|GNU Octave Manual Version 3|
by John W. Eaton, David Bateman, Søren Hauberg
Paperback (6"x9"), 568 pages
RRP £24.95 ($39.95)
1.2 Simple Examples
The following chapters describe all of Octave's features in detail, but before doing that, it might be helpful to give a sampling of some of its capabilities.
If you are new to Octave, I recommend that you try these examples to begin learning Octave by using it. Lines marked with ‘octave:13>’ are lines you type, ending each with a carriage return. Octave will respond with an answer, or by displaying a graph.
1.2.1 Creating a Matrix
To create a new matrix and store it in a variable so that it you can refer to it later, type the command
octave:1> A = [ 1, 1, 2; 3, 5, 8; 13, 21, 34 ]
Octave will respond by printing the matrix in neatly aligned columns. Ending a command with a semicolon tells Octave to not print the result of a command. For example
octave:2> B = rand (3, 2);
will create a 3 row, 2 column matrix with each element set to a random value between zero and one.
To display the value of any variable, simply type the name of the
variable. For example, to display the value stored in the matrix
B, type the command
1.2.2 Matrix Arithmetic
Octave has a convenient operator notation for performing matrix
arithmetic. For example, to multiply the matrix
A by a scalar
value, type the command
octave:4> 2 * A
To multiply the two matrices
B, type the command
octave:5> A * B
and to form the matrix product
transpose (A) * A,
type the command
octave:6> A' * A
1.2.3 Solving Linear Equations
To solve the set of linear equations
Ax = b,
use the left division operator, ‘\’:
octave:7> A \ b
This is conceptually equivalent to
inv (a) * b,
but avoids computing the inverse of a matrix directly.
If the coefficient matrix is singular, Octave will print a warning message and compute a minimum norm solution.
1.2.4 Integrating Differential Equations
Octave has built-in functions for solving nonlinear differential
equations of the form
-- = f (x, t)
with the initial condition
x(t = t0) = x0
For Octave to integrate equations of this form, you must first provide a
definition of the function
This is straightforward, and may be accomplished by entering the function body directly on the command line. For example, the following commands define the right hand side function for an interesting pair of nonlinear differential equations. Note that while you are entering a function, Octave responds with a different prompt, to indicate that it is waiting for you to complete your input.
octave:8> function xdot = f (x, t) > > r = 0.25; > k = 1.4; > a = 1.5; > b = 0.16; > c = 0.9; > d = 0.8; > > xdot(1) = r*x(1)*(1 - x(1)/k) - a*x(1)*x(2)/(1 + b*x(1)); > xdot(2) = c*a*x(1)*x(2)/(1 + b*x(1)) - d*x(2); > > endfunction
Given the initial condition
x0 = [1; 2];
and the set of output times as a column vector (note that the first output time corresponds to the initial condition given above)
t = linspace (0, 50, 200)';
it is easy to integrate the set of differential equations:
x = lsode ("f", x0, t);
lsode uses the Livermore Solver for Ordinary
Differential Equations, described in A. C. Hindmarsh, ODEPACK, a
Systematized Collection of ODE Solvers, in: Scientific Computing, R. S.
Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pages 55--64.
1.2.5 Producing Graphical Output
To display the solution of the previous example graphically, use the command
plot (t, x)
If you are using a graphical user interface, Octave will automatically create a separate window to display the plot.
To save a plot once it has been displayed on the screen, use the print command. For example,
print -deps foo.eps
will create a file called ‘foo.eps’ that contains a rendering of the current plot.
explains more options for the
1.2.6 Editing What You Have Typed
At the Octave prompt, you can recall, edit, and reissue previous commands using Emacs- or vi-style editing commands. The default keybindings use Emacs-style commands. For example, to recall the previous command, press Control-p (usually written C-p for short). Doing this will normally bring back the previous line of input. C-n will bring up the next line of input, C-b will move the cursor backward on the line, C-f will move the cursor forward on the line, etc.
A complete description of the command line editing capability is given in this manual in section 2.4 Command Line Editing.
1.2.7 Help and Documentation
Octave has an extensive help facility. The same documentation that is available in printed form is also available from the Octave prompt, because both forms of the documentation are created from the same input file.
In order to get good help you first need to know the name of the command
that you want to use. This name of the function may not always be
obvious, but a good place to start is to just type
This will show you all the operators, reserved words, functions,
built-in variables, and function files. An alternative is to search the
documentation using the
lookfor function. This function is
described in section 2.3 Commands for Getting Help.
Once you know the name of the function you wish to use, you can get more help on the function by simply including the name as an argument to help. For example,
will display the help text for the
Octave sends output that is too long to fit on one screen through a
more. Type a RET to advance one
line, a SPC to advance one page, and q to exit the pager.
The part of Octave's help facility that allows you to read the complete text of the printed manual from within Octave normally uses a separate program called Info. When you invoke Info you will be put into a menu driven program that contains the entire Octave manual. Help for using Info is provided in this manual in section 2.3 Commands for Getting Help.
|ISBN 095461206X||GNU Octave Manual Version 3||See the print edition|