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Kai-Chun Fan

Introduction to. MAT rix LAB oratory. Kai-Chun Fan. 2010.12.30. Agenda. Basic Usages for Mathematics Coding environments Files I/O Statistic tools Plot tools. 基本操作畫面. >> (prompt) …. How to Use MATLAB. >> DEMO >> HELP [ SIGNAL ] % same as man [ SIGNAL ] in UNIX

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Kai-Chun Fan

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  1. Introduction to MATrix LABoratory Kai-Chun Fan 2010.12.30

  2. Agenda • Basic Usages for Mathematics • Coding environments • Files I/O • Statistic tools • Plot tools

  3. 基本操作畫面 >>(prompt) …

  4. How to Use MATLAB >> DEMO >> HELP [ SIGNAL ] % same as man [ SIGNAL ] in UNIX >> google is your good friend.

  5. 基本數學運算 >> (5*2+1.3-0.8)*10/25 (return) ans = 4.2000 >> x = (5*2+1.3-0.8)*10/25 (return) x = 4.2000 % %為 comment sign % defaultvariable data type:double % MATLAB stores the result in double ans % in default

  6. 基本數學運算 >> (5*2+1.3-0.8)*10/25 (return) ans = 4.2000 >> x = (5*2+1.3-0.8)* … (return) 10/25 (return) x = 4.2000 % 式子太長可用 … 換行

  7. Appendix

  8. Vector & Matrix % vector >> x = [1 3 5 2] (return) x = 1 3 5 2 % matrix >> x = [1 3; 5 2] (return) x = 1 3 5 2

  9. X = 3 X 為一個1 x 1 matrix[3]

  10. Vector & Matrix >> x = [1 3 5 2]; (return) >> y = 2 * x + 1 (return) y = 3 7 11 5 % y is an array for 2 * x(i) + 1

  11. >> x = [1 3 5 2]; (return) >> y = 2 * x + 1 (return) y = 3 7 11 5 >> x = [1 3 5 2] (return) x = 1 3 5 2 >> y = 2 * x + 1 (return) y = 3 7 11 5 ; 抑制輸出

  12. Operators for Vector and Matrix M = A◎B－－ ◎處可為 加法(+)、減法(-)、乘法(*)、左除(\)、右除(/) M = A.◎B－－ ◎處可為 乘法(*)、乘幂(^)、左除(\)、右除(/) M = A◎c－－ ◎處可為 加法(+)、減法(-)、乘法(*)、乘幂(^)、右除(/) M = c◎B－－ ◎處可為 加法(+)、減法(-)、乘法(*)、乘幂(^)、左除(\)、右除(./)

  13. Special Operators • M = A .◎ B >>x = [1 2]; >> y = [118 59]; >> x .* y ans = 118 118 >> x * y error

  14. Index for Vector & Matrix % variable(index) >> x = [1 3 5 2]; (return) >> x(1) = 118 (return) x = 118 3 5 2 >> x = [1 3; 5 2]; (return) >> x(2, 1) = 118 (return) x = 1 3 118 2 % index starts from 1, not 0.

  15. Index for Vector & Matrix % range index >> x = [1 2 3; 4 5 6; 7 8 9]; (return) >> x(2, 1:3) (return) ans = 4 5 6 >> x(1:3, 2) (return) ans = 2 5 8

  16. Add & Delete % add element >> x = [1 3 5 2]; (return) >> x(6) = 631 (return) x = 1 3 5 2 0 631 % delete element >> x(3) = []; (return) >> x (return) x= 1 3 2 0 631

  17. Catenate & Inverse % catenate a = 1 2 3 4 5 6 >> a = [a; 7 8 9]; >> a = [a(1,:) 118; a(2,:) 118; a(3,:) 118] a = 1 2 3 118 4 5 6 118 7 8 9 118 % inverse a = 39 39 889 >> a’ a = 39 39 889

  18. % start [: different] : end >> x = 7 : 13 x = 7 8 9 10 11 12 13 >> y = 7 : 1 : 13 y = 7 8 9 10 11 12 13 >> z = 7 : 4 : 13 z = 7 11 : >> a = [1:3; 10:10:30] a = 1 2 3 10 20 30

  19. Variables in Workspace % information >> whos (return) name size bytes class a 2x4 64 double array b 4x2 64 double array ans 1x1 8 double array x 1x1 8 double array y 1x1 8 double array z 1x1 8 double array grand total is 20 elements using 160 bytes % release >> clear a >> a ??? Undefined function or variable ‘a'.

  20. Code in Files % write your code in files, *.m % for example, kerker.m >> kerker (return)

  21. For-loop % for <variable> = <vector> % … % end % in kerker.m for i = 0:2:4, for j = 1:2, h(i/2+1, j) = i/(j*4); end end disp(h) % display, like “cout” format rat % use fraction to display disp(h) % output >> kerker (return) 0 0 0.5 1 2 0.5 0 0 1/2 1 2 1/2

  22. While-loop % while <condition> % … % end x = zeros(1,6); % create an 1 x 6 ZERO matrix while i <= 6, x(i) = 1/i; i = i + 1; end

  23. if % if <condition> % … % end % in world118.m if rand(1,1) > 0.5, % create an 1x1 matrix with random elements disp('Given random number is greater than 0.5.'); end >> world118 Given random number is greater than 0.5.

