is global, CLEAR X removes X from the current workspace but leaves it accessible to any functions declaring it global. CLEAR GLOBAL X completely removes the global variable X. CLEAR FUN clears the function specified. If FUN has been locked by MLOCK it will remain in memory. Use a partial path (see PARTIALPATH) to distiguish between different overloaded versions of FUN. For instance, 'clear inline/display' clears only the INLINE method for DISPLAY,leaving any other implementations in memory. CLEAR ALL, CLEAR FUN, or CLEAR FUNCTIONS also have the side effect of removing debugging breakpoints and reinitializing persistent variables since the breakpoints for a function and persistent variables are cleared whenever the m-file changes or is cleared. Use the functional form of CLEAR, such as CLEAR('name'), when the variable name or function name is stored in a string.see also WHO, WHOS, MLOCK, MUNLOCK, PERSISTENT. clear Matlab

31 3 Matlab M Matlab Matlab clear Matlab Matlab Matlab pack Matlab Matlab Matlab pack 3.4 Matlab Matlab 4 Matlab Command File Preference format pi format Matlab pi format short format long format short e e format long e e format short g format long g format hex fb54442d18 16 format bank format format rat 355/113

32 20 Matlab 6 Matlab pi format debug Stucture address =fba34a8 m=1 n=1 pr=8bc8148 pi= short g Matlab 3.5 Matlab Command History Matlab Matlab diary Command Diary >> help diary DIARY Save text of MATLAB session. DIARY filename causes a copy of all subsequent command window input and most of the resulting command window output to be appended to the named file. If no file is specified, the file 'diary' is used. DIARY OFF suspends it. DIARY ON turns it back on. DIARY,by itself,toggles the diary state. 3.6 Matlab computer >> computer PCWIN Windows 98 PC version Matlab >> version (R12)

33 3 Matlab 21 ver Matlab >> ver MATLAB Version (R11) on PCWIN MATLAB license Number: MATLAB Toolbox Version 5.3 (R11) 15-Jan-1999 Mastering MATLAB Toolbox Version Jun-1999 Symbolic Math Toolbox Version 2.1 (R11) 11-Sep-1998 Signal Processing Toolbox Version 4.2 (R11) 10-Jul-1998 Optimization Toolbox Version 2.0 (R11) 09-Oct-1998 Control System Toolbox Version 4.2 (R11) 15-Jul-1998 Simulink Version 3.0 (R11) 01-Sep-1998 license hostid Matlab >> hostid '51483' >> license Matlab 3.7 Matlab Matlab search path Matlab Matlab Matlab MatlabPath Matlab cow >>cow Matlab 1. cow Matlab 2. cow 3. cow.m 4. Matlab cow.m 5. cow Matlab Matlab cow Matlab Matlab cow.m Matlab Matlab

34 22 Matlab Matlab Matlab M 4 11 Matlab Matlab Matlab Matlab 11 Matlab Matlab Matlab File Set Path Matlab Matlab Matlab Matlab Command Matlab Matlab matlabpath Command path addpath rmpath Matlab

35 4 M Matlab Command Matlab Matlab Matlab Matlab M Matlab M.m example1.m 4.1 M M Matlab File New M-file Matlab M % script M-file example1.m erasers = 4; % number of each item pads = 6; tape = 2; items = erasers + pads + tape cost = erasers*25 + pads*52 + tape*99 average_cost = cost/items Run F5 File Save M example.m Matlab.m >> example1 items = 12 cost = 610 average_cost = Matlab example1

36 24 Matlab 6 Matlab example1 Matlab M example1 Matlab Matlab example1.m Command M Matlab M Matlab M echo on Matlab Command echo on echo off echo M example1.m M erasers pads tape F5 M Matlab example1.m Matlab M beep disp(variablename) echo input keyboard pause or pause(n) waitforbuttonpress Command M return M n Matlab Command Matlab disp >> items items = 12 >> disp(items) 12 input example.m

37 4 M 25 % script M-file example1.m erasers = 4; % Number of each item pads = 6; tape = input('enter the number of rolls of tape purchased>'); items = erasers + pads + tape cost = erasers*25 + pads*52 + tape*99 average_cost = cost/items M >> example1 Enter the number of rolls of tape purchased > 3 items = 13 cost = 709 average_cost = input Matlab >> example1 Enter the number of rolls of tape purchased > round(sqrt(13))-1 items = 13 cost = 709 average_cost = round(sqrt(13)) 1 echo % script M-file example1.m echo on erasers = 4; % Number of each item pads = 6; tape = input('enter the number of rolls of tape purchased>'); items = erasers + pads + tape cost = erasers*25 + pads*52 + tape*99 average_cost = cost/items echo off >> example1 erasers = 4; % Number of each item pads = 6;

