黄金分割比

format

for循环

%% For loop
   x = 42
   for k = 1:12
      x = sqrt(1+x);
      disp(x)
   end

while循环

%% While loop
   x = 42;
   k = 1;
   while abs(x-sqrt(1+x)) > 5e-5
      x = sqrt(1+x);
      k = k+1;
   end
   k

绘图语句

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

黄金螺旋线


function golden_spiral
% GOLDEN_SPIRAL  Explosion of golden rectangles.
%    GOLDEN_SPIRAL  Constructs a continuously expanding sequence
%    of golden rectangles and inscribed quarter circles.

%   Copyright 2020 The MathWorks, Inc.
%  
%   Text used in the show_quote function:
%   Jones, Robert Bishop. 揂ristotle METAPHYSICA Book 13 Part 3.� Aristotle METAPHYSICA Book 13 Part 3 
%       Mathematics, Harmonics, Optics, Good and Beauty, 25 Nov. 1996, 
%       www.rbjones.com/rbjpub/philos/classics/aristotl/m11303c.htm.

   % Initialize_variables
   klose = [];
   
   % Golden ratio
   phi = (1+sqrt(5))/2;

   % Control speed of zooming in控制缩放速度
   n = 48;
   f = phi^(1/n);

   % Scaling
   a = 1;
   s = phi;
   t = 1/(phi+1);

   % Centers
   x = 0;
   y = 0;

   % A square
   us = [-1 1 1 -1 -1];
   vs = [-1 -1 1 1 -1];

   % Four quarter circles四分之一圆
   theta = 0:pi/20:pi/2;
   u1 = 2*cos(theta) - 1;
   v1 = 2*sin(theta) - 1;
   u2 = 2*cos(theta+pi/2) + 1;
   v2 = 2*sin(theta+pi/2) - 1;
   u3 = 2*cos(theta+pi) + 1;
   v3 = 2*sin(theta+pi) + 1;
   u4 = 2*cos(theta-pi/2) - 1;
   v4 = 2*sin(theta-pi/2) + 1;
   
   initialize_graphics

   % Loop
   k = 0;
   while get(klose,'Value') == 0
      if k <= 285
          if mod(k,n) == 0
             scaled_power
             switch mod(k/n,4)
                case 0, up
                case 1, left
                case 2, down
                case 3, right
             end
          end
          zoom_in
          k = k+1;
      else
          break
      end
   end
   pause(1)   
   clf
   show_quote

% ------------------------------------

   function scaled_power
      a = s;
      s = phi*s;
      t = phi*t;
   end % scaled_power

% ------------------------------------

   function zoom_in
      axis(f*axis)
      drawnow
   end % zoom_in

% ------------------------------------

   function right
      x = x + s;
      y = y + t;
      line(x+a*us,y+a*vs,'Color','black')
      line(x+a*u4,y+a*v4)
   end % right

% ------------------------------------

   function up
      y = y + s;
      x = x - t;
      line(x+a*us,y+a*vs,'Color','black')
      line(x+a*u1,y+a*v1)
   end % up

% ------------------------------------

   function left
      x = x - s;
      y = y - t;
      line(x+a*us,y+a*vs,'Color','black')
      line(x+a*u2,y+a*v2)
   end % left

% ------------------------------------

   function down
      y = y - s;
      x = x + t;
      line(x+a*us,y+a*vs,'Color','black')
      line(x+a*u3,y+a*v3)
   end % down

% ------------------------------------

   function initialize_graphics
      clf reset
      set(gcf,'Color','white','Menubar','none','Numbertitle','off', ...
          'Name','The Golden Spiral')
      shg
      axes('Position',[0 0 1 1])
      axis(3.5*[-1 1 -1 1])
      axis square
      axis off
      line(us,vs,'Color','black')
      line(u4,v4)
      klose = uicontrol('Units','normal','Position',[.04 .04 .12 .04], ...
         'Style','togglebutton','String','close','Visible','on');
      drawnow
    end % initialize graphics

    function show_quote  
      large_text = cell(4,1);
      large_text{1} = transform('Gur puvrs sbezf bs ornhgl ner');
      large_text{2} = transform('beqre naq flzzrgel naq qrsvavgrarff,');
      large_text{3} = transform('juvpu gur zngurzngvpny fpvraprf');
      large_text{4} = transform('qrzbafgengr va n fcrpvny qrterr.');
      medium_text = transform('- Nevfgbgyr');

      text(0.5, 0.6, large_text, 'HorizontalAlignment', 'center', 'Color', [0 0.4470 0.7410], 'FontWeight', 'bold', 'FontSize', 14);
      text(0.5, 0.4, medium_text, 'HorizontalAlignment', 'center', 'Color', [0 0.4470 0.7410], 'FontWeight', 'bold', 'FontSize', 12);

      axis off      
      drawnow
    end % show quote

    function s2 = transform(s1)
      m25=1:256;i17=97;m25(i17:i17+25)=[i17+13:i17+25 i17:i17+12];
      i17=65;m25(i17:i17+25)=[i17+13:i17+25 i17:i17+12];
      s2=char(m25(s1));
    end % transform
end % golden_spiral

习题

符号运算

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

固定点

function fixedpoint(f,xmin,xmax,xstart);
% FIXEDPOINT  Illustrate fixed point iteration.
% fixedpoint(f,xmin,xmax,xstart) tries to solve x = f(x).
% Examples
%   f = @(x) sqrt(1+x); fixedpoint(f, -1, 4, 0)  (Default)
%   f = @(x) 1./x+1; fixedpoint(f, .5, 2.5, 1)
%   f = @(x) cos(x); fixedpoint(f, -pi/4, pi/2, 0)
%   a = sqrt(2); f = @(x) a.^x; fixedpoint(f, 1, 5, 3)
%   a = 3+randn, f = @(x) a*x.*(1-x); ...
%      fixedpoint(f, 0, 1, .5), title([num2str(a) '*x*(1-x)'])  

% Default example

if nargin == 0
   f = @(x) sqrt(1 + x);
   xmin = -1;
   xmax = 4;
   xstart = 0;
end

% Iteration

x = xstart;
y = f(x);
n = 1;
while (x(n) ~= y(n)) & (n < 50) & (max(abs(y)) < 100)
   n = n+1;
   x(n) = y(n-1);
   y(n) = f(x(n));
end

% Plot

t = sort([xmin:(xmax-xmin)/256:xmax x]);
x = [x; x];
y = [x(1) y(1:n-1); y];
plot(t,t,'-',t,f(t),'-',x(:),y(:),'k-',x(end),y(end),'ro');
axis tight square
set(zoom(gcf),'ActionPostCallback','zoomer')

WHY

why,help why
for k= 1:40,why,end
type why
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

   help hello_world
   format loose

%% Array operations

   h = 'hello world'
   h'
   fliplr(h)
   flipud(h')
   diag(h)
   sort(h)

%% Characters

   x = real(h)
   char(x)
   char(max(h))
   char(x+3)

%% Plots

   H = upper(h)
   
   figure(1)
   plot(x,'*-')
   title(H)
   
   figure(2)
   bar(x)
   set(gca,'xticklabel',{H(:)})
   set(2,'pos',get(1,'pos')+[30 -30 0 0])
   
   figure(3)
   p = pie(x);
   for k = 1:11
      set(p(2*k),'string',H(k))
   end
   set(3,'pos',get(1,'pos')+[60 -60 0 0])

Goldrect

% GOLDRECT

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