MATLAB (an abbreviation of "MATrix LABoratory") is a and environment developed by . MATLAB allows manipulations, plotting of and data, implementation of s, creation of s, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the allowing access to abilities. An additional package, , adds graphical multi-domain simulation and for and s. As of 2020, MATLAB has more than 4 million users worldwide. MATLAB users come from various backgrounds of , , and .



MATLAB was invented by mathematician and computer programmer . The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the and started developing MATLAB for his students as a hobby. He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, . This was followed by code for linear equations in 1971. In the beginning (before version 1.0) MATLAB "was not a programming language; it was a simple interactive matrix calculator. There were no programs, no toolboxes, no graphics. And no ODEs or s." The first early version of MATLAB was completed in the late 1970s. The software was disclosed to the public for the first time in February 1979 at the in California. Early versions of MATLAB were simple with 71 pre-built functions. At the time, MATLAB was distributed for free to universities. Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses. In the 1980s, Cleve Moler met . They decided to reprogram MATLAB in C and market it for the IBM desktops that were replacing mainframe computers at the time. John Little and programmer Steve Bangert re-programmed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.

Commercial development

MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference in . , Inc. was founded to develop the software and the MATLAB programming language was released. The first MATLAB sale was the following year, when Nick Trefethen from the bought ten copies. By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use. The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks. Many of the toolboxes were developed as a result of students that used MATLAB in academia, then brought the software with them to the private sector. Over time, MATLAB was re-written for early operating systems created by , , , and for Unix PCs. Version 3 was released in 1987. The first MATLAB compiler was developed by in the 1990s. In 2000, MathWorks added a Fortran-based library for linear algebra in MATLAB 6, replacing the software's original LINPACK and EISPACK subroutines that were in C. MATLAB's Parallel Computing Toolbox was released at the 2004 Supercomputing Conference and support for graphics processing units (GPUs) was added to it in 2010.

Recent history

Some especially large changes to the software were made with version 8 in 2012. The user interface was reworked and 's functionality was expanded. By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.


The MATLAB application is built around the MATLAB programming language. Common usage of the MATLAB application involves using the "Command Window" as an interactive mathematical or executing text files containing MATLAB code.


Variables are defined using the assignment operator, =. MATLAB is a programming language because types are implicitly converted. It is an inferred typed language because variables can be assigned without declaring their type, except if they are to be treated as symbolic objects, and that their type can change. Values can come from s, from computation involving values of other variables, or from the output of a function. For example: >> x = 17 x = 17 >> x = 'hat' x = hat >> x = *4, pi/2x = 12.0000 1.5708 >> y = 3*sin(x) y = -1.6097 3.0000

Vectors and matrices

A simple array is defined using the colon syntax: ''initial'':''increment'':''terminator''. For instance: >> array = 1:2:9 array = 1 3 5 7 9 defines a variable named array (or assigns a new value to an existing variable with the name array) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the ''initial'' value), increments with each step from the previous value by 2 (the ''increment'' value), and stops once it reaches (or is about to exceed) 9 (the ''terminator'' value). The ''increment'' value can actually be left out of this syntax (along with one of the colons), to use a default value of 1. >> ari = 1:5 ari = 1 2 3 4 5 assigns to the variable named ari an array with the values 1, 2, 3, 4, and 5, since the default value of 1 is used as the increment. is one-based, which is the usual convention for in mathematics, unlike zero-based indexing commonly used in other programming languages such as C, C++, and Java. Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to terminate each row. The list of elements should be surrounded by square brackets []. Parentheses () are used to access elements and subarrays (they are also used to denote a function argument list). >> A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1] A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 >> A(2,3) ans = 11 Sets of indices can be specified by expressions such as 2:4, which evaluates to , 3, 4/code>. For example, a submatrix taken from rows 2 through 4 and columns 3 through 4 can be written as: >> A(2:4,3:4) ans = 11 8 7 12 14 1 A square of size ''n'' can be generated using the function eye, and matrices of any size with zeros or ones can be generated with the functions zeros and ones, respectively. >> eye(3,3) ans = 1 0 0 0 1 0 0 0 1 >> zeros(2,3) ans = 0 0 0 0 0 0 >> ones(2,3) ans = 1 1 1 1 1 1 a vector or a matrix is done either by the function transpose or by adding dot-prime after the matrix (without the dot, prime will perform for complex arrays): >> A = ; 2 B = A.', C = transpose(A) A = 1 2 B = 1 2 C = 1 2 >> D = 3 ; 1 5 D.' D = 0 3 1 5 ans = 0 1 3 5 Most functions accept arrays as input and operate element-wise on each element. For example, mod(2*J,n) will multiply every element in ''J'' by 2, and then reduce each element modulo ''n''. MATLAB does include standard for and while loops, but (as in other similar applications such as ), using the notation is encouraged and is often faster to execute. The following code, excerpted from the function ''magic.m'', creates a ''M'' for odd values of ''n'' (MATLAB function meshgrid is used here to generate square matrices ''I'' and ''J'' containing ''1:n''): ,I= meshgrid(1:n); A = mod(I + J - (n + 3) / 2, n); B = mod(I + 2 * J - 2, n); M = n * A + B + 1;