38 26 Matlab 6 input('enter the number of rolls of tape purchased >'); Enter the number of rolls of tape purchased > 2 items= erasers + pads + tape items = 12 cost = erasers*25 + pads*52 + tape*99 cost = 610 average_cost = cost/items average_cost = echo off echo echo 4.2 Matlab M matlabrc.m startup.m matlabrc.m Matlab M Figure Matlab matlabrc.m pathdef.m Matlab pathdef.m matlabrc.m Matlab M startup.m M startup.m Matlab startup.m addpath path Matlab format compact graymon startup.m colordef startup.m M quit startup.m Matlab toolbox/local startup.m Matlab Matlab File Exit Matlab Matlab exit quit Matlab Matlab finish.m M Matlab finish.m quit cancel % FINISH Confirm Desire for Quitting MATLAB question = 'Are You Sure You Want To Quit? ';

39 4 M 27 button = questdlg(question, 'Exit Request', 'Yes', 'No', 'No'); switch button case 'No' quit cancel; % how to cancel quitting! end % 'Yes' lets script and MATLAB end.

40 5 Matlab 5.1 y=sin(x) 0 x sin(x) x 0.1 sin(x) x=0 0.1, x x y X y x y x y x x y x 1 x y 5 y 5 x n x n Matlab >> x = [0.1*pi.2*pi.3*pi.4*pi.5*pi.6*pi.7*pi.8*pi.9*pi pi] x = Columns 1 through Columns 8 through >> y = sin(x) y = Columns 1 through Columns 8 through Matlab x

41 5 29 x Matlab x y Matlab [1 2i i] 5 [(1 2i) i] [1 2i i] x Matlab x Matlab x(1) x x(2) x >> x(3) % The third elemnet of x >> y(5) % The fifth element of y Matlab >> x(1:5) x 1 5 1:5 1 5 >> x(7:end) x 7 end x >> y(3:-1:1) : 1:1 3 1 >> x(2:2:7)

42 30 Matlab x :2: >> y([ ]) [ ] y [ ] y >> y([ ]) Matlab 1 >> y(3.2) Warning:Subscript indices must be integer values. Ans = >> y(3.7) Warning:Subscript indices must be integer values. Ans = >> y(11.6) Warning:Subscript indices must be integer values.??? Index exceeds matrix dimensions. Matlab Matlab y y 12 Matlab 5.3 x x x

43 5 31 >> x = (0:0.1:1)*pi x = columns 1 through columns 8 through >> x = linspace(0,pi,11) x = columns 1 through columns 8 through (0:0.1:1) x Matlab linspace x linspace(first_value,last_value,number_of_values) Matlab linspace Matlab logspace >> logspace(0,2,11) columns 1 through columns 8 through logspace(first_exponent,last_exponent,number_of_values) logspace linspace logspace >> a = [1:7] a = >> b = [linspace(1,7,5)] b =

44 32 Matlab 6 >> a = (1:7)'%change row to column a = >> a = 1:5, b =1:2:9 a = b = >> c = [b a] c = c b a b a >> d = [a(1:2:5) 1 0 1] d = d d a Matlab

45 5 33 x=[2 2*pi sqrt(2) 2 3j] x=first:last x=first:increment:last x=linspace(first,last,n) x=logspace(first,last,n) x x first 1 last last x=[first:last] Matlab x first increment last last x first last n x 10 first 10 last n 5.4 >> c = [1;2;3;4;5] c = start:increment:end linspace logspace Matlab ' >> a = 1:5 a = >> b = a' b = 1 2 3

46 34 Matlab a b >> w = b' w = Matlab '. ' >> c = a. ' c = ' ' >> d = a + i*a d = Columns 1 through i i i i columns i a i >> e = d' e = i i i i i e d >> f = d.' f = i i i i = 1

47 i i f d >> g = [ ; ] g = g Matlab 5 >> g = [ ] g = Matlab >> h = [ ]??? All rows in the bracketed expression must have the same number of columns. Matlab 5.5 x >> g g 2 >> 2*g - 1

48 36 Matlab g 2 1 >> 2*g/ g >> g % recall previous array g = >> h [ ; ; ] % create new array h = >> g + h % add h to g on an element-by-element basis >> ans h % subtract h from the previous answer to get g back >> 2*g h % multiplies g by 2 and subtracts h from the result

49 >> 2*(g h) % use parenthese to change order of operation >> g.*h * g h Matlab >> g*h??? Error using ==> * Inner matrix dimensions must agree. >> g./h >> h.\g Matlab Matlab

50 38 Matlab 6 >> 1./g >> f=[ ; ; ] % create numerator by scalar expansion f = >> f./g >> f./h Matlab >> g/h Warning:Rank deficient, rank = 1 tol =5.3291e >>h/g Warning:Rank deficient,rank = 2 tol = e g h Matlab ^.^

51 5 39 >> g,h % recalls the arrays used earlier g = h = >> g.^2 Ans = g >> g^2??? Error using ==> ^ Matrix must be square. >> g.^ g >> l./g >> 2.^g g ij g ij g

