GNU Octave

GNU Octave is software featuring a high-level programming language, primarily intended for numerical computations. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language.
Since it is part of the GNU Project, it is free software under the terms of the GNU General Public License.
Other free alternatives to MATLAB include Scilab and FreeMat. Octave is more compatible with MATLAB than Scilab is, and FreeMat has not been updated since June 2013.
History.
The project was conceived around 1988. At first it was intended to be a companion to a chemical reactor design course. Real development was started by John W. Eaton in 1992. The first alpha release dates back to 4 January 1993 and on 17 February 1994 version 1.0 was released. Version 4.0.0 was released on 29 May 2015.
The program is named after Octave Levenspiel, a former professor of the principal author. Levenspiel was known for his ability to perform quick back-of-the-envelope calculations.
Developments.
In addition to use on desktops for personal scientific computing, Octave is used in academia and industry. For example, Octave was used on a massive parallel computer at Pittsburgh Supercomputing Center to find vulnerabilities related to guessing social security numbers.
Acceleration with OpenCL or CUDA is also possible with use of GPUs.
Octave, the language.
The Octave language is an interpreted programming language. It is a structured programming language (similar to C) and supports many common C standard library functions, and also certain UNIX system calls and functions. However, it does not support passing arguments by reference.
Octave programs consist of a list of function calls or a script. The syntax is matrix-based and provides various functions for matrix operations. It supports various data structures and allows object-oriented programming.
Its syntax is very similar to MATLAB, and careful programming of a script will allow it to run on both Octave and MATLAB.
Because Octave is made available under the GNU General Public License, it may be freely changed, copied and used. The program runs on Microsoft Windows and most Unix and Unix-like operating systems, including Linux and macOS.
Notable features.
Command and variable name completion.
Typing a TAB character on the command line causes Octave to attempt to complete variable, function, and file names (similar to Bash's tab completion). Octave uses the text before the cursor as the initial portion of the name to complete.
Command history.
When running interactively, Octave saves the commands typed in an internal buffer so that they can be recalled and edited.
Data structures.
Octave includes a limited amount of support for organizing data in structures. In this example, we see a structure "x" with elements "a", "b", and "c", (an integer, an array, and a string, respectively):
octave:1> x.a = 1; x.b = [1, 2; 3, 4]; x.c = "string";
octave:2> x.a
ans = 1
octave:3> x.b
ans =
 1 2
 3 4
octave:4> x.c
ans = string
octave:5> x
x =
 a = 1
 b =
 1 2
 3 4
 c = string
Short-circuit boolean operators.
Octave's 'codice_1' and 'codice_2' logical operators are evaluated in a short-circuit fashion (like the corresponding operators in the C language), in contrast to the element-by-element operators 'codice_3' and 'codice_4'.
Increment and decrement operators.
Octave includes the C-like increment and decrement operators 'codice_5' and 'codice_6' in both their prefix and postfix forms.
Octave also does augmented assignment, e.g. 'codice_7'.
Unwind-protect.
Octave supports a limited form of exception handling modelled after the 'codice_8' of Lisp. The general form of an unwind_protect block looks like this:
unwind_protect
 body
unwind_protect_cleanup
 cleanup
end_unwind_protect
As a general rule, GNU Octave recognizes as termination of a given 'codice_9' either the keyword 'codice_10' (which is compatible with the MATLAB language) or a more specific keyword 'codice_11'. As a consequence, an 'codice_8' block can be terminated either with the keyword 'codice_13' as in the example, or with the more portable keyword 'codice_10'.
The "cleanup" part of the block is always executed. In case an exception is raised by the "body" part, "cleanup" is executed immediately before propagating the exception outside the block 'codice_8'.
GNU Octave also supports another form of exception handling (compatible with the MATLAB language):
try
 body
catch
 exception_handling
end
This latter form differs from an 'codice_8' block in two ways. First, "exception_handling" is only executed when an exception is raised by "body". Second, after the execution of "exception_handling" the exception is not propagated outside the block (unless a 'codice_17' statement is explicitly inserted within the "exception_handling" code).
Variable-length argument lists.
