GNU Octave 2020

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There are several tools that can help us to learn machine learning algorithms such as Matlab, NumPy, R, and Octave, etc. Among them, we're going to use Octave which seems to be most effective in terms of learning curve and features it has.

So, let's install Octave from sourceforge.net.

To customize the prompt, we use PS1(). In this case, we want to switch it to ">> ".

PS1 (">> ")

To check current directory:

>> pwd
ans = C:\Octave\3.2.4_gcc-4.4.0\bin

To draw histogram from the Gaussian distribution with 50 intervals:

>> w = 5 + sqrt(10)*(randn(1,1000))
>> hist(w,50)

Then, we get this picture:

>> % Matrix
>> m = [1 2; 3 4; 5 6]
m =
   1   2
   3   4
   5   6
>> size(m)
ans =
   3   2
>> m(2,:)  % 2nd row only
ans =

   3   4
>> m(:,2)  % 2nd column only
ans =

   2
   4
   6
>> m([1:3],:)  % all
ans =

   1   2
   3   4
   5   6

>> m([1 3],:)  % 1st & 3rd rows only
ans =

   1   2
   5   6

To check the variable:

>> who
Variables in the current scope:

ans  m    w

>> whos  % for more info
Variables in the current scope:

  Attr Name        Size                     Bytes  Class
  ==== ====        ====                     =====  =====
       ans         1x29                        29  char
       m           3x2                         48  double
       w           1x1000                    8000  double

Total is 1035 elements using 8077 bytes

Here is how to load a data file:

>> cd 'c:\test'
>> load('population.txt')
>> who
Variables in the current scope:

ans         m           population  w

>> whos
Variables in the current scope:

  Attr Name            Size                     Bytes  Class
  ==== ====            ====                     =====  =====
       ans             1x7                          7  char
       m               3x2                         48  double
       population     19x2                        304  double
       w               1x1000                    8000  double

Total is 1051 elements using 8359 bytes

>> population
population =

      1    200
   1000    310
   1750    791
   1800    978
   1850   1262
   1900   1650
   1950   2519
   1955   2756
   1960   2982
   1965   3335
   1970   3692
   1975   4068
   1980   4435
   1985   4831
   1990   5263
   1995   5674
   2000   6070
   2005   6454
   2010   6972

Here is how to remove data:

>> whos
Variables in the current scope:

  Attr Name            Size                     Bytes  Class
  ==== ====            ====                     =====  =====
       ans             1x7                          7  char
       m               3x2                         48  double
       population     19x2                        304  double
       w               1x1000                    8000  double

Total is 1051 elements using 8359 bytes

>> clear w
>> whos
Variables in the current scope:

  Attr Name            Size                     Bytes  Class
  ==== ====            ====                     =====  =====
       ans             1x7                          7  char
       m               3x2                         48  double
       population     19x2                        304  double

Total is 51 elements using 359 bytes

Here is how to save data: take the most recent population data from 11th row to 19th row, and then save it to recent.data file.

>> v = population(11:19)
v =

   1970   1975   1980   1985   1990   1995   2000   2005   2010

>> save recent.data v;

The saved recent.data file looks like this:

# Created by Octave 3.2.4, Tue Jul 02 15:53:33 2013 Pacific Daylight Time 
# name: v
# type: matrix
# rows: 1
# columns: 9
 1970 1975 1980 1985 1990 1995 2000 2005 2010

>> m(:,2) = [10; 11; 12;]  % assign new values to 2nd column
m =

    1   10
    3   11
    5   12
>> m = [m, [100; 101; 102]] % append another column
m =

     1    10   100
     3    11   101
     5    12   102
>> n = [1000; 1001; 1002]
n =

   1000
   1001
   1002

>> r = [m n]  % column-wise append 
r =

      1     10    100   1000
      3     11    101   1001
      5     12    102   1002
>> n = [1000 1001 1002]
n =

   1000   1001   1002
>> s = [m; n]  % row-wise append
s =

      1     10    100
      3     11    101
      5     12    102
   1000   1001   1002
>> s(:)  % put all elements of m into a column vector
ans =

      1
      3
      5
   1000
     10
     11
     12
   1001
    100
    101
    102
   1002
>> clear  % clear all
>> % Matrix Multiplication
>>
>> A = [1 2; 3 4; 5 6]
A =

   1   2
   3   4
   5   6

>> size(A)
ans =

   3   2

>> B = [10 11; 12 13;]
B =

   10   11
   12   13

>> size(B)
ans =

   2   2

>> C = A * B
C =

    34    37
    78    85
   122   133
>> size(C)
ans =

   3   2

>> % Element-wise multiplication using dot(.)
>> B = [10 11; 12 13; 14 15;]
B =

   10   11
   12   13
   14   15

>> A.*B
ans =

   10   22
   36   52
   70   90
>> A
A =

   1   2
   3   4
   5   6

>> A.^2  % A[i]^2
ans =

    1    4
    9   16
   25   36
>> A
A =

   1   2
   3   4
   5   6

>> 1./A  % inverse each element of A
ans =

   1.00000   0.50000
   0.33333   0.25000
   0.20000   0.16667
>> A'  % transpose of A
ans =

   1   3   5
   2   4   6
>> max(A) % column-wise max
ans =

   5   6
>> A <= 4 % element-wise comparison
ans =

   1   1
   1   1
   0   0

>> A = magic(9)  % Magic Square
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)  % column
ans =

   369   369   369   369   369   369   369   369   369

>> sum(A,2)  % row
ans =

   369
   369
   369
   369
   369
   369
   369
   369
   369
>> eye(9)
ans =

Diagonal Matrix

   1   0   0   0   0   0   0   0   0
   0   1   0   0   0   0   0   0   0
   0   0   1   0   0   0   0   0   0
   0   0   0   1   0   0   0   0   0
   0   0   0   0   1   0   0   0   0
   0   0   0   0   0   1   0   0   0
   0   0   0   0   0   0   1   0   0
   0   0   0   0   0   0   0   1   0
   0   0   0   0   0   0   0   0   1

>> sum(A .*eye(9))
ans =

   47   68    8   20   41   62   74   14   35

>> A.*eye(9)  % diagonal terms of A
ans =

   47    0    0    0    0    0    0    0    0
    0   68    0    0    0    0    0    0    0
    0    0    8    0    0    0    0    0    0
    0    0    0   20    0    0    0    0    0
    0    0    0    0   41    0    0    0    0
    0    0    0    0    0   62    0    0    0
    0    0    0    0    0    0   74    0    0
    0    0    0    0    0    0    0   14    0
    0    0    0    0    0    0    0    0   35
>> sum(sum(A.*eye(9))) % sum of the diagonal terms of A
ans =  369
>> flipud(A.*eye(9))
ans =

    0    0    0    0    0    0    0    0   35
    0    0    0    0    0    0    0   14    0
    0    0    0    0    0    0   74    0    0
    0    0    0    0    0   62    0    0    0
    0    0    0    0   41    0    0    0    0
    0    0    0   20    0    0    0    0    0
    0    0    8    0    0    0    0    0    0
    0   68    0    0    0    0    0    0    0
   47    0    0    0    0    0    0    0    0

>> 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
>> A *pinv(A)
ans =

  1.0000e+000  -1.2514e-014  6.1479e-015
  2.4633e-016  1.0000e+000  1.3878e-017
  -6.1062e-015  1.2382e-014  1.0000e+000

>> t = [0: 0.02: 2.0];
>> ys = sin(4*pi*t);
>> plot(t,ys)
>> hold on
>> yc = cos(4*pi*t);
>> plot(t,yc,'r')
>> xlabel('time')
>> ylabel('y')
>> legend('sin', 'cos')
>> title('Sin and Cos')

We can also save the plot:

>> print -dpng 'sin_cos.png'

To remove the picture, just type 'close'.

>> close

We can have two separate pictures on two windows: one for each window.

>> figure(1);plot(t,ys);
>> figure(2);plot(t,yc);

We can also draw two pictures side by side on one window using grid plot.

>> subplot(1,2,1):plot(t,ys);
>> subplot(1,2,2):plot(t,yc);axis[0 0.5 -1 1];

Note that we re-scale the second picture using 'axis' command.

We can clear the picture using 'clf'.

>> clf;

We can also convert the value to color.

>> 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
>> imagesc(A)

We can refine it more with magic square 25, and then add color bar on the right side of the picture.

>> imagesc(magic(25)), colorbar;

>> v = zeros(10, 1) % vector with 10 elements
v =

   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
>> for i = 1:10,
>      v(i) = i^3;
>  end;
>> v
v =

      1
      8
     27
     64
    125
    216
    343
    512
    729
   1000