52 40 Matlab 6 >> g.^h g ij h ij g ij h ij g h h 1 >> g.^(h-1) A = [a 1 a 2 a n ] B = [b 1 b 2 b n ] c = < > A+c = [a 1 +c a 2 +c a n +c] A-c = [a 1 -c a 2 c a n c] A*c = [a 1 *c a 2 *c a n *c] A/c =c\a = [a 1 /c a 2 /c a n /c] A+B = [a 1 +b 1 a 2 +b 2 a n +b n ] A.*B = [a 1 *b 1 a 2 *b 2 a n *b n ] A./B = [a 1 /b 1 a 2 /b 2 a n /b n ] B.\A = [a 1 /b 1 a 2 /b 2 a n /b n ] A.^c = [a 1^c a 2^c a n^c] c.^a = [c^ a 1 c^a 2 c^a n ] A.^B = [a 1^ b 1 a 2^ b 2 a n^ b n ] 5.7 Matlab 1 0

53 5 41 >> ones(3) >> zeros(2,5) >>size(g) 3 4 >> ones(size(g)) ones(n) zeros(n) Matlab n n 1 0 ones(r,c) zeros(r,c) Matlab r c ones zeros size >> eye(4) >> eye(2,4) >> eye(4,2) eye 1 0 A(i,i) 0 i=1:min(r,c) min(r,c) A >> rand(3)

54 42 Matlab >> rand(1,5) >> b = eye(3) b = >> rand(size(b)) rand 0 1 >> randn(2) >> randn(2,5) randn 0 >> a = 1:4 % start with a simple vector a = >> diag(a) % place elements on the main diagonal >> diag(a,1) % place elements 1 place up from diagonal >> diag(a,-2) % place elements 2 places down from diagonal

55 diag >> d = pi; % choose pi for this example >> d*ones(3,4) % slowest method (scalar-array multiplication) >> d+zeros(3,4) % slower method (scalar-array addition) >> d(ones(3,4)) % fast method (array addressing) >> repmat(d,3,4) % fastest method (optimum array addressing) d(ones(r,c)) r c 1 d 1 repmat(d,r,c) repmat d D(r*c) = d; %a row vector whose (r*c)-th element is d D(:)= d; %scalar expansion to fill all elements of D with d D = reshape(d,r,c); %reshape the vector into the desired r-by-c shape

56 44 Matlab 6 Matlab r c d reshape r c repmat reshape 5.8 Matlab Matlab Matlab Matlab >> A = [1 2 3;4 5 6;7 8 9] A = >> A(3,3) = 0 % set element in 3rd row, 3rd column to zero A = >> A(2,6) = 1 % set element in 2nd row, 6th column to one A = A 6 A 0 >> A(:,4) = 4 A = A 4 4 Matlab 4 Matlab >> A(:,4) = [4;4;4] A =

57 5 45 >> A(:,4) = [4 4 4] % but a row can't be squeezed into a column!??? In an assignment A(:,matrix) = B,the number of elements in the subscript of A and the number of columns in B must be the same. >> A = [1 2 3;4 5 6;7 8 9]; % restore original data >> B = A(3:-1:1,1:3) B = >> B = A(end:-1:1,1:3) % same as above B = A B end end 3 >> B = A(3:-1:1,:) B = :3 A 3 >> C = [A B(:,[1 3])] C = C B A >> B = A(1:2,2:3) B = >> B = A(1:2,2:end) % same as above B = A B end

58 46 Matlab 6 >> C = [1 3] C = 1 3 >> B = A(C,C) B = C A start:increment:end start:end A B >> B = A(:) B = A A B >> B = B. ' B = >> B = reshape(a,1,9) % reshape A into 1-by-9 B = >> B = reshape(a,[1 9]) B = reshape >> B = A % copy A into B B = >> B(:,2) = [] B =

59 B B B [ ] >> C = B. ' C = >> reshape(b,2,3) % reshape is not equivalent to transpose reshape I I >> C(2,:) = [] C = C 2 >> A(2,:) = C A = C A 2 >> B = A(:,[ ]) % create new B array B = >>B = A(:,2+zeros(1,4)) % [ ]=2+zeros(1,4) B = >>B = repmat(a(:,2),1,4) % replicate 2nd column into 4 columns B =

60 48 Matlab 6 A 2 4 B >>A, C % show A and C again A = C = >> A(2,2) = []??? Index empty matrix assignment is not allowed. Matlab >>C = A(4,:)??? Indexed exceeds matrix dimensions. A 4 Matlab A(r,c) (r,c) 0 A(r,c) A A(r,c) >>C(1:2,:) =A??? In an assignment A(matrix,:) = B, the number of columns in A and B must be the same. >>C (3:4,:) = A(2:3,:) C = A 2 3 A C 2 4 Matlab C 2 0 >>A = [1 2 3;4 5 6;7 8 9] % fresh data A = 1 2 3

