GNU Octave

GNU Octave is an interpreted language for numerical computation, with a syntax kept close to MATLAB so that scripts written for one often run on the other. The matrix is the basic data type: operators work element-wise or as linear algebra depending on context, and slicing, broadcasting and logical indexing belong to the language rather than to a library.

A standard installation covers linear systems and matrix factorisations, eigenvalues, polynomials, interpolation, numerical integration, solvers for ordinary and differential-algebraic equations, optimisation and basic statistics, plus two- and three-dimensional plotting. Code is written as .m script and function files. The graphical interface offers an editor, a command window, a variable browser and a documentation viewer, and the same interpreter runs headless for batch work.

Further domains — signal processing, image handling, control, symbolic algebra — come from separate packages installed with the pkg command. Compatibility with MATLAB is broad but not total: the commercial toolboxes and Simulink have no counterpart here.