MATLAB supports structure data types. Since all variables in MATLAB are arrays, a more adequate name is "structure array", where each element of the array has the same field names. In addition, MATLAB supports dynamic field names (field look-ups by name, field manipulations, etc.).


When creating a MATLAB function, the name of the file should match the name of the first function in the file. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores. Variables and functions are case sensitive.

Function handles

MATLAB supports elements of by introducing function handles, or function references, which are implemented either in .m files or anonymous/nested functions.

Classes and object-oriented programming

MATLAB supports including classes, , virtual dispatch, packages, semantics, and semantics. However, the syntax and calling conventions are significantly different from other languages. MATLAB has value classes and reference classes, depending on whether the class has ''handle'' as a super-class (for reference classes) or not (for value classes). Method call behavior is different between value and reference classes. For example, a call to a method: object.method(); can alter any member of ''object'' only if ''object'' is an instance of a reference class, otherwise value class methods must return a new instance if it needs to modify the object. An example of a simple class is provided below: classdef Hello methods function greet(obj) disp('Hello!') end end end When put into a file named hello.m, this can be executed with the following commands: >> x = Hello(); >> x.greet(); Hello!

Graphics and graphical user interface programming

MATLAB has tightly integrated graph-plotting features. For example, the function ''plot'' can be used to produce a graph from two vectors ''x'' and ''y''. The code: x = 0:pi/100:2*pi; y = sin(x); plot(x,y) produces the following figure of the : MATLAB supports three-dimensional graphics as well: MATLAB supports developing (GUI) applications. UIs can be generated either programmatically or using visual design environments such as ''GUIDE'' and ''App Designer''.

MATLAB and other languages

MATLAB can call functions and subroutines written in the programming languages or . A wrapper function is created allowing MATLAB data types to be passed and returned. s (MATLAB executables) are the dynamically loadable object files created by compiling such functions. Since 2014 increasing two-way interfacing with was being added. Libraries written in , , or can be directly called from MATLAB, and many MATLAB libraries (for example or support) are implemented as wrappers around Java or ActiveX libraries. Calling MATLAB from Java is more complicated, but can be done with a MATLAB toolbox which is sold separately by , or using an undocumented mechanism called JMI (Java-to-MATLAB Interface), (which should not be confused with the unrelated that is also called JMI). Official MATLAB API for Java was added in 2016. As alternatives to the based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to or . Libraries also exist to import and export . While MATLAB is the most popular commercial numerical computation software package, other alternatives are available, such as the open source computation language , the statistics programming language , the computing environment and the computational language .

Withdrawal from China

In 2020, Chinese state media reported that MATLAB had withdrawn services from two Chinese universities as a result of US sanctions, and said this will be responded to by increased use of open-source alternatives and by developing domestic alternatives.

Release history

MATLAB is updated twice per year. In addition to new features and other improvements, each release has new bug fixes and smaller changes. The number (or release number) is the version reported by Concurrent License Manager program . For a complete list of changes of both MATLAB and official toolboxes, consult the MATLAB release notes.

See also

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Further reading

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External links

* * {{DEFAULTSORT:Matlab Domain-specific programming languages