Octave
Install
Refer https://www.gnu.org/software/octave/.
- Ubuntu:
apt-get install octave gnuplot - Max OSX:
brew tap homebrew/science && brew update && brew upgrade && brew install octave
Basic operations
Normal Equation: theta = inv(X'*X)*X'*y
What if X’X is non-invertible? theta = pinv(X'*X)*X'*y
PS1('>> ');
>> a=pi;
>> disp(a);
3.1416
>> disp(sprintf('2 decimals: %0.2f', a))
2 decimals: 3.14
>> A=[1 2;3 4; 5 6];
>> v=[1 2 3];
>> s=[1;2;3];
>> v=1:0.1:2
v =
1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000
>> ones(2,3)
ans =
1 1 1
1 1 1
zeros(1,3)
rand(3,3) % Return a matrix with random elements uniformly distributed on the interval (0, 1)
randn(3,3) % Return a matrix with normally distributed pseudo-random elements having zero mean and variance one
>> eye(4)
ans =
Diagonal Matrix
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
w = -6 + sqrt(10)*randn(1,10000);
hist(w)
hist(w, 50)
help eye
help rand
>> A=eye(3);
>> sz=size(A)
sz =
3 3
>> load data.dat % load data from file
>> data
data =
3232 3
2322 4
212 3
232 5
2342 3
>> who
Variables in the current scope:
A ans data sz
>> whos
Variables in the current scope:
Attr Name Size Bytes Class
==== ==== ==== ===== =====
A 3x3 24 double
ans 1x5 5 char
data 5x2 80 double
sz 1x2 16 double
Total is 26 elements using 125 bytes
>> save hello.dat data; % save data to file
>> clear % clear all vars
>> data
data =
3232 3
2322 4
212 3
232 5
2342 3
>> data(1,1)
ans = 3232
>> data([1,3],:) % get first line and third line data
ans =
3232 3
212 3
>> data(:, 2) % get second column data
ans =
3
4
3
5
3
>> data(:) % put all data in a single vector
ans =
3232
2322
212
232
2342
3
4
3
5
3
>> A=ones(3,2)
A =
1 1
1 1
1 1
>> B=eye(2)
B =
Diagonal Matrix
1 0
0 1
>> A*B
ans =
1 1
1 1
1 1
>> C=rand(3,2)
C =
0.24450 0.46890
0.60861 0.15189
0.12748 0.86532
>> A.*C
ans =
0.24450 0.46890
0.60861 0.15189
0.12748 0.86532
>> A.^2
ans =
1 1
1 1
1 1
>> v=[1;2;3]
v =
1
2
3
>> exp(v)
ans =
2.7183
7.3891
20.0855
>> 1./v
ans =
1.00000
0.50000
0.33333
>> v+1
ans =
2
3
4
C =
0.24450 0.46890
0.60861 0.15189
0.12748 0.86532
>> C'
ans =
0.24450 0.60861 0.12748
0.46890 0.15189 0.86532
octave:5> A
A =
1 2
3 4
2 3
octave:6> B
B =
2 2 3
3 2 90
octave:7> A*B
ans =
8 6 183
18 14 369
13 10 276
>> max(v)
ans = 3
>> max(A)
ans =
3 4
>> A=magic(3)
A =
8 1 6
3 5 7
4 9 2
>> [r,c]=find(A<3)
r =
1
3
c =
2
3
A =
8 1 6
3 5 7
4 9 2
>> max(A)
ans =
8 9 7
>> max(A, [], 1) % max of each column
ans =
8 9 7
>> max(A, [], 2) % max of each row
ans =
8
7
9
>> 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)
ans =
369 369 369 369 369 369 369 369 369
>> sum(A,2)
ans =
369
369
369
369
369
369
369
369
369
>> sum(sum(A))
ans = 3321
>> flipud(eye(3))
ans =
Permutation Matrix
0 0 1
0 1 0
1 0 0
>> A=magic(3)
A =
8 1 6
3 5 7
4 9 2
>> inv(A)
ans =
0.147222 -0.144444 0.063889
-0.061111 0.022222 0.105556
-0.019444 0.188889 -0.102778
>> pinv(A)
ans =
0.147222 -0.144444 0.063889
-0.061111 0.022222 0.105556
-0.019444 0.188889 -0.102778
>> A*inv(A)
ans =
1.0000e+00 7.6328e-17 -4.1633e-17
-2.7756e-17 1.0000e+00 6.9389e-17
2.0817e-17 2.0817e-17 1.0000e+00
>> v=zeros(10,1);
>> for i=1:10,
> v(i)=2^i;
> end
>> v
v =
2
4
8
16
32
64
128
256
512
1024
>> i=1;
>> while i<=5
> v(i)=100;
> i=i+1;
> end
>> v
v =
100
100
100
100
100
64
128
256
512
1024
>> clc
>> v=1:20;
>> if v(1)==1
> disp('v(1)==1')
> else
> disp('false')
> end
v(1)==1
% function definition
% # cat sq.m
function y=sq(x)
y=x*x;
Plot
>> t=[0:0.01:0.98];
>> y1=sin(2*pi*t);
>> plot(t,y1)
>>
>> y2=cos(2*pi*t);
>> plot(t,y2);
>>
>> plot(t,y1, 'b');hold on;plot(t, y2, 'r')
>>
>> plot(t,y1, 'b');hold on;plot(t, y2, 'r')
>> xlabel('time')
>> ylabel('value')
>> legend('sin', 'sos')
>> title('my plot')
>> print -dpng test.png
>> figure(1); plot(t, y1);
>> figure(2); plot(t, y2);
>> subplot(1,2,1); 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)
>> figure(3); imagesc(A); colorbar