An Octave primer

Here is a simple Octave Primer. Octave is a powerful language for implementing Machine Learning algorithms. As I have mentioned its strength is its simplicity. I am including some basic commands with which you can get by implementing fairly complex code

%%Matrix
A matrix can be created as a = [1 2 3; 4 7 8; 12 35 14]; % This is 3 x 3 matrix
Matrix multiplication can be done between m x n * n x k matrix as follows

a = [4 56 3; 2 3 4]; b = [23 1; 3 12; 34 12]; % a = 3 x 2 matrix b = 2 x 3 matrix
c = a*b; %% c = 3 x 2 * 2 * 3 = 3 x 3 matrix

c =
362 712
191 86

%%Inverse of a matrix can be obtained by
d = pinv(c);
octave-3.2.4.exe:37> d = pinv(c)
d =
-8.2014e-004 6.7900e-003
1.8215e-003 -3.4522e-003

%%Transpose of a matrix
e = c'; % e is the transpose of done

octave-3.2.4.exe:38> e = c'
e =
362 191
712 86

The following operations are done on all elements of a matrix or a vector
k = 5;
a = [1 2; 3 4; 5 6]; k = 5.23;
c = k * a;
d = a - 2
e = a / 5
f = a .* a % Dot product
g = a .^2; % Square each elements

%% Select slice of matrix
b = a(:,2); % Select column 2 of matrix a (all rows)
c = a(2,:) % Select row of matrix 'a' (all columns)

d = [7 8; 8 9; 10 11; 12 13]; % 4 rows 2 columns
d(2:3,:); %Select from rows 2 to 3 (all columns)

octave-3.2.4.exe:41> d
d =
7 8
8 9
10 11
12 13
octave-3.2.4.exe:43> d(2:3,:)
ans =
8 9
10 11

%% Appending rows to matrix
a = [ 4 5; 5 6; 5 7; 9 8]; % 4 x 2
b = [ 1 3; 2 4]; % 2 x 2
c = [ a; b] % stack a over b
d = [b ; a] % stack b over a*b

octave-3.2.4.exe:44> a = [ 4 5; 5 6; 5 7; 9 8] % 4 x 2
a =
4 5
5 6
5 7
9 8

octave-3.2.4.exe:45> b = [ 1 3; 2 4] % 2 x 2
b =
1 3
2 4

octave-3.2.4.exe:46> c = [ a; b] % stack a over b
c =
4 5
5 6
5 7
9 8
1 3
2 4

octave-3.2.4.exe:47> d = [b ; a] % stack b over a*b
d =
1 3
2 4
4 5
5 6
5 7
9 8

%% Appending columns
a = [ 1 2 3; 3 4 5]; b = [ 1 2; 3 4];
c = [a b];
d = [b a];

octave-3.2.4.exe:48> a = [ 1 2 3; 3 4 5]
a =
1 2 3
3 4 5

octave-3.2.4.exe:49> b = [ 1 2; 3 4]
b =
1 2
3 4

octave-3.2.4.exe:50> c = [a b]
c =
1 2 3 1 2
3 4 5 3 4

octave-3.2.4.exe:51> d = [b a]
d =
1 2 1 2 3
3 4 3 4 5
%%Size of a matrix
[c d ] = size(a);

Creating a matrix of all zeros or ones
d = ones(3,2);
e = zeros(4,3);

%Appending an intercept term to a matrix
a = [1 2 3; 4 5 6]; %2 x 3
b = ones(2,1);
a = [b a];

%% Plotting
Creating 2 vectors
x = [1 3 4 5 6];
y = [5 6 7 8 9];
plot(x,y);

%%Create labels
xlabel("X values); ylabel("Y values);
axis([1 10 4 10]); % Set the range of x and y
title("Test plot);

%%Creating a 3D scatter plot
If we have 3 column csv file then we can load the data as follows
data = load('values.csv');
X = data(:, 1:2);
y = data(:, 3);
scatter3(X(:,1),X(:,2),y,[],[240 15 15],'x'); % X(:,1) - x axis X(:,2) - yaxis y[] - z axis

%% Drawing a 3D mesh
x = linspace(0,xrange + 20,10);
y = linspace(1,yrange+ 20,10);
[XX, YY ] = meshgrid(x,y);

[a b] = size(XX)

Draw the mesh
for i=1:a,
for j= 1:b,
ZZ(i,j) = [1 (XX(i,j)-mu(1))/sigma(1) (YY(i,j) - mu(2))/sigma(2) ] * theta;
end;
end;
mesh(XX,YY,ZZ);

For more details please see post Informed choices using Machine Learning 2- Pitting Kumble, Kapil and B S Chandra

%% Creating different polynomial equations
Let X be a feature vector
then
X = [X X.^2 X^3] %X X^2 X^3

This can be created using a for loop as follows
for i= 1:n
xtemp = xinput .^i;
x = [x xtemp];
end;

 

Finally while doing multivariate regression if we wanted to create polynomial terms of higher we could do as follows. Let us say we have a feature vector X made of 3 features x1, x2,

Let us say we wanted to create a polynomial of the form x1^2 x1.x2 x2^2 then we could create X as

X = [X(:,1) .^2 X(:,1) . X(:,2) X(:,2) .^2]

As you can see Octave is really powerful language for Machine Learning and has just a few handful of constructs with which one can implement powerful Machine Learning algorithms