GNU Octave is a high-level interpreted language, primarily intended for numerical computations.
(via GNU Octave)
- not equal
- logical AND
- logical OR
- logical XOR
; at the end of a line will suppress the output
v = 1:5 creates a 1x5 Matrix (linear vector) with the numbers one to five.
v = 1:0.1:2 also creates a vector but with the numbers from one to two with a step size of 0.1.
>> v = 1:5 v = 1 2 3 4 5 >> 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
To display the 5th number of this vectors use
v(5). Beware that ocatve is 1 based.
Displaying a range of numbers use
v(3:5) to display the 3rd, 4th, and 5th number.
help _function name_ will give you the man page of this function.
ones(x [, y]) creates a matrix with ones. If only
x is provided it is a squared matrix of size
y is provides it has the size x cross y.
zeros(x [, y]) behaves the same as
ones() but will give a zero-matrix.
rand(x [, y]) Return a matrix with random elements uniformly distributed on the interval (0, 1).
randn(x [, y]) Return a matrix with normally distributed random elements having zero mean and variance one. The arguments are handled the same as the arguments for
hist(x [, y]) Produce histogram counts of plots.
y is the number of buckets.
eye(x [, y]]) Produces an identity matrix.
size(A [, DIM]) Return the number of rows and colums of A.
DIM = 1 number rows
DIM = 2 number columns
length(A) Return the length of the object A. For Matrix objects, the length is the number of rows or columns, whichever is greater (this odd definition is used for compatibility with MATHLAB).
log(a) % natural logarithm abs(a) % absolute value sign(a) % signum function exp(a) % compute e^a
who Lists currently defined varibales matchin the given pattern.
whos Provide detailed information on currently defined variables.
sum(A,1) sums up all columns.
sum(A,2) sums up all rows
prod(a) takes the product of each column
floor(a) rounds down
ceil(a) rounds up
clear will clear all variables or only the ones who are named.
Save and Load Data
You can save and load data in octave easily with the two commands
To save a specific variable
v to the file
save filename.dat v; % save data of v in binary format save filename.txt v --ascii % save data of v in readable version
Loading data is as simple as saving.
% both are equivalent load filename.dat load('filename.dat')
The file will be saved in the current directory and will be loaded from the current dir.
A be the matrix:
A = [1 2; 3 4; 5 6]
A = 1 2 3 4 5 6
The semicolon indicates a new row and a space or comma is a new column. Instead of typing a semicolon it is also possible to hit
Output last element in Matrix
>> A(end, end) ans = 6
% show number in first row and second column >> A(1,2) ans = 2 % show second row: colon means 'all' >> A(2,:) ans = 3 4 % show second column >> A(:,2) ans = 2 4 6
Assign new Data
% replace second column by 10, 11, and 12 >> A(:,2) = [10,11,12] % in this case it doesn't matter if comma or semicolon is used >> A(:,2) = [10;11;12]
>> B = [20 21; 22 23; 24 25] >> C = [A B] % A B ans = 1 2 3 4 5 6 20 21 22 23 24 25 >> D = [A; B] % A append B ans = 1 2 20 21 3 4 22 23 5 6 24 25
Transpose a matrix or a vector
>> A' ans = 1 3 5 2 4 6
max values and find()
>> max(magic(4)) % returns a 1x4 vector with max-values per column ans = 16 14 15 13 >> [val, ind] = max(magic(4)) % retuns 2 vectors: 1. values, 2. indexes val = 16 14 15 13 ind = 1 4 4 1
To find the largest value in a matrix you can either chain to
max() functions or take the complete matrix.
>> max(max(A)); % Both are equivalent >> max(A(:)) ans = 6
You can search thru matrices and vectors with a condition
>> find(A < 3) % returns a index-vector where number < 3 ans = 1 4
Flipping a matrix
Sometimes it is necessary to flip a matrix upsidedown.
>> flipud(A) ans = 5 6 3 4 1 2
Hint: useful in combination with the identity matrix
Sum of diagonals in a square matrix
Example: A magic matrix is a square matrix where the sum of rows, columns and diagonals are the same result. Let's check the sum of diagonals
>> M = magic(4); >> sum(sum(M.*eye(4))) % sum of diagonal top left to bottom right ans = 34 >> sum(sum(M.* flipud(eye(4) ))) % sum of diagonal bottom left to top right ans = 34
There exists serveral ways to create a inverse matrix in octave
>> inv(M) % warning: yes >> pinv(M) % warning: no >> M^-1 % warning: no >> M\eye(size(M)) % warning: yes
plot(x, y) plot a graph with
x as x-axis and
y as y-axis.
y has to match in length.
hold on will plot updated in the current plot instead of replace the current plot.
plot(x, y2, 'r') will plot a graph in red.
axis([a b c d]) X-axis will start at
a and goes to
b, and Y-axis will start from
c and goes to
axis([0.5 1 -1 1])
clf; clear figure
imagesc(A) grid of colors for matrix
colorbar display colorbar, kind of legend
colormap gray display only gray-scale
imagesc(A), colorbar, colormap gray;
print -dpng 'myPlot.png' export plot as PNG file. For other format see
close close the plot, as simple as that.
figure(1); plot(x, y) plot graph as figure 1
figure(2); plot(x, y2) plot graph as figure 2
subplot(x,y,POS); plot multiple graphs in one windows as a X-by-Y grid at position
>> subplot(1,2,1); >> plot(x, y); >> subplot(1,2,2); >> plot(x, y2);
Functions & control statements
Functions are saved in files with the file-ending
.m for MATHLAB. The syntax is quite simple:
function y = function_name(x) y = x^2; % y is the return value % x is a parameter % is also possible to return multiple values function [y1, y2] = function_name(x) y1 = x^2 y2 = x^3
Call your function in octave like
function_name(5). You have to be in the same dir as the file or add it to your search-path (
while-loops are easy and useful in octave.
>> for i=1:10 >> disp(i) >> end; >> i = 1; >> while (i ~= 10) >> disp(i); >> i = i+1; >> endwhile;
It is also possible to use
% i = 10 >> if (i == 10) >> sprintf('yes') >> else >> sprintf('no') >> endif ans = yes
The following commands can be used within octave:
It is possible to change octave's prompt. Use
PS1('>> '); to change the promt to
disp(a); will display the variable
a. Useful in loops or conditions.
magic(x) Create an N-by-N magic square.
For more controll in displaying stuff use
sprintf('%i', a);. It follows the C-standard.
format long or
format short adjusts the length of output in octave.
addpath('_path_') will add a path to the search-path for octave. I.e. Octave will also look in this path for functions and files.