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MATLAB迭代

作者：weixin_40725706 | 2024-03-01 21:00:35

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MATLAB迭代

目录

黄金分割比

习题

符号运算

固定点

WHY

hello world

Goldrect

黄金分割比

format

 

 for循环

  1. %% For loop
  2.    x = 42
  3.    for k = 1:12
  4.       x = sqrt(1+x);
  5.       disp(x)
  6.    end

while循环

  1. %% While loop
  2.    x = 42;
  3.    k = 1;
  4.    while abs(x-sqrt(1+x)) > 5e-5
  5.       x = sqrt(1+x);
  6.       k = k+1;
  7.    end
  8.    k

绘图语句

  1. %% Plot
  2.    x = -pi: pi/256: pi;
  3.    y = tan(sin(x)) - sin(tan(x));
  4.    z = 1 + tan(1);
  5.    plot(x,y,'-', pi/2,z,'ro')  %pi/2,z为点坐标
  6.    xlabel('x')
  7.    ylabel('y')
  8.    title('tan(sin(x)) - sin(tan(x))')

黄金螺旋线

  1.  
  2. function golden_spiral
  3. % GOLDEN_SPIRAL  Explosion of golden rectangles.
  4. %    GOLDEN_SPIRAL  Constructs a continuously expanding sequence
  5. %    of golden rectangles and inscribed quarter circles.
  6.  
  7. %   Copyright 2020 The MathWorks, Inc.
  8. %  
  9. %   Text used in the show_quote function:
  10. %   Jones, Robert Bishop. 揂ristotle METAPHYSICA Book 13 Part 3.� Aristotle METAPHYSICA Book 13 Part 3 
  11. %       Mathematics, Harmonics, Optics, Good and Beauty, 25 Nov. 1996, 
  12. %       www.rbjones.com/rbjpub/philos/classics/aristotl/m11303c.htm.
  13.  
  14.    % Initialize_variables
  15.    klose = [];
  16.    
  17.    % Golden ratio
  18.    phi = (1+sqrt(5))/2;
  19.  
  20.    % Control speed of zooming in控制缩放速度
  21.    n = 48;
  22.    f = phi^(1/n);
  23.  
  24.    % Scaling
  25.    a = 1;
  26.    s = phi;
  27.    t = 1/(phi+1);
  28.  
  29.    % Centers
  30.    x = 0;
  31.    y = 0;
  32.  
  33.    % A square
  34.    us = [-1 1 1 -1 -1];
  35.    vs = [-1 -1 1 1 -1];
  36.  
  37.    % Four quarter circles四分之一圆
  38.    theta = 0:pi/20:pi/2;
  39.    u1 = 2*cos(theta) - 1;
  40.    v1 = 2*sin(theta) - 1;
  41.    u2 = 2*cos(theta+pi/2) + 1;
  42.    v2 = 2*sin(theta+pi/2) - 1;
  43.    u3 = 2*cos(theta+pi) + 1;
  44.    v3 = 2*sin(theta+pi) + 1;
  45.    u4 = 2*cos(theta-pi/2) - 1;
  46.    v4 = 2*sin(theta-pi/2) + 1;
  47.    
  48.    initialize_graphics
  49.  
  50.    % Loop
  51.    k = 0;
  52.    while get(klose,'Value') == 0
  53.       if k <= 285
  54.           if mod(k,n) == 0
  55.              scaled_power
  56.              switch mod(k/n,4)
  57.                 case 0, up
  58.                 case 1, left
  59.                 case 2, down
  60.                 case 3, right
  61.              end
  62.           end
  63.           zoom_in
  64.           k = k+1;
  65.       else
  66.           break
  67.       end
  68.    end
  69.    pause(1)   
  70.    clf
  71.    show_quote
  72.  
  73. % ------------------------------------
  74.  
  75.    function scaled_power
  76.       a = s;
  77.       s = phi*s;
  78.       t = phi*t;
  79.    end % scaled_power
  80.  
  81. % ------------------------------------
  82.  
  83.    function zoom_in
  84.       axis(f*axis)
  85.       drawnow
  86.    end % zoom_in
  87.  
  88. % ------------------------------------
  89.  
  90.    function right
  91.       x = x + s;
  92.       y = y + t;
  93.       line(x+a*us,y+a*vs,'Color','black')
  94.       line(x+a*u4,y+a*v4)
  95.    end % right
  96.  
  97. % ------------------------------------
  98.  
  99.    function up
  100.       y = y + s;
  101.       x = x - t;
  102.       line(x+a*us,y+a*vs,'Color','black')
  103.       line(x+a*u1,y+a*v1)
  104.    end % up
  105.  
  106. % ------------------------------------
  107.  
  108.    function left
  109.       x = x - s;
  110.       y = y - t;
  111.       line(x+a*us,y+a*vs,'Color','black')
  112.       line(x+a*u2,y+a*v2)
  113.    end % left
  114.  
  115. % ------------------------------------
  116.  
  117.    function down
  118.       y = y - s;
  119.       x = x + t;
  120.       line(x+a*us,y+a*vs,'Color','black')
  121.       line(x+a*u3,y+a*v3)
  122.    end % down
  123.  
  124. % ------------------------------------
  125.  
  126.    function initialize_graphics
  127.       clf reset
  128.       set(gcf,'Color','white','Menubar','none','Numbertitle','off', ...
  129.           'Name','The Golden Spiral')
  130.       shg
  131.       axes('Position',[0 0 1 1])
  132.       axis(3.5*[-1 1 -1 1])
  133.       axis square
  134.       axis off
  135.       line(us,vs,'Color','black')
  136.       line(u4,v4)
  137.       klose = uicontrol('Units','normal','Position',[.04 .04 .12 .04], ...
  138.          'Style','togglebutton','String','close','Visible','on');
  139.       drawnow
  140.     end % initialize graphics
  141.  
  142.     function show_quote  
  143.       large_text = cell(4,1);
  144.       large_text{1} = transform('Gur puvrs sbezf bs ornhgl ner');
  145.       large_text{2} = transform('beqre naq flzzrgel naq qrsvavgrarff,');
  146.       large_text{3} = transform('juvpu gur zngurzngvpny fpvraprf');
  147.       large_text{4} = transform('qrzbafgengr va n fcrpvny qrterr.');
  148.       medium_text = transform('- Nevfgbgyr');
  149.  
  150.       text(0.5, 0.6, large_text, 'HorizontalAlignment', 'center', 'Color', [0 0.4470 0.7410], 'FontWeight', 'bold', 'FontSize', 14);
  151.       text(0.5, 0.4, medium_text, 'HorizontalAlignment', 'center', 'Color', [0 0.4470 0.7410], 'FontWeight', 'bold', 'FontSize', 12);
  152.  
  153.       axis off      
  154.       drawnow
  155.     end % show quote
  156.  
  157.     function s2 = transform(s1)
  158.       m25=1:256;i17=97;m25(i17:i17+25)=[i17+13:i17+25 i17:i17+12];
  159.       i17=65;m25(i17:i17+25)=[i17+13:i17+25 i17:i17+12];
  160.       s2=char(m25(s1));
  161.     end % transform
  162. end % golden_spiral
  163.  
  164.

