GNU Octave is a high-level interpreted language, primarily intended for numerical computations.
(via GNU Octave)
- not equal
~= - logical AND
&& - logical OR
|| - logical XOR
xor(1,0)
A semicolon ; 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 x. If 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 rand.
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), 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.
You can save and load data in octave easily with the two commands save and load.
To save a specific variable v to the file filename.dat
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.
Let 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 enter.
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
% 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
>> A'
ans =
1 3 5
2 4 6
>> 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 matrixes and vectors with a condition
>> find(A < 3) % returns a index-vector where number < 3
ans =
1
4
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 flipud(eye(4))
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. x and 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 d. Example 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
Example: imagesc(A), colorbar, colormap gray;
xlabel('Zoidberg'), ylabel('Bender'), legend('fry', 'lila'), title('Futurama')
print -dpng 'myPlot.png' export plot as PNG file. For other format see help plot
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 POS
>> subplot(1,2,1);
>> plot(x, y);
>> subplot(1,2,2);
>> plot(x, y2);
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 (addpath()).
for- and 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 if-conditions
% i = 10
>> if (i == 10)
>> sprintf('yes')
>> else
>> sprintf('no')
>> endif
ans = yes
The following commands can be used within octave:
cdpwdls [-la]dir
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.