Octave Language Learning

Octave为GNU项目下的开源软件,可以快速实现算法的一种原型语言。在线Web地址：

Octave is a free open source software under the GNU prject,which can rapidly implement algorithm.

Installation on Archlinux：sudo pacman -S octave,enter the shell：octave,shows the following:

GNU Octave, version 5.1.0
Copyright (C) 2019 John W. Eaton and others.
This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  For details, type 'warranty'.

Octave was configured for "x86_64-pc-linux-gnu".

Additional information about Octave is available at https://www.octave.org.

Please contribute if you find this software useful.
For more information, visit https://www.octave.org/get-involved.html

Read https://www.octave.org/bugs.html to learn how to submit bug reports.
For information about changes from previous versions, type 'news'.

octave:1>

Basic opeation

common variables

octave:5> 1+1
ans =  2
octave:6> 3-6
ans = -3
octave:7> 5*3
ans =  15
octave:8> 4/5
ans =  0.80000
octave:9> 1==2 %false
ans = 0
octave:10> 1==1 %true
ans = 1
octave:11> 1 && 0 % AND
ans = 0
octave:12> 1 || 0 % OR
ans = 1

use PS1() to change the default prompt:

octave:14> PS1('( つ•̀ω•́)つ ')
( つ•̀ω•́)つ A = [1,2,3;4,5,6;7,8,9]
A =

   1   2   3
   4   5   6
   7   8   9
( つ•̀ω•́)つ PS1('>>')
>>

semicolon supress output

>> a = 3
a =  3
>> a = 3;
>> a
a = 3
>> a;

disp() is used to display,sprintf() is used to format string output:

>>pi = 3.1415926;
>>disp(pi)
 3.1416
>>disp(sprintf('pi is: %0.2f',pi))
pi is: 3.14

format [long|short] is used to change the precision.

matrix and vector

A is a 3x2 matrix,x is a 3x1 vector,y is a 1x3 vector.
ones() returns a matrix with all elements 1.
zeros() returns a matrix with all elements 0.
rand() returns a matrix with all elements random number.
eye() returns a identity matrix.
size() returns the size of the matrix.
length() returns the larger dimension of the matrix,for vector it returns the length of it.
A(x,y) returns the A[x][y] element.

>>A = [1,2,3;4,5,6]
A =

   1   2   3
   4   5   6

>>A(1,3)
ans =  3

>>A(2,:) % means every element along that column/row
ans =

   4   5   6

>>A(:,[1,2])
ans =

   1   2
   4   5

>>size(A)
ans =

   2   3

>>x = [3;4;5]
x =

   3
   4
   5

>>y = [1,2,3]
y =

   1   2   3

>>v = 1:6 
v =

   1   2   3   4   5   6

>>v = [1 2 3 4]
v =

   1   2   3   4

>>length(A)
ans =  3
>>length(v)
ans =  4

>>ones(2,3)
ans =

   1   1   1
   1   1   1

>>eye(3)
ans =

Diagonal Matrix

   1   0   0
   0   1   0
   0   0   1

>>A = [A,[7;8]] % append a column to matrix
A =

   1   2   3   7
   4   5   6   8

>>A(:) % put all elements of A into a single vector
ans =

   1
   4
   2
   5
   3
   6
   7
   8

>>A = [A;[9,10,11,12]] % append a row to the matrix
A =

    1    2    3    7
    4    5    6    8
    1    2    3    4
    9   10   11   12

use hist() to plot a histogram

>>w = randn(1,10000)
>>hist(w)

Data Persist

use help <cmd> to refer to the manual of cmd

>>help eye
>>help rand

use pwd to get present working directory,use cd to change directory,ls to list the files:

>>pwd
ans = /home/xuranus
>>cd ~/Desktop/
>>pwd
ans = /home/xuranus/Desktop

use who to list all the variable in current working space while whos list the detail. save(filename) can save all the data to the disk,when the second variable is speified like save('xxx',v),only the specified variable v will be persisted .clear can clear all the data,and then we use whoagain to check if there exists any variable(of course there doesn’t).By using load(filename) we can restore the variable we cleared from file.

>>who
Variables in the current scope:
A    a    ans  p    pi   v    w    x    y
>>save('test1.dat')
>>ls
test.dat
>>clear
>>who
>>load('test1.dat')
>>whos
Variables in the current scope:

   Attr Name        Size                     Bytes  Class
   ==== ====        ====                     =====  ===== 
        A           2x3                         48  double
        a           1x1                          8  double
        ans         1x21                        21  char
        p           3x1                         24  double
        pi          1x1                          8  double
        v           1x4                         32  double
        w           1x10000                  80000  double
        x           3x1                         24  double
        y           1x3                         24  double

Total is 10042 elements using 80189 bytes

Computing On Data

. denotes element wise operation,which is different from common matrix arthmetic operation.
pinv() returns the reverse of A.
A' means transpose of matrix A.

