Note for learning Octave
This post is for recording memos of learning Octave.
Installation
Install cygwin. Then add octave, gnuplot, xterm, xorg-server, xinit.
Operations
octave:1> 5+6
ans = 11
octave:2> 1/2
ans = 0.50000
octave:3> 2^6
ans = 64
octave:4> 6*7
ans = 42
octave:5> 1 == 2
ans = 0
octave:6> 1 ~= 2
ans = 1
octave:7> 1 && 0
ans = 0
octave:8> 1 || 0
ans = 1
octave:9> xor(1, 0)
ans = 1
Variables
octave:1> a = 1
a = 1
octave:2> b = 'str'
b = str
octave:3> c = 1.2; % semicolon supressing output
octave:4> d = 'OK' % comment
d = OK
octave:5> e=pi % pi is a reserved variable
e = 3.1416
octave:6> e
e = 3.1416
octave:9> format long
octave:10> e
e = 3.14159265358979
octave:11> format short
octave:12> e
e = 3.1416
octave:4> whos % use whos or who to show all variables in memory
Variables in the current scope:
Attr Name Size Bytes Class
==== ==== ==== ===== =====
ans 1x30 30 char
v 2x3 48 double
Total is 36 elements using 78 bytes
octave:6> clear % use clear to clean all variables in memory
Matrix related
octave:13> A = [1,2; 3,4; 5,6;] % 3x2 Matrix
A =
1 2
3 4
5 6
octave:15> A = [1,2; % Could do it in separate lines
> 3,4]
A =
1 2
3 4
octave:16> V = [1;2;3;4] % 4x1 colomn vector
V =
1
2
3
4
octave:21> v = 1:5
v =
1 2 3 4 5
octave:22> v = 1:0.2:3 % 1x11 row vector, start from 1, step with 0.2, end at 3
v =
Columns 1 through 8:
1.0000 1.2000 1.4000 1.6000 1.8000 2.0000 2.2000 2.4000
Columns 9 through 11:
2.6000 2.8000 3.0000
octave:22> ones(2,3) % generate a 2x3 matrix of all 1
ans =
1 1 1
1 1 1
octave:23> c = 8*ones(2,3)
c =
8 8 8
8 8 8
octave:24> zeros(1,3) % generate a 1x3 matrix of all 0
ans =
0 0 0
octave:25> rand(2,3) % generate a 2x3 martix filled with random number
ans =p
0.65891 0.64509 0.18112
0.97003 0.22631 0.37190
octave:2> I = eye(2) % generate a 2x2 identity matrix
I =
Diagonal Matrix
1 0
0 1
octave:14> I(2,:) % ":" means every element along that row/column
ans =
0 1
octave:15> A = [1 2; 3 4; 5 6]
A =
1 2
3 4
5 6
octave:16> A(:,2) = [7;8;9] % change the second column's value
A =
1 7
3 8
5 9
octave:17> A = [A, [10;11;12]] % append an column vector to right
A =
1 7 10
3 8 11
5 9 12
octave:18> size(A) % return matrix A's size
ans =
3 3
octave:19> A(:) % put all elements of A into a single vector
ans =
1
3
5
7
8
9
10
11
12
octave:22> A
A =
1 2
3 4
octave:23> B
B =
5 6
7 8
octave:24> [A B] % append B to the right of A
ans =
1 2 5 6
3 4 7 8
octave:25> [A ; B] % append B to the bottom of A
ans =
1 2
3 4
5 6
7 8
Display
octave:1> e=pi % pi is a reserved variable
e = 3.1416
octave:2> disp(e)
3.1416
octave:3> disp(sprintf('2 decimals: %0.2f', e))
2 decimals: 3.14
octave:12> hist(A) % display a histogram graphic for the matrix A
octave:2> PS1('>> ') % Change the prompt for the command line
>>
Data Save/Load
octave:1> v = rand(2,3)
v =
0.45578 0.13747 0.11531
0.43958 0.81255 0.42648
octave:2> save test.txt v % save v into test.txt in current directory
octave:8> load test.txt % load data from file test.txt into memory
octave:9> whos
Variables in the current scope:
Attr Name Size Bytes Class
==== ==== ==== ===== =====
v 2x3 48 double
Total is 6 elements using 48 bytes
octave:10> save test.txt v -ascii % save as ASCII type
Computation Operations
octave:1> A = [1 2 ; 3 4]
A =
1 2
3 4
octave:5> B = [10 11; 12 13]
B =
10 11
12 13
octave:6> A * B
ans =
34 37
78 85
octave:7> A .* B % Multiply each item in A to the corresponding item in B.