  24. break

  25. Appendix

  26. nan NaN C o n s t a n t s pi eps i n f ior j nargin nargout realmax realmin

  27. File I/O • Like C language • Read from file filepointer = fopen(‘filename’); variable = fscanf(filepointer, format, [m n]); fclose(filepointer);

  28. File I/O Example fp = fopen('sinx.txt');A = fscanf(fp, '%g %g', [2 inf]); fclose(fp);>> A = A'A =0 0.31420.6283 0.94251.2566 1.57081.8850 2.19912.5133 2.82743.1416 00.3090 0.58780.8090 0.95111.0000 0.95110.8090 0.58780.3090 0

  29. File I/O % load filename x = filename(m, n) load sinx.txtA = sinx.txt(:, 1:2); % A = sinx.txt(inf, 1:2);>> AA =0 0.31420.6283 0.94251.2566 1.57081.8850 2.19912.5133 2.82743.1416 00.3090 0.58780.8090 0.95111.0000 0.95110.8090 0.58780.3090 0

  30. Random Number Generators 均勻分佈亂數 rand常態分佈亂數 randn常態亂數(Normal (Gaussian))-normrnd貝他亂數(Beta)-betarnd二項式亂數(Binomial)- binorndX's亂數(Chi square)-chi2rnd極值亂數(Extreme value)-evrnd指數亂數(Exponential)-exprndF亂數(F)-frnd伽瑪亂數(Gamma)-gamrnd伽瑪亂數(Gamma (unit scale))-randg幾何亂數(Geometric)-geornd超幾何亂數(Hypergeometric)-hygernd反威夏亂數(Inverse Wishart)-iwishrnd常態對數亂數(Lognormal)-lognrnd多變異亂數(Multivariate normal)-mvnrnd多變T亂數(Multivariate t)-mvtrnd負二項式亂數(Negative binomial)-nbinrnd非中央F亂數(Noncentral F)-ncfrnd非中央亂數(Noncentral)-nctrnd非中央X's亂數(Noncentral Chi-square)-ncx2rnd波義松亂數(Poisson)-poissrnd定群樣本亂數(finite population)-randsample魏利亂數(Rayleigh)-raylrndT亂數(T)- trnd離散均勻亂數(Discrete uniform)-unidrnd均勻亂數(Uniform)-unifrnd魏伯亂數(Weibull)-wblrnd威夏亂數矩陣(Wishart)-wishrnd % *nd are not “dname.”

  31. Random Number Generators random(‘dname', mean, var, m, n)

  32. xy - Plane Basic • plot(…) • x-axis: linear scale • y-axis: linear scale • loglog(…) • x-axis: log scale • y-axis: log scale • semilogx(…) • x-axis: log scale • y-axis: linear scale • semilogy(…) • x-axis: linear scale • y-axis: log scale

  33. KER plot(x1) - y-axis adopts the column number plot(x1, y1) plot(x1, y1, LineSpec, ‘PropertyName’, Property value,‘PropertyName’, Property value, …) - LineWidth, MarkerEdgeColor, MarerFaceColor, MarkerSize, …

  34. 2 or More than 2 lines plot(set1, set2, …) plot(set1) hold on; plot(set2) … plot(x1, x2)

  35. x = -pi:0.1:pi; y = sin(x); plot(x,y)

  36. x = -pi:pi/10:pi; y = tan(sin(x)) - sin(tan(x)); plot(x,y,'--rs',... 'LineWidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','g',... 'MarkerSize',10)

  37. LineSpec

  38. 其它線參數 點我 http://www.mathworks.com/help/techdoc/ref/plot.html

  39. Other Properties for Plots axis([xmin, xman, ymin, ymax]) - range of x-axis and y-axis. - the dot out of the range will not be presented. xlabel(‘name for x-axis’) ylabel(‘name for y-axis’) title(‘title for the plot’) test(x, y, text, alignment base, position) - notes for a specific point legend(‘note for line1’, ‘note for line2’, …) grid on; - show the grid line

  40. x = -pi:.1:pi; y = sin(x); p = plot(x,y) xlabel('-\pi \leq \Theta \leq \pi') ylabel('sin(\Theta)') title('Plot of sin(\Theta)') text(-pi/4,sin(-pi/4),'\leftarrow sin(-\pi\div4)',... 'HorizontalAlignment','left') set(p,'Color','red','LineWidth',2) set(gca,'XTick',-pi:pi/2:pi) set(gca,'XTickLabel',{'-pi','-pi/2','0','pi/2','pi'})

  41. subplot subplot(i, j, #) plot(); subplot(4, 2, 1:2) % #1&#2 subplot(4, 2, [1 3 5]) % #1&#3&#5

  42. Other types of plots

  43. boxplot • x1 = normrnd(5, 1, 100, 1); • x2 = normrnd(6, 1, 100, 1); • boxplot([x1, x2], 'notch', 'on')

  44. boxplot • x = randn(100,25); • subplot(2,1,1) boxplot(x) • subplot(2,1,2) boxplot(x,'plotstyle','compact')

  45. plotyy • x = 0:0.01:10;y1 = 100*exp(-0.1*x).*sin(x);y2 = 0.8*exp(-0.5*x).*sin(10*x);[ax,h1,h2] = plotyy(x,y1,x,y2,‘plot’);set(get(ax(1),‘Ylabel’),‘String’,‘左側 y1 函數’)set(get(ax(2),‘Ylabel’),‘String’,‘右側 y2 函數’)set(h1,‘Linewidth’,4)set(h2,‘LineStyle’,‘:’,‘color’,'k')xlabel('時間 0-10 \mus')title('指令plotyy之應用')

  46. ezplot • ezplot(‘u*sin(u)+v*cos(v)-2')

  47. bar x =1:10; y =rand(size(x)); bar(x,y)

  48. errorbar x = linspace(0, 2*pi, 30); y = sin(x); e = std(y) * ones(size(x)); errorbar(x, y, e)

  49. fplot • fplot(func, range); • % sampled more precisely • fplot('sin(1/x)', [0.02 0.2])

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