>>> A = [1 2; 3 4; 5 6]
A =

   1   2
   3   4
   5   6

>>> B = [4 5 6;7 8 9]
B =

   4   5   6
   7   8   9

>>> A'
ans =

   1   3   5
   2   4   6

>>> A*B
ans =

   18   21   24
   40   47   54
   62   73   84

>>> A.*B
error: product: nonconformant arguments (op1 is 3x2, op2 is 2x3)
>>> C = [6 7 8;9 10 11]
C =

    6    7    8
    9   10   11

>>> B.*C
ans =

   24   35   48
   63   80   99

>>> B./C
ans =

   0.66667   0.71429   0.75000
   0.77778   0.80000   0.81818

>>> B.+C
ans =

   10   12   14
   16   18   20

>>> A.^2 % element-wise square
ans =

    1    4
    9   16
   25   36

when a single parameter function applied to vector or matrix, it performs an element-wise operation.

>>> v = 1:6
v =

   1   2   3   4   5   6

>>> log(v)
ans =

   0.00000   0.69315   1.09861   1.38629   1.60944   1.79176

the use of max(vector):

>> A
A =

   1   2
   3   4
   5   6

>> v = 1:6
v =

   1   2   3   4   5   6

>> max(v) % return the maximum number
ans =  6
>> [num,index] = max(v) % return the maximum number and corresponding index
num =  6
index =  6
>> max(A)
ans =

   5   6

>> v>3 % return each element is larger than 3 or not
ans =

  0  0  0  1  1  1

octave:10> find(v>3) % filter the element larger than 3
ans =

   4   5   6

magic() returns a nxn matrix whose row, column, diagnoal add up to the same thing.

>> magic(3)
ans =

   8   1   6
   3   5   7
   4   9   2

prod() returns the product of vector.
sum() return the sum of the vector.
ceil() means get rounded up while floor() means get rounded down.

>>> v = [1 6 4 3.5]
v =

   1.0000   6.0000   4.0000   3.5000

>>> prod(v) 
ans =  84
>>> sum(v)
ans =  14.500
>>> floor(v)
ans =

   1   6   4   3

>>> ceil(v)
ans =

   1   6   4   4

max(A1,A2) returns a new matrix ,every element of which is the larger one.
max(A,[],1) compares the first dimension(the column) and returns a vector ,the ith element is the maximum in the ith column.
if you need to find the maximum number in A,you can type max(max(A)) or max(A(:))

>>> A = magic(3)
A =

   8   1   6
   3   5   7
   4   9   2

>>> B = A'
B =

   8   3   4
   1   5   9
   6   7   2

>>> max(A,B)
ans =

   8   3   6
   3   5   9
   6   9   2

>>> max(A,[],1)
ans =

   8   9   7

>>> max(A,[],2)
ans =

   8
   7
   9

sum(A) and sum(A,1) returns the sum of each column in matrix A.
sum(A,2) return the sum of each row in matrix.
if we need to calculate sum of all elements in A, we can use sum(sum(A)) or sum(A(:))

>>> A
A =

   17   24    1    8   15
   23    5    7   14   16
    4    6   13   20   22
   10   12   19   21    3
   11   18   25    2    9

>>> sum(A)
ans =

   65   65   65   65   65

>>> sum(A,1)
ans =

   65   65   65   65   65

>>> sum(A,2)
ans =

   65
   65
   65
   65
   65

Plotting Data

>> t = [0:0.01:0.98]; % vector t from 0 - 0.98 step 0.01
>> y = sin(2*pi*4*t); % vector y
>> plot(t,y)
>> close % close the plotting window

>> t = [0:0.01:0.98]; % vector t from 0 - 0.98 step 0.01
>> y1 = sin(2*pi*4*t); % vector y
>> plot(t,y1);
>> hold on % wait for another plot
>> y2 = cos(2*pi*4*t);
>> plot(t,y2)
>> ylabel('value')
>> xlabel('time')
>> legend('sin','cos') % legend
>> title('my plot')
>> print -dpng 'myplot.png' % save to file
>> close

if you want to plot figure in mutiple windows:

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

>> subplot(1,2,1) % divides plot a 1x2 grid,acesss the 1st element
>> plot(t,y1)
>> subplot(1,2,2)
>> plot(t,y2)
>> axis([0.5 1 -1 1])

>> A = magic(5)
A =

   17   24    1    8   15
   23    5    7   14   16
    4    6   13   20   22
   10   12   19   21    3
   11   18   25    2    9

>> imagesc(A)
>> imagesc(A),colorbar,colormap gray % comma chaining of function call

Control Statement

for

>> v = 1:10
>> for i=1:10,
>   v(i) = 2^i;
> end;
>> v
v =
      2      4      8     16     32     64    128    256    512   1024

v = zeros(10, 1);
for i = 1:10
  for j = 1:10
    v(i) = v(i) + A(i, j) * x(j);
  end
end

while

>> v = 1:10
>> while i<=5,
>   v(i) = 100
>   i = i+1;
> end;
>> v
v = 
    100    100    100    100    100     6    7    8    9   10

>> v = 1:10
>> while true,
>    v(i) = 100
>    i = i+1;
>    if i == 6,
>      break;
>    end;
> end;
>> v
v = 
    100    100    100    100    100     6    7    8    9   10

if

>> v = 1:10
v =

    1    2    3    4    5    6    7    8    9   10

>> if v(1)==1,
>   disp('value is one');
> elseif v(1)==2,
>   disp('value is two');
> end;
value is one

functions

define a octave function and write to file squareAndCube.m (function name must correspond to filename):

function [y1,y2] = squareAndCube(x)

y1 = x^2;
y2 = x^3;

end;

enter the octave shell:

>> addpath('path to the file')
>> squareAndCube(4)
ans =  16