Basics of Octave

What is Octave

A high level programming language for quickly prototyping and developing machine learning algorithms. Once the algorithms have been developed, they can be properly implemented in other programming languages such as C++, Java etc.

Installation

On Ubuntu, run

sudo apt-get update && sudo apt-get install octave

Common Commands

Documentation can be found here https://octave.org/doc/interpreter/. Some common commands are,

  • octave starts the interpreter
  • help <functionname> displays documentation for a built in function. For example, help plot will bring up help information for plotting.

Basic operators

  • +, -, *, /, ^
  • == - equality operator
  • ~= - inequality operator
  • && - the AND logical operator
  • || - the OR logical operator
  • xor(<number>, <number>) - the XOR operator
  • , - chain two commands and carry them out together. Mostly for putting multiple commands on the same line.

Other keywords

  • % - comment
  • ; - supress the print output
  • 0 means false and all other numbers mean true

Functions

  • PS1('>> '); - change the octave prompt

  • disp() - print the value of a variable, or a string

  • sprintf('something %0.2f', pi) - print optional arguments under the control of the template string template and returns a string

  • format or format options such as format long, format short etc. changes the number of characters to be displayed

  • sqrt()

  • hist() plot a histogram

  • size(A) or size(A, DIM) return a row vector with the size (number of elements) of each dimension for the object A. When given a second argument, DIM, return the size of the corresponding dimension.

  • length() Return the length of the object A. The length is 0 for empty objects, 1 for scalars, and the number of elements for vectors. For matrix or N-dimensional objects, the length is the number of elements along the largest dimension (equivalent to 'max (size (A))').

  • max(X) - Find maximum values in the array X. For a vector argument, return the maximum value. For a matrix argument, return a row vector with the maximum value of each column. For a multi-dimensional array, 'max' operates along the first non-singleton dimension.

  • magic(N)

    Create an N-by-N magic square.

    A magic square is an arrangement of the integers '1:n^2' such that the row sums, column sums, and diagonal sums are all equal to the same value.

    Note: N must be a scalar greater than or equal to 3. If you supply N less than 3, magic returns either a nonmagic square, or else the degenerate magic squares 1 and [].

  • find(N)

  • flipud(X) - Flip the matrix upside down.

Implementation of bash commands

  • pwd shows the current working directory
  • cd
  • ls
  • quit or exit exit Octave

Common tasks

  • a = 1, a = pi - define variable a and assign it a number
  • a = 'hi' - string assignment

Matrix

Define a matrix

  • A = [1, 2; 3 4; 5 6;] defines a 3 x 2 matrix
  • A = [1 2 3;] defines a 1 x 3 matrix
  • A = ones(2, 3) generates a 2 x 3 matrix of all ones
  • A = zeros(2, 3) generates a 2 x 3 matrix of all zeros
  • A = rand(2, 3) generates a 2 x 3 matrix of random numbers drawn uniformly between 0 and 1
  • A = randn(2, 3) generates a 2 x 3 matrix of random numbers drawn from gaussian distribution with mean zero and variance one
  • eye(4) - generates a 4 x 4 identity matrix

Define a vector

  • v = [1; 2; 3;] defines a vector
  • v = 1:0.1:2 defines a row vector (also 1 x 11 matrix), with each number increasing by 0.1
  • v = 1:6 defines a row vector (also 1 x 6 matrix)

Move data around

Load data from file and save data to disk,

  • load file or load('<filename>.ext') loads a file
  • who shows the variables in memory
  • whos shows the variables in memory with more details
  • clear or clear <variable_name> to remove all variables or a particular variable from the memory
  • <vector_name>(1:10) takes the first 10 rows of the vector
  • save <filename>.mat <variable_name> save values in variable to file on disk
  • save <filename>.txt <variable_name> -asci save values in variable to file on disk that is human readable

Data indexing,

  • <matrix_variable>(1, 2) get the value at row 1 and column 2
  • <matrix_variable>(2, :) get the all values in the second row
  • <matrix_variable>(:, 2) get the all values in the second column
  • <matrix_variable>([1, 3], :) from row 1 and row 3, get all columns
  • <matrix_variable>(:, 2) = [1; 2; 3;] replace the second column with the new vector
  • A = [A, [100; 101; 102]] append a vector to the right of matrix A
  • A(:) put all elements of A into a single column vector
  • C = [A B] or C = [A, B] concatinating A and B by putting B on the right side of A
  • C = [A : B] concatinating A and B by putting B at the bottom of A
  • A(:) - Turn matrix into a vector.