ans =
10 22
36 52
octave:8> A .^ 2 % Do the carry for each item
ans =
1 4
9 16
octave:9> -A % -1 * A
ans =
-1 -2
-3 -4
octave:10> A' % transpose of A
ans =
1 3
2 4
octave:15> [val, ind] = max(B(2,:)) % get the maximun number of second row, val is the maximun number and ind is the index of it
val = 13
ind = 2
octave:16> A < 3 % item wise operation, 1 means true and 0 means false
ans =
1 1
0 0
octave:20> [r, c] = find (A > 2) % r means row, c means column. These two array point to the position of items that satisfied with the condition.
r =
2
2
c =
1
2
octave:28> C = [1 2 3 4 ]
C =
1 2 3 4
octave:29> sum(C)
ans = 10
octave:30> prod(C)
ans = 24
octave:31> sum(A,1) % sum all elements in each column. 1 means column wise.
ans =
4 6
octave:32> sum(A,2) % sum all elements in each row. 2 means row wise.
ans =
3
7
octave:35> flipud(eye(3)) % Return a copy of eye(3) with the order of the rows reversed.
ans =
Permutation Matrix
0 0 1
0 1 0
1 0 0
octave:38> pinv(A) % Return the pseudoinverse of A
ans =
-2.00000 1.00000
1.50000 -0.50000
octave:39> A * pinv(A)
ans =
1.0000e+00 -4.4409e-16
1.3323e-15 1.0000e+00
Plotting Data
octave:15> x = [0:0.01:1]
octave:16> y1 = sin(4*pi*x)
octave:17> plot(x, y1) % we can see a graph with a sin(x) from 0 to 4pi
octave:18> y2 = cos(4*pi*x)
octave:19> plot(x, y2) % we can see a new graph with a cos(x) from 0 to 4pi
octave:20> hold on % this command will not clean the graph if a new graph is going to plot
octave:21> plot(x, y1, 'r') % there is a graph has the mixed sin(x) and cos(x) graph together will be shown. and the sin(x) will be drawn in red color.
octave:35> xlabel('time')
octave:36> ylabel('value')
octave:37> legend('sin', 'cos')
octave:38> title('my plot')
octave:40> print -dpng 'test.png' % output the graph to png format
octave:241 close % close the graph
octave:46> figure(1)
octave:47> plot(x, y1)
octave:48> figure(2)
octave:49> plot(x, y2)
octave:55> subplot(1,2,1) % divide plot to a 1x2 grid, and access the first element
octave:56> plot(x, y1)
octave:57> subplot(1,2,2) % access the second element
octave:58> plot(x, y2)
octave:60> axis([0.5, 1, -1, 1]) % change axis to x [0.5 to 1], y [-1 to 1]
octave:76> imagesc(rand(8:8))
octave:78> imagesc(rand(8:8)), colorbar, colormap gray % draw a colorbar and change the colormap to gray
octave:87> colormap default % change back to the normal colormap
octave:99> imagesc(magic(11)) % magic will return a magic matrix, and this can show the relationship between each element.
Control statement: for , while, if
octave:7> v = zeros(10,1)
v =
0
0
0
0
0
0
0
0
0
0
octave:8> for i=1:10
> v(i) = 2^i;
> end
octave:9> v
v =
2
4
8
16
32
64
128
256
512
1024
octave:12> i=1
i = 1
octave:13> while i<=5,
> v(i)=100,
> i=i+1,
> end;
octave:14> v
v =
100
100
100
100
100
64
128
256
512
1024
octave:16> if i==1,
> disp(1);
> elseif i==2,
> disp(2);
> else,
> disp(3)
> end;
1
Custom function
We can create a plain text file with name test1.m. Following is the content.
function y = test1(x)
y = x^2;
Than cd to the path of test1.m, and run the function.
octave:1> test1(2)
y = 4
ans = 4
Vectorization
Vectorization will make the computation more efficient.
For example, we have following vectors.
`u = [u1,u2,u3] , v = [v1,v2,v3] , w = [w1,w2,w3]`
Here is the implementation using iteration
for j = 1:3,
u(j) = 2 * v(j) + 5 w(j);
end
We can simplify it to do it as following
u = 2 * v + 5 * w
Here is another example, If `theta = [[theta1],[theta2],[theta3]], x = [[x1],[x2],[x3]],
h_theta(x) = sum_(j=0)^n theta_j x_j`
After vertorization
`h_theta(x) = theta^T x`