61 >>A(:,2:3) % a peek at what's addressed next >> G(1:6) = A(:,2:3) G = A 2 3 G A 1 2 G A G >> H = ones(6,1); % create a column array >> H(:) = A(:,2:3) % fill H without changing its shape H = : A 2 3 H >> A(2,:) = 0 A = A >> A(2,:) = [0 0 0] A = Matlab

62 50 Matlab 6 >> A(1,[1 3]) = pi A = reshape >> D(2*4) = 2 % create array with 8 elements D = >> D(:) = 2 % scalar expansion D = >> D = reshape(d,2,4) % reshape D = D(2*4)=2 8 2 D(:) D 2 >> A =reshape (1:12,3,4) ' A = >> r = [3 2 1] r = A i r(i) >> Ar = [A(:,1)-r(1) A(:,2)-r(2) A(:,3)-r(3)] Ar =

63 5 51 >> R =r([ ],:) % duplicate r to have 4 rows R = >> Ar = A R % now use element by element subtraction Ar = ones size repmat R >> R =r(ones(size(a,1),1),:) % historically this is Tony's trick R = >> R =repmat(r,size(a,1),1) % often faster than Tony's trick R = size(a,1) A Matlab 1 2 >> D =reshape(1:12,3,4) % new data D = >> D(2) 2 >> D(5) 5 >>D(end) 12

64 52 Matlab 6 >> D(4:7) Matlab sub2ind ind2sub >> sub2ind(size(d),2,4) % find single index from row and column 11 >> [r,c] = ind2sub(size(d),11) % find row and column from single index r = 2 c = size D True(1) False(0) >> X = -3:3 % Create data X = >> abs(x)> x 1 1 True 1 0 False >> y = x(abs(x)>1) Y = y x 1 abs(x)>1 [ ] >> y =x([ ])??? Index into matrix is negative or zero. See release notes on changes to logical indices. abs(x)>1 [ ] [ ] Matlab [ ]

65 Matlab logical >> y =x(logical([ ])) y = Matlab logical 1 >> B = [5 3;2-4] % new data B = >> x = abs(b)>2 % logical result x = >> y = B(x) % grab True values y = Matlab A(r,c) A(r,:) A(:,c) A(:) A(k) A(x) r c A r A c A A A(:) A k A A(:) x A x A

66 54 Matlab Matlab sort >> X = randperm(8) % new data X = >> xs = sort(x) % sort ascending xs = >> [xs,idx] = sort(x) % return sort inder as well xs = idx = sort,xs(k)=x(idx(k)) Matlab [a,b] b a >> xsd = xs(end:-1:1) xsd = >> idxd = idx(end:-1:1) idxd = sort >> A = [randperm(6);randperm(6); randperm(6); randperm(6)] % new data A = >> [As,idx] = sort(a) As =

67 idx = sort 2 Matlab >> [tmp,idx] = sort(a(:,4)); % sort 4-th column only >> As = A(idx,:) % rearrange rows in all columns using idx As = As A 4 >> As = sort(a,2) % sort across 2-nd dimension As = >> As = sort(a,1) % same as sort(a) As = sort 2 A(r,c) sort(a,1) A(r,c) sort(a,2) sort 5.10 Matlab find

68 56 Matlab 6 >> x = -3:3 x = >> k = find(abs(x)>1) % finds those subscripts where abs(x)>1 k = >> y = x(k) % creates y using the indices in k. y = >> y = x(abs(x)>1) % creates the same y vector by logical addressing y = find >> A = [1 2 3; 4 5 6;7 8 9] % new data A = >> [i,j] = find(a>5) % i and j are not equal to sqrt(-1) anymore i = j = i j A(i(1),j(1)) A A>5 find >> k = find(a>5) k = >> A(k) % look at elements greater than 5 7

69 >> A(k) = 0 % set elements addressed by k to zero A = >> A = [1 2 3;4 5 6;7 8 9] % restore data A = >> A(i,j) % this is A([ ],[ ]) >> A(i,j) = 0 % this is A([ ],[ ]) also A = A(i,j) A(k) Matlab A(i,j) >> [A(3,1) A(3,2) A(2,3) A(3,3) A(3,1) A(3,2) A(2,3) A(3,3) A(2,1) A(2,2) A(2,3) A(2,3) A(3,1) A(3,2) A(2,3) A(3,3)] i j i j A(i,j) A(k) A(i,j) >> diag(a(i,j)) 7 8

70 58 Matlab diag(a( i,j))=a(k) A(k) A(i,j) 0 >>A(3,1)=0; A(3,2)=0; A(3,3)=0; A(3,3)=0; % i(1) with all j >>A(3,1)=0; A(3,2)=0; A(3,3)=0; A(3,3)=0; % i(2) with all j >>A(2,1)=0; A(2,2)=0; A(2,3)=0; A(2,3)=0; % i(3) with all j >>A(3,1)=0; A(3,2)=0; A(3,3)=0; A(3,3)=0; % i(4) with all j A = find A(i,j) A(k) i =find(x) [r,c]=find(x) X 0 X 0 find Matlab max min >> V = rand(1,6) % new data V = >> max(v) % return maximum value >> [mx,i] =max(v) % maximum value and its index mx = i = 4 >> min(v) % return minimum value >> [mn,i] = min(v) % minimum value and its index mn = i =

71 min max >> A rand(4,6) % new data A= >> [mx,r] =max(a) mx = r = >> [mn,r] = min(a) mn = r = mx A r min max >> mmx = max(mx) % apply max again to prior result mmx = >> [mmx,i] = max(a(:)) % reshape A as a column vector first mmx = i = 8 max(max(a)) mmx=a(i) min max find >> x= [ ] x = >> mx = max(x) mx = 6 >> i = find(x==mx) % indices of values equal to mx

72 60 Matlab 6 i = 3 7 min max 5.11 Matlab >> A = [1 2 3; 4 5 6;7 8 9] % fresh data A = >> flipud(a) % flip array in up-down direction >> fliplr(a) % flip array in the left-right direction >> rot90(a) % rotate array 90 degrees counterclockwise >> rot90(a,2) % rotate array 2*90 degrees counterclockwise >> B = 1:12 % more data B = >> reshape(b,2,6) % reshape to 2 row, 6 columns, fill by columns >> reshape(b,[2 6]) % equivalent to above

73 >> reshape(b,3,4) % reshape to 3 rows, 4 columns, fill by columns >> reshape(a,3,2) % A has more than 3*2 elements, OOPS!??? To RESHAPE the number of elements must not change. >> reshape(a,1,9) % stretch A into a row vector >> A % remember what A is A = >> diag(a) % extract diagonal using diag >> diag(ans) % remember this? same function, different action >> triu(a) % extract upper triangular part >> tril(a) % extract lower triangular part >> tril(a) diag(diag(a)) % lower triangular part with no diagonal >> a =[1 2;3 4] % a smaller data array a =

74 62 Matlab >> b = [0 1;-1 0] % another smaller data array b = >> kron(a,b) % the Kronecker tensor product of a and b kron(a,b) >> [1*b 2*b 3*b 4*b] >> kron(b,a) % the Kronecker tensor product of b and a kron(b,a) >> [0*a 1*a -1*a 0*a] kron(a,b) repmat >> a % recall data a = >> repmat(a,1,3) % replicate a once down, 3 across

75 >> repmat(a,[1 3]) % equivalent to above >> [a a a] % equivalent to above >> repmat(a,2,2) % replicate a twice down, twice across >> repmat(a,2) % same as repmat(a,2,2) and repmat (a,[2 2]) >> [a a; a a] % equivalent to above repmat reshape repmat repmat(a,n) repmat(a,[n,n]) repmat(d,size(a)) size >> A=reshape(1:12,[3 4]) % new data A = >> repmat(pi,size(a)) % pi replicated to be the size of A

76 64 Matlab Matlab size length numel >> A = [ ; ] A = >> s = size(a) s = 2 4 size >> [r,c] = size(a) r = 2 c = 4 size >> r = size(a,1) % number of rows r = 2 >> c = size(a,2) % number of columns c = 4 size size 2 A(r,c) r size(a,1) A(r,c) size(a,2) numel >> numel(a) ans= 8 length >> length(a) ans= 4 length

77 5 65 >> B = -3:3 B = >> length(b) % length of a row vector 7 >> length(b') % length of a column vector 7 size length 0 >> c = [] % you can create an empty variable! c = [] >> size(c) ans= 0 0 >> d = zeros(3,0) % an array with one dimension nonzero! d = Empty matrix:3-by-0 >> size(d) 3 0 >> length(d) 0 >> max(size(d)) % maximum of elements of size(d) Warning:Use length(x) instead of max(size(x)) when x might be empty. 3 Matlab 0 0 length Matlab s=size(a) [r,c]=size(a) r=size(a,1) c=size(a,2) n=length(a) n=max(size(a)) n=numel(a) s A r c A A A A max(size(a)) A 0 0 A A A length(a) A A 0 A

78 66 Matlab Matlab C (malloc calloc free) Matlab Matlab Matlab Matlab >> P = zeros(100); Matlab >> P =rand(5,6); >> P = zeros(5,6); % same size as earlier >> P = ones(6,5); % same number of elements as earlier Matlab / / a a=2 a=1 a / >> P(3,3) = 1; P(3,3)

79 5 67 >> P(8,1) = 1; >> size(p) 8 5 P Matlab / >> P(:) = ones(1,40); Matlab / P >> size(p) 8 5 Matlab global Matlab >> A = zeros(10); >> B = zeros(10); >> C = B; A B 10 C B C B C C B C B B C Matlab B C myfunc(a,b,c) a b c M

80 68 Matlab 6 >> prod(size(a)) 100 size(a) prod size(a) >> tmp=size(a); >> prod(tmp) 100 size(a) Matlab proc >> A=1:5 A = >> B= 6:10; >> A=[A;B] A = >> C = 11:15; >> A = [A:C] A = A >> A=zeros(3,5) % grab all required memory up front A = >> A(1,:)=1:5; % no memory allocation here >>B=6:10;

81 5 69 >>A(2,:)=B; % no memory allocation here >> C=11:15; >> A(3,:)=C % no memory allocation here A = A A P=zeros(100);P=rand(5,6); P(3,3)=1; P(8,1)=1; P=zeros(5,6);P=ones(5,6) / / / / P(:)=rand(1,30) P / B=zeros(10);C=B; C B B B C prod(size(a))tmp=size(a);prod(tmp) myfunc(a,b,c) a b c / A=zeros(3,5);A(1,:)=1:5; A(2,:)=6:10;A(3,:)=11:15; / /

82 6 Matlab 5 Matlab n 3 (page) >> A = zeros(4,3,2) A(:,:,1) = A(:,:,2) = ones rand randn >> A = zeros(2,3) % start with a 2-D array A = >>A(:,:,2) = ones(2,3) % add a second page to go 3-D!

83 6 71 A (:,:,1) = A (:,:,2) = >> A (:,:,3) = 4 % add a third page by scalar expansion A (:,:,1) = A (:,:,2) = A (:,:,3) = reshape repmat n >> B = reshape(a,2,9) % 2-D data, stack pages side-by-side B = >> B = [A(:,:,1) A(:,:,2) A(:,:,3)] % equivalent to above B = >> reshape(b,2,3,3) % recreate A! ans(:,:,1) = ans(:,:,2) = ans(:,:,3) = >> reshape (B,[2 3 3])% alternative to reshape (B,2,3,3,) ans(:,:,1)= ans(:,:,2)= ans(:,:,3)=

84 72 Matlab reshape >> C ones(2,3) % new data >> C = >> repmat(c,1,1,3) % this form not allowed above 2-D!??? Error using ==> repmat Too many input arguments. >> repmat(c,[1 1 3]) ans(:,:,1) = ans(:,:,2) = ans(:,:,3) = C cat n >> a = zeros(2); % new data >> b = ones(2); >> c = repmat(2,2,2); >>D = cat (3,a,b,c) % concatenate a,b,c along the 3rd dimension D(:,:,1) = D(:,:,2) = D(:,:,3) = >> D = cat(4,a,b,c) % try the 4th dimension! D(:,:,1,1) = D(:,:,1,2) = D(:,:,1,3) =

85 >> D(:,1,:,:) % look at elements in column 1 ans(:,:,1,1) = 0 0 ans(:,:,1,2) = 1 1 ans(:,:,1,3) = 2 2 >> size(d) D Matlab n squeeze (singleton dimension) 1 >>E = squeeze(d) % squeeze dimension 4 down to dimension 3 E(:,:,1) = E(:,:,2) = E(:,:,3) = >> size(e) E D >> v(1,1,:) = 1:6 % a vector along the page dimension v(:,:,1) =

86 74 Matlab 6 1 v(:,:,2) = 2 v(:,:,3) = 3 v(:,:,4) = 4 v(:,:,5) = 5 v(:,:,6) = 6 >> squeeze(v) % squeeze it into a column vector >> v(:) % this always creates a column vector reshape >> F =cat(3,2+zeros(2,4),ones(2,4),zeros(2,4)) % new 3-D array F(:,:,1) = F(:,:,2) = F(:,:,3) = >> G = reshape(f,[3 2 4]) % change it to 3 rows, 2 columns, 4 pages G(:,:,1) = G(:,:,2) =

87 G(:,:,3) = G(:,:,4) = >> H = reshape(f,[4 3 2]) % or 4 row, 3 columns, 2 pages H(:,:,1) = H(:,:,2) = >> K = reshape(f,2,12) % 2 rows, 12 columns,1 page K = n reshape reshape reshape G K F sub2ind ind2sub >> sub2ind(size(f),1,1,1) % 1st row, 1st column, 1st page is element 1 1 >> sub2ind(size(f),1,2,1) % 1st row,2nd column,1st page is element 3 3 >> sub2ind(size(f),1,2,3) % 1st element,2nd column,3rd page is element >> [r,c,p]=ind2sub(size(f),19) % inverse of above r = 1

88 76 Matlab 6 c = p = 2 3 flipud fliplr n flipdim >> M = reshape(1:18,2,3,3) % new data M(:,:,1) = M(:,:,2) = M(:,:,3) = >> flipdim(m,1) % flip row order ans(:,:,1) ans(:,:,2) = ans(:,:,3) = >> flipdim(m,2) % flip column order ans(:,:,1) = ans(:,:,2) = ans(:,:,3) = >> flipdim(m,3) % flip page order ans(:,:,1)= ans(:,:,2)= ans(:,:,3)=