习题

符号运算

  1. x=sym('x'),length(char(x)) %字符数组的长度
  2. for k = 1:10
  3.     x=sqrt(1+x),length(char(x))
  4. end

固定点

  1. function fixedpoint(f,xmin,xmax,xstart);
  2. % FIXEDPOINT  Illustrate fixed point iteration.
  3. % fixedpoint(f,xmin,xmax,xstart) tries to solve x = f(x).
  4. % Examples
  5. %   f = @(x) sqrt(1+x); fixedpoint(f, -1, 4, 0)  (Default)
  6. %   f = @(x) 1./x+1; fixedpoint(f, .5, 2.5, 1)
  7. %   f = @(x) cos(x); fixedpoint(f, -pi/4, pi/2, 0)
  8. %   a = sqrt(2); f = @(x) a.^x; fixedpoint(f, 1, 5, 3)
  9. %   a = 3+randn, f = @(x) a*x.*(1-x); ...
  10. %      fixedpoint(f, 0, 1, .5), title([num2str(a) '*x*(1-x)'])  
  11.  
  12. % Default example
  13.  
  14. if nargin == 0
  15.    f = @(x) sqrt(1 + x);
  16.    xmin = -1;
  17.    xmax = 4;
  18.    xstart = 0;
  19. end
  20.  
  21. % Iteration
  22.  
  23. x = xstart;
  24. y = f(x);
  25. n = 1;
  26. while (x(n) ~= y(n)) & (n < 50) & (max(abs(y)) < 100)
  27.    n = n+1;
  28.    x(n) = y(n-1);
  29.    y(n) = f(x(n));
  30. end
  31.  
  32. % Plot
  33.  
  34. t = sort([xmin:(xmax-xmin)/256:xmax x]);
  35. x = [x; x];
  36. y = [x(1) y(1:n-1); y];
  37. plot(t,t,'-',t,f(t),'-',x(:),y(:),'k-',x(end),y(end),'ro');
  38. axis tight square
  39. set(zoom(gcf),'ActionPostCallback','zoomer')

WHY

  1. why,help why
  2. for k= 1:40,why,end
  3. type why
  4. edit why

Matlab中why函数（一个无用但有趣的函数）_matlab好玩的函数_gxgdcyy的博客-CSDN博客

hello world

  1.    help hello_world
  2.    format loose
  3.  
  4. %% Array operations
  5.  
  6.    h = 'hello world'
  7.    h'
  8.    fliplr(h)
  9.    flipud(h')
  10.    diag(h)
  11.    sort(h)
  12.  
  13. %% Characters
  14.  
  15.    x = real(h)
  16.    char(x)
  17.    char(max(h))
  18.    char(x+3)
  19.  
  20. %% Plots
  21.  
  22.    H = upper(h)
  23.    
  24.    figure(1)
  25.    plot(x,'*-')
  26.    title(H)
  27.    
  28.    figure(2)
  29.    bar(x)
  30.    set(gca,'xticklabel',{H(:)})
  31.    set(2,'pos',get(1,'pos')+[30 -30 0 0])
  32.    
  33.    figure(3)
  34.    p = pie(x);
  35.    for k = 1:11
  36.       set(p(2*k),'string',H(k))
  37.    end
  38.    set(3,'pos',get(1,'pos')+[60 -60 0 0])

Goldrect

  1. % GOLDRECT
  2.  
  3. phi=(1+sqrt(5))/2;                  
  4. x=[0 phi phi 0 0];          %行数组x和y各包含5个元素；
  5. y=[0 0 1 1 0];              %分别是(0,0)(phi,0),(phi,1),(0,1),(0,0);      
  6. u=[1 1];
  7. v=[0 1];                    %矩形分割线；
  8. plot(x,y,'b',u,v,'b--')
  9. text(phi/2,1.05,'\phi')           %在（phi/2,1.05）处标记；
  10. text((1+phi)/2,-.05,'\phi-1')
  11. text(-.05,.5,'1')
  12. text(.5,-.05,'1')
  13. axis equal                       %使x和y方向的刻度长短相等；
  14. axis off                          %使坐标轴消隐；
  15. set(gcf,'color','white')           %gcf是指get current figure-将背景色设为白色；

 

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