Octave has a mechanism for handling functions that take an unspecified number of arguments without explicit upper limit. To specify a list of zero or more arguments, use the special argument codice_18 as the last (or only) argument in the list.
function s = plus (varargin)
 if (nargin==0)
 s = 0;
 else
 s = varargin{1} + plus (varargin{2:nargin});
 end
end
Variable-length return lists.
A function can be set up to return any number of values by using the special return value codice_19. For example:
function varargout = multiassign (data)
 for k=1:nargout
 varargout{k} = data(:,k);
 end
end
C++ integration.
It is also possible to execute Octave code directly in a C++ program. For example, here is a code snippet for calling codice_20:
ColumnVector NumRands(2);
NumRands(0) = 10;
NumRands(1) = 1;
octave_value_list f_arg, f_ret;
f_arg(0) = octave_value(NumRands);
f_ret = feval("rand", f_arg, 1);
Matrix unis(f_ret(0).matrix_value());
C and C++ code can be integrated into GNU Octave by creating oct files, or using the MATLAB compatible MEX files.
MATLAB compatibility.
Octave has been built with MATLAB compatibility in mind, and shares many features with MATLAB:
Octave treats incompatibility with MATLAB as a bug; therefore, it could be considered a software clone, which does not infringe software copyright as per "Lotus v. Borland" court case.
MATLAB scripts from the MathWorks' FileExchange repository in principle are compatible with Octave. However, while they are often provided and uploaded by users under an Octave compatible and proper open source BSD license, the fileexchange's Terms of use prohibit any usage beside MathWorks' proprietary MATLAB.
Syntax compatibility.
There are a few purposeful, albeit minor, syntax additions:
Function compatibility.
Many, but not all, of the numerous MATLAB functions are available in GNU Octave, some of them accessible through packages in Octave Forge. The functions available as part of either core Octave or Forge packages are listed online.
A list of unavailable functions is included in the Octave function __unimplemented.m__. Unimplemented functions are also listed under many Octave Forge packages in the Octave Wiki.
When an unimplemented function is called the following error message is shown:
 octave:1> guide
 warning: the 'guide' function is not yet implemented in Octave
 Please read <http://www.octave.org/missing.html> to learn how you can contribute missing functionality.
 error: 'guide' undefined near line 1 column 1
User interfaces.
Octave comes with an official graphical user interface (GUI) and an integrated development environment (IDE) based on Qt. It has been available since Octave 3.8, and has become the default interface (over the command line interface) with the release of Octave 4.0. 
It was well-received by EDN contributor, who said "[Octave] now has a very workable GUI."
Several 3rd-party graphical front-ends have also been developed, like ToolboX for coding education.
GUI applications.
With Octave code, the user can create GUI applications . Below are some examples:
Button, edit control, checkbox
f = figure;
b1 = uicontrol (f, "string", "A Button", "position",[10 10 150 40]);
e1 = uicontrol (f, "style", "edit", "string", "editable text", "position",[10 60 300 40]);
c1 = uicontrol (f, "style", "checkbox", "string", "a checkbox", "position",[10 120 150 40]);
Textbox
prompt = {"Width", "Height", "Depth"};
defaults = {"1.10", "2.20", "3.30"};
rowscols = [1,10; 2,20; 3,30];
dims = inputdlg (prompt, "Enter Box Dimensions", rowscols, defaults);
Listbox with message boxes.
my_options = {"An item", "another", "yet another"};
[sel, ok] = listdlg ("ListString", my_options, "SelectionMode", "Multiple");
if (ok == 1)
 msgbox ("You selected:");
 for i = 1:numel (sel)
 msgbox (sprintf ("\t%s", my_options{sel(i)}));
 endfor
else
 msgbox ("You cancelled.");
endif
Radiobuttons
f = figure;
gp = uibuttongroup (f, "Position", [ 0 0.5 1 1])
b1 = uicontrol (gp, "style", "radiobutton", "string", "Choice 1", "Position", [ 10 150 100 50 ]);
b2 = uicontrol (gp, "style", "radiobutton", "string", "Choice 2", "Position", [ 10 50 100 30 ]);
b3 = uicontrol (f, "style", "radiobutton","string", "Not in the group","Position", [ 10 50 100 50 ]);
Packages.
Octave also has packages available for free. Those packages are located at Octave-Forge . Available packages are: