octave tutorial 2

Computing on Data

• matrix multiply

    a = [1 2; 3 4; 5 6]
    a =
      
       1   2
       3   4
       5   6
  
    b = [11 22; 33 44; 55 66]
    b =
      
       11   22
       33   44
       55   66
  
      
    c = [1 1; 2 2]
    c =
      
       1   1
       2   2
  
    a * c 
    >>
    ans =
  
        5    5
       11   11
       17   17
  
    % 單乘一個 (times element y only)
    a .* b
    ans =
      
        11    44
        99   176
       275   396
  
    % .(times element y only) 
    a .^2
    ans =
  
     1    4
     9   16
    25   36
      
    v = [1; 2; 3]
    v =
      
       1
       2
       3
      
    1 ./ v
    ans =
      
       1.00000
       0.50000
       0.33333
  

• log
  • wiki
  • khan-academy

    v = [1; 2; 3]
    v =
      
       1
       2
       3
      
    log(v)
    ans =
      
       0.00000
       0.69315
       1.09861
      
  

• exp
  • wiki
  • khan-academy

    exp(v)
    ans =
  
    2.7183
    7.3891
   20.0855 
  

• transpose

   A = [1 2; 3 4; 5 6]
   A =
  
   1   2
   3   4
   5   6
  
   A'
   ans =
  
   1   3   5
   2   4   6
  

• max

  a = [1 15 2 0.5]
  a =
  
    1.00000   15.00000    2.00000    0.50000 
  
  max(a)
  15
  
  A = [1 2; 3 4; 5 6];
  max(A)
  ans = 
     5  6
  
  
  a < 3
  ans =
  
  1  0  1  1
  
  find(a< 3)
  ans =
  
   1   3   4
  

• magic

   % A magic square is an arrangement of the integers '1:n^2' such that
     the row sums, column sums, and diagonal sums are all equal to the
     same value.
      
   A = magic(3)
   A =
  
   8   1   6
   3   5   7
   4   9   2
  
   A = magic(9)
   A =
     
      47   58   69   80    1   12   23   34   45
      57   68   79    9   11   22   33   44   46
      67   78    8   10   21   32   43   54   56
      77    7   18   20   31   42   53   55   66
       6   17   19   30   41   52   63   65   76
      16   27   29   40   51   62   64   75    5
      26   28   39   50   61   72   74    4   15
      36   38   49   60   71   73    3   14   25
      37   48   59   70   81    2   13   24   35
     
   sum(A, 1)
   ans =
     
      369   369   369   369   369   369   369   369   369
  
   sum(A, 2)
   ans =
     
      369
      369
      369
      369
      369
      369
      369
      369
      369
  

• sum
• prod
• floor

• ceil

• flipud

       flipud(eye(9))
   ans =
     
   Permutation Matrix
     
      0   0   0   0   0   0   0   0   1
      0   0   0   0   0   0   0   1   0
      0   0   0   0   0   0   1   0   0
      0   0   0   0   0   1   0   0   0
      0   0   0   0   1   0   0   0   0
      0   0   0   1   0   0   0   0   0
      0   0   1   0   0   0   0   0   0
      0   1   0   0   0   0   0   0   0
      1   0   0   0   0   0   0   0   0
  

• pinv

   A = magic(3)
   A =
     
      8   1   6
      3   5   7
      4   9   2
     
   pinv(A)
   ans =
     
      0.147222  -0.144444   0.063889
     -0.061111   0.022222   0.105556
     -0.019444   0.188889  -0.102778
     
   temp = pinv(A);
   temp* A
   ans =
     
      1.00000   0.00000  -0.00000
     -0.00000   1.00000   0.00000
      0.00000   0.00000   1.00000
  

Plotting Data

• plot

   t = [0 : 0.01 : 0.98]
   y1 = sin(2*pi*4*t)
   plot(t, y1)
   y2 = cos(2*pi*4*t)
   plot(t, y2)
  

• plot in the same plot

   t = [0 : 0.01 : 0.98]
   y1 = sin(2*pi*4*t)
   y2 = cos(2*pi*4*t)
   plot(t, y1)
   hold on;
   plot(t, y2, 'r') % 紅色的線
   xlabel('time')
   ylabel('value')
   legend('sin', 'cos')
   title('my plot')
  

• 出圖

   print -dpng 'xxx.png'
  

• close
  • close plot
• figure

   figure(1): plot(t, y1);
   figure(2): plot(t, y2)
  

• subplot

   subplot(1, 2, 1); % Divides plot a 1 x2 grid, access first element
   plot(t,y1)
   subplot(1, 2, 2)
   plot(t,y2)
  

• imagesc % 水水的格子

   A = magic(9);
   imagesc(A)
  
   % colorbar
   imagesc(A), colorbar, colormap gray;