89 6 77 shiftdim r c p 1 c p r >> M % recall data M(:,:,1) = M(:,:,2) = M(:,:,3) = >> shiftdim(m,1) % shift one dimension ans(:,:,1) = ans(:,:,2) = >> shiftdim(m,2) % shift two dimensions ans(:,:,1) = ans(:,:,2) = ans(:,:,3) = M 3 M shiftdim

90 78 Matlab 6 >> M % recall data M(:,:,1) = M(:,:,2) = M(:,:,3) = >> size(m) % M has 2 rows,3 columns, and 3 pages >> shiftdim(m,-1) % shift dimensions out by 1 ans(:,:,1,1) = 1 2 ans(:,:,2,1) = 3 4 ans(:,:,3,1) = 5 6 ans(:,:,1,2) = 7 8 ans(:,:,2,2) = 9 10 ans(:,:,3,2) = ans(:,:,1,3) = ans(:,:,2,3) = ans(:,:,3,3) = >> size(ans) r c c r permute ipermute n permute shiftdim >> M % recall data M(:,:,1) = 1 3 5

91 M(:,:,2) = M(:,:,3) = >> permute(m,[2 3 1] % same as shiftdim(m,1) ans(:,:,1) = ans(:,:,2) = >> shiftdim(m,1) ans(:,:,1) = ans(:,:,2) = [2 3 1] >> permute(m,[2 1 3]) ans(:,:,1) = ans(:,:,2) = ans(:,:,3) = [2 1 3] permute Permute ORDER

92 80 Matlab 6 >> permute(m,[2 1 1])??? Error using ==> permute ORDER cannot contain repeated permutation indices. >> permute(m,[2 1 4])??? Error using ==> permute ORDER contains an invalid permutation index. permute shiftdim(m, 1) >> permute(m,[ ]) ans(:,:,1,1) = 1 2 ans(:,:,2,1) = 3 4 ans(:,:,3,1) = 5 6 ans(:,:,1,2) = 7 8 ans(:,:,2,2) = 9 10 ans(:,:,3,2) = ans(:,:,1,3) = ans(:,:,2,3) = ans(:,:,3,3) = singleton M ipermute permute n >> M % recall data M(:,:,1)= M(:,:,2) = M(:,:,3) = >> permute(m,[3 2 1]) % sample permutation

93 6 81 ans(:,:,1) = ans(:,:,2) = >> ipermute(m,[3 2 1]) % back to original data ans(:,:,1) = ans(:,:,2) = size size numel >> size(m) % return array of dimensions >>numel(m) % number of elements 18 >> [r,c,p] = size(m) % return individual variables r = 2 c = 3 p = 3 >> r =size(m,1) % return just rows 2 >> c = size(m,2) % return just columns c = 3 >> p = size(m,3) % return just pages p =

94 82 Matlab 6 3 >> v = size(m,4) % default for all higher dimensions v = 1 ndims >> ndims(m) 3 >> ndims(m(:,:,1)) % just the 2-D first page of M 2 M(:,:,1) ndims >> length(size(m)) 3 n ones(r,c, )zeros(r,c, )rand(r,r, )randn(r,c, ) reshape(b,2,3,3) reshape(b,[2 3 3]) repmat(c,[1 1 3]) cat(3,a,b,c) squeeze(d) sub2ind(size(f)),1,1,1) [r,c,p]=ind2sub(size(f),19) flipdim(m,1) shiftdim(m,2) permute(m,[2 1 3] ipermute(m,[2 1 3]) size(m) [r,c,p]=size(m) r=size(m,1) c=size(m,2) p=size(m,3) ndims(m) numel(m) n 1 n flipud fliplr n n

95 7 Matlab 5 cell array structure container Matlab 7.1 Matlab Matlab Matlab Matlab cell Matlab

96 84 Matlab 6 {} Matlab >> clear A % make sure A is not being used >> A(1,1) = { [1 2 3; 4 5 6; 7 8 9]}; >> A(1,2) = { 2+3i }; % semicolons suppress display >> A(2,1) = { 'A character string'}; >> A(2,2) = { 12:-2:0 } % no semicolon, so display requested A= [3 3 double] [ i] 'A character string' [1 7 double] Matlab A 2 2 Matlab Matlab cell indexing >> A{1,1} = [1 2 3; 4 5 6; 7 8 9]; >> A{1,2} = 2+3i; >> A{2,1} = 'A character string'; >> A{2,2} = 12:-2:0; A = [3 3 double] [ i] 'A character string' [1 7 double] A{1,1} A (content indexing) {} ( ) A(i,j)={x} A(i,j)=x Matlab x A i,j A(i,j) A{i,j} { ( ) celldisp Matlab >> celldisp(a) >> A{1,1} = >> A{2,1} = A character string

97 7 85 >> A{1,2} = i >> A{2,2} = celldisp >> A{2,2} % content addressing >> A(2,2) % cell indexing [1x7 double] >> A{1,:} % address contents of the first row i >> A(1,:) [3 3 double] [ i] ans >> B = {[1 2] 'John Smith';2+3i,5} B= [1 2 double] 'John Smith' [ i] [ 5] 0 cell [ ] >> C =cell(2,3) C = [] [] [] [] [] [] >> C(1,1) = 'This doesn' 't work'??? Conversion to cell from char is not possible.