Compute on data

  • A * B
  • A .* B - element-wise multiplication; multiple each element in A by the corresponding element in B
  • A .^ 2 - element-wise squaring of A; take the sqaure of each element in A
  • 1 ./ A - element-wise inverse of A; calculate the inverse of each element in A
  • -X or -1 * X - element-wise negative of X
  • X' - Transpose X.
  • [val, ind] = max(a) - Get the max value and its index from the vector a.
  • a < 3 - Do element-wise comparison
  • find(a < 3) - Get the index of the elements in vector a that are smaller than 3
  • max(rand(3), rand(3)) - Take the element-wise of two random 3 x 3 matrices.
  • max(A, [], 1) - Take the max value of each column in matrix A.
  • max(max(A)) - Find the single biggest value in matrix A.
  • sum(A, 1), sum(A, 2), sum(sum(magic(9) .* eye(9))) - Find the sum of each column, row or diagonal of matrix.

The period (i.e. .) is usually used to denote element wise operations in Octave.

  • log(X) - compute the natural logarithm, ln(x), for each element of X

  • exp(X) - compute e^x for each element of X

  • abs(X) - compute the absolute value of each element in X

  • find(X)

  • sum(y)

    Sum of elements along dimension DIM.

    If DIM is omitted, it defaults to the first non-singleton dimension.

  • prod(y) - Return the product of all elements in y.

  • floor(y) - Round down the elements of y.

  • ceil(y) - Round up the elements of y.

  • pinv(X) - Get the inverse of the matrix X.

Plotting

check help plot for more details

  • plot(x, y, 'r')

  • hold on;

    Retain plot data and settings so that subsequent plot commands are displayed on a single graph. Line color and line style are advanced for each new plot added.

  • xlabel('time'), ylabel('value') - Set the labels along x and y axises

  • legend('sin', 'cos') - Add legends

  • title('my plot') - Add title to figure

  • print -dpng 'myPlot.png' - Save the plot.

  • close - Close the current figure.

  • axis([0.5 1 -1 1]) - Zoom the x axis to be from 0.5 to 1 and set the y axis to be from -1 to 1

  • clf - clear a figure

  • Two figures

    figure(1);
plot(x, y1);
figure(2);
plot(x, y2);

  • subplot()

    % divide plot into a 1 x 2 grid, access first element
subplot(1, 2, 1);
plot(x, y1);

% access second element
subplot(1, 2, 2);
plot(x, y2);

  • imagesc(A)

    A = magic(5);

% for visualising a matrix
% running 3 commands at a time: plot matrix, add color bar and color map.
% use comma to chain function calls
imagesc(A), colorbar, colormap gray;

Control statements

  • for loop

    indicies = 1:10;
for i = indicies,
    disp(i);
end;

  • while loop

    v = rand(10, 1);
i = 1;
while i <= 5,
    v(i) = 100;
    i = i + 1;
end;

    v = rand(10, 1)

i = 1;
while true,
    v(i) = 999;
    i = i + 1;
    if i == 6,
        break;
    end;

end;

  • if ... else ...

    i = 2;

if i == 1,
    disp('The value is 1.');
elseif i == 2,
    disp('The value is 2.');
else
    disp('The value is not one or two');
end;

  • Functions

    % create a file with the function name as the file name such as `squarethisnumber.m`, then inside it,

function y = squarethisnumber(x)

y = x^2;

    then the function can be invoked as following in the same directory,

    squarethisnumber(5);

    use addpath(<path>); to tell Octave where to look for function files.

    A function can return multiple parameters, for example inside the file squareAndCubeThisNumber.m,

    function [y1, y2] = squareAndCubeThisNumber(x)

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

    then it can be invoked as,

    [a, b] = squareAndCubeThisNumber(5);

    As a complete example, assume we have the training set as below,

    xy
    11
    22
    33

    and the form of the hypothesis is h(x) = Θ0 + Θ1x.

    Then,

    % the design matrix
X = [1 1; 1 2; 1 3;];

% the labels
y = [1; 2; 3;];

% Θ
Θ = [0; 1;];

% then the cost i.e. overall error for all training examples is
J = costFunction(X, y, Θ);

    and costFunction will be defined in costFunction.m as,

    function J = costFunction(X, y, theta)

% X is the "design matrix" containing our training examples
% y is the class labels

m = size(X, 1);                        % number of training examples
predictions = X * theta;               % predictions of hypothesis on all m examples
squareErrors = (predictions - y) .^ 2; % squared errors

J = 1/(2*m) * sum(squareErrors);

References

  1. Octave for GNU/Linux