Octave For Machine Learning
Create Matrices of Different Dimensions
Let’s start with generating a matrix. The following code in octave will generate
a 3x3 matrix and store it in variable A.
A = [1 2 3; 4 5 6; 7 8 9]The semicolon seperates the rows and space seperates the elements of a row.
$ A = \begin{bmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{bmatrix}$
Let’s see another example of how to create a matrix. This time the size is 6x2.
A = [1 2; 3 4; 5 6; 7 8; 9 10; 11 12]$ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8 \\ 9 & 10 \\ 11 & 12\end{bmatrix}$
Create A Vector
Now, how do we create a vector like the following one?
$ A = \begin{bmatrix} 1 \\ 3 \\ 5 \\ 7 \\ 9 \\ 11\end{bmatrix}$
As you can infer, the code will be like following. Just one element in each row will let us create a vector of any size.
A = [1; 3; 5; 7; 9; 11]Create A Matrix of Consecutive Values
Try the following command to easily create matrix:
A = [1:6; 7:12]$ A = \begin{bmatrix}1 & 2 & 3 & 4 & 5 & 6\\ 7 & 8 & 9 & 10 & 11 & 12\end{bmatrix}$
You can add several rows by delimiting the rows with a semicolon.
Create A Matrix With Fixed Step Size
If you want to create a matrix with values that increases by some fixed value, you can try the code below.
A = [1 : 0.2 : 2; 2 : 0.2 : 3]The above code generates a matrix where the first row starts from 1, increases by 0.2 upto 2. So, we get 6 columns in the row. The same thing happens to the second row where it starts from 2 and ends at 3. This is a convenient way to generate matrix with a fixed step size.
$ A = \begin{bmatrix}
1.0000 & 1.2000 & 1.4000 & 1.6000 & 1.8000 & 2.0000 \
2.0000 & 2.2000 & 2.4000 & 2.6000 & 2.8000 & 3.0000
\end{bmatrix}$
Create A Matrix of Ones
A = ones (4, 4)The above code create a 4x4 matrix of all ones.
$ A = \begin{bmatrix}1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1\end{bmatrix}$
Create A Matrix of Zeroes
A = zeros (4, 4)The above code create a 4x4 matrix of all zeroes.
$ A = \begin{bmatrix}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}$
Create Identity Matrix
A = eye (4, 4)The above code create a 4x4 identity matrix.
$ A = \begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$
Create A Matrix With Random Values
A = rand (4, 4)The above code create a 4x4 matrix where every element has a random value between 0 and 1.
$ A = \begin{bmatrix}
0.873222 & 0.190867 & 0.408141 & 0.424057 \
0.626970 & 0.337635 & 0.639046 & 0.247549 \
0.255936 & 0.901785 & 0.583927 & 0.192788 \
0.047349 & 0.858707 & 0.055897 & 0.023689
\end{bmatrix}$
Create A Matrix With Gaussian Random Distribution
A = randn (4, 4)The above code create a 4x4 matrix where every element is drawn from a Gaussian random distribution
with mean 0 and variance/standard deviation 1.
$ A = \begin{bmatrix}
-2.723828 & -0.060662 & 1.026164 & 0.410187 \
1.174451 & 1.401109 & -1.574397 & 0.897547 \
-1.104706 & -1.490367 & 0.636317 & -0.938956 \
2.108468 & 0.966823 & 0.348221 & 0.106186
\end{bmatrix}$