98 86 Matlab 6 Matlab >> C(1,1) = { 'This does work' } C = 'This does work' [] [] [] [] [] >> C{2,3} = 'This works too' C = 'This does work' [] [] [] [] 'This works too' Matlab 7.2 Matlab [ ] >>A % recall prior cell arrays A = [3 3 double] [ i] 'A character string' [1 7 double] >> B B = [1 2 double] 'John Smith' [ i] [ 5] >> C=[A;B] C = [3 3 double] [ i] 'A character string' [1 7 double] [1 2 double] 'John Smith' [ i] [ 5] >> D = C([1 3],:) % first and third rows D =

99 7 87 [3 3 double] [1 2 double] [ i] 'John Smith' >> C (3,:) = [] C = [3 3 double] [ i] 'A character string' [1 7 double] [ i] [ 5] reshape >> X = cells(3,4); >> size(x) % size of the cell array, not the contents 3 4 >> Y = reshape(x,6,2); >> size(y) 6 2 reshape size repmat Matlab Matlab reparray repmat >> Y % recall data Y = [] [] [] [] [] [] [] [] [] [] [] [] >> Z = repmat(y,1,3) Z = [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] []

100 88 Matlab 6 [] [] [] [] [] [] 7.3 >> B % recall cell array B = [1 2 double] 'John Smith' [ i] [ 5] >> x =B{2,2} % content addressing uses {} x = 5 x 5 x class >> class(x) % return argument's data type double class x double >> y = B(2,2) % cell indexing uses( ) y = [5] >> y = B(4) % same as above using single index y = [5] >> calss(y) % y is not a double, but a cell! cell >> class(y{1}) % but the contents of y is a double! double True=1 False=0 >> iscell(y) % yes, y is a cell 1 >> iscell(y{1}) % contents of y is NOT a cell

101 >> isa(y, 'cell') %yes, y is a cell 1 >> isdouble(y{1}) % this function does't exist (yet?)??? Undefined function or variable 'isdouble' >> isnumeric(y{1}) % contents of y is numerical 1 >> isa(y{1},'double')% contents of y is a double 1 >> isa(y{1},'numeric') % contents of y is also numeric 1 >> isa(y{1},'cell') % contents of y is NOT a cell 0 >> B{:,2} John Smith Ans = 5 >> d=b{:,2}??? Illegal right-hand side in assignment.too many elements. d 2 1 >> A % recall prior data A = [3 3 double] [ i] 'A character string' [1 7 double] >> celldisp(a) % display contents A{1,1} = A{2,1} =

102 90 Matlab 6 A character string A{1,2} = i A{2,2} = >> A{1,1}(3,:) % third row of 3-by-3 array >> A{4}(2:5) % second through fifth elements of A{2,2} >> A{1,2}(2) % second element doesn't exist??? Index exceeds matrix dimensions. >> A{2,1}(3:11) % extract part of the character string character 7.4 Matlab >> a = ones(2,3); >> b =zeros(2,1); >> c =(3:4) '; >> d =[a,b,c] % same as [a b c] d = >> d = cat(2,a,b,c) d = >> [m,n] =size(d) m = 2 n = 5 Matlab

103 7 91 >> F = {a b c} % create a cell array F = [2 3 double] [2 1 double] [2 1 double] >> d = cat(2,f{:}) % same as cat (2,a,b,c) d = >> d = cat(2,f{:}) % not content addressing d = [2 3 double] [2 1 double] [2 1 double] cat(2,f{:}) Matlab cat(2,f{1},f{2},f{3}) cat(2,a,b,c) F{:} F{:} cat(2,f(:)) >> d = [F{:}] d = >> d = [F{1}, F{2}, F{3}] % what is implied by the above d = >> e = [F{2:3}] % can also content address any subset e = >> e = [F{2},F{3}] % what is implied by the above e = lists comma-separated list deal deal >> celldisp(f) % recall data F{1} = F{2} =

104 92 Matlab F{3} = 3 4 >> [r,s,t] = deal(f{:}) % deal out contents of F r = s = t = r s t r=f{1} s=f{2} t=f{3} >> [r,s,t] = deal(f{1}, F{2}, F{3}) r = s = 0 0 t = 3 4 deal deal output deal >> [G{:}] = deal(a,b,c)??? Error using ==> deal The number of outputs should match the number of inputs. >> [G{1:3}] = deal(a,b,c) G = [2 3 double] [2 1 double] [2 1 double] >> F ={a b c} F = [2 3 double] [2 1 double] [2 1 double] >> isequal(f,g) % True since F =G 1