MATLAB (an abbreviation of "MATrix LABoratory"^{[22]}) is a proprietary multiparadigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
Paradigm  multiparadigm: functional, imperative, procedural, objectoriented, array 

Designed by  Cleve Moler 
Developer  MathWorks 
First appeared  late 1970s 
Stable release  R2022b^{[1]}
/ September 15, 2022 
Typing discipline  dynamic, weak 
Filename extensions  .m, .p,^{[2]} .mex*,^{[3]} .mat,^{[4]} .fig,^{[5]} .mlx,^{[6]} .mlapp,^{[7]} .mltbx,^{[8]} .mlappinstall,^{[9]} .mlpkginstall^{[10]} 
Website  mathworks.com 
Influenced by  
Influenced  

Developer(s)  MathWorks 

Initial release  1984 
Stable release  R2022b^{[1]}
/ September 15, 2022 
Written in  C/C++, MATLAB 
Operating system  Windows, macOS, and Linux^{[20]}^{[21]} 
Platform  IA32, x8664 
Type  Numerical computing 
License  Proprietary commercial software 
Website  mathworks.com 
Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multidomain simulation and modelbased design for dynamic and embedded systems.
As of 2020, MATLAB has more than 4 million users worldwide.^{[23]} They come from various backgrounds of engineering, science, and economics.
MATLAB was invented by mathematician and computer programmer Cleve Moler.^{[24]} The idea for MATLAB was based on his 1960s PhD thesis.^{[24]} Moler became a math professor at the University of New Mexico and started developing MATLAB for his students^{[24]} as a hobby.^{[25]} He developed MATLAB's initial linear algebra programming in 1967 with his onetime thesis advisor, George Forsythe.^{[24]} This was followed by Fortran code for linear equations in 1971.^{[24]}
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 FFTs."^{[26]}
The first early version of MATLAB was completed in the late 1970s.^{[24]} The software was disclosed to the public for the first time in February 1979 at the Naval Postgraduate School in California.^{[25]} Early versions of MATLAB were simple matrix calculators with 71 prebuilt functions.^{[27]} At the time, MATLAB was distributed for free^{[28]}^{[29]} to universities.^{[30]} Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.^{[31]}^{: 5 }
In the 1980s, Cleve Moler met John N. Little. They decided to reprogram MATLAB in C and market it for the IBM desktops that were replacing mainframe computers at the time.^{[24]} John Little and programmer Steve Bangert reprogrammed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.^{[25]}
MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference in Las Vegas.^{[24]}^{[25]} MathWorks, Inc. was founded to develop the software^{[29]} and the MATLAB programming language was released.^{[27]} The first MATLAB sale was the following year, when Nick Trefethen from the Massachusetts Institute of Technology bought ten copies.^{[25]}^{[32]}
By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use.^{[25]} The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks.^{[28]} Many of the toolboxes were developed as a result of Stanford students that used MATLAB in academia, then brought the software with them to the private sector.^{[25]}
Over time, MATLAB was rewritten for early operating systems created by Digital Equipment Corporation, VAX, Sun Microsystems, and for Unix PCs.^{[25]}^{[27]} Version 3 was released in 1987.^{[33]} The first MATLAB compiler was developed by Stephen C. Johnson in the 1990s.^{[27]}
In 2000, MathWorks added a Fortranbased library for linear algebra in MATLAB 6, replacing the software's original LINPACK and EISPACK subroutines that were in C.^{[27]} 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.^{[27]}
Some especially large changes to the software were made with version 8 in 2012.^{[34]} The user interface was reworked^{[citation needed]} and Simulink's functionality was expanded.^{[35]} By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.^{[27]}
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 shell or executing text files containing MATLAB code.^{[36]}
Variables are defined using the assignment operator, =
. MATLAB is a weakly typed programming language because types are implicitly converted.^{[37]} 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,^{[38]} and that their type can change. Values can come from constants, 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 = [3*4, pi/2]
x =
12.0000 1.5708
>> y = 3*sin(x)
y =
1.6097 3.0000
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.
Indexing is onebased,^{[39]} which is the usual convention for matrices in mathematics, unlike zerobased 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 [2, 3, 4]
. 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 identity matrix 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
Transposing a vector or a matrix is done either by the function transpose
or by adding dotprime after the matrix (without the dot, prime will perform conjugate transpose for complex arrays):
>> A = [1 ; 2], B = A.', C = transpose(A)
A =
1
2
B =
1 2
C =
1 2
>> D = [0, 3 ; 1, 5], D.'
D =
0 3
1 5
ans =
0 1
3 5
Most functions accept arrays as input and operate elementwise 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 R), using the vectorized notation is encouraged and is often faster to execute. The following code, excerpted from the function magic.m, creates a magic square M for odd values of n (MATLAB function meshgrid
is used here to generate square matrices I and J containing 1:n):
[J,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.^{[40]} 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^{[41]} (field lookups 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.^{[42]}
gbImage = imread('ecg.png');
grayImage = rgb2gray(rgbImage); % for nonindexed images
level = graythresh(grayImage); % threshold for converting image to binary,
binaryImage = im2bw(grayImage, level);
% Extract the individual red, green, and blue color channels.
redChannel = rgbImage(:, :, 1);
greenChannel = rgbImage(:, :, 2);
blueChannel = rgbImage(:, :, 3);
% Make the black parts pure red.
redChannel(~binaryImage) = 255;
greenChannel(~binaryImage) = 0;
blueChannel(~binaryImage) = 0;
% Now recombine to form the output image.
rgbImageOut = cat(3, redChannel, greenChannel, blueChannel);
imshow(rgbImageOut);
MATLAB supports elements of lambda calculus by introducing function handles,^{[43]} or function references, which are implemented either in .m files or anonymous^{[44]}/nested functions.^{[45]}
MATLAB supports objectoriented programming including classes, inheritance, virtual dispatch, packages, passbyvalue semantics, and passbyreference semantics.^{[46]} 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 superclass (for reference classes) or not (for value classes).^{[47]}
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!
MATLAB has tightly integrated graphplotting 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 sine function:
MATLAB supports threedimensional graphics as well:
[X,Y] = meshgrid(10:0.25:10,10:0.25:10);
f = sinc(sqrt((X/pi).^2+(Y/pi).^2));
mesh(X,Y,f);
axis([10 10 10 10 0.3 1])
xlabel('{\bfx}')
ylabel('{\bfy}')
zlabel('{\bfsinc} ({\bfR})')
hidden off

[X,Y] = meshgrid(10:0.25:10,10:0.25:10);
f = sinc(sqrt((X/pi).^2+(Y/pi).^2));
surf(X,Y,f);
axis([10 10 10 10 0.3 1])
xlabel('{\bfx}')
ylabel('{\bfy}')
zlabel('{\bfsinc} ({\bfR})')
 
This code produces a wireframe 3D plot of the twodimensional unnormalized sinc function:  This code produces a surface 3D plot of the twodimensional unnormalized sinc function:  
MATLAB supports developing graphical user interface (GUI) applications.^{[48]} UIs can be generated either programmatically or using visual design environments such as GUIDE and App Designer.^{[49]}^{[50]}
MATLAB can call functions and subroutines written in a programming languages C or Fortran.^{[51]} A wrapper function is created allowing MATLAB data types to be passed and returned. MEX files (MATLAB executables) are the dynamically loadable object files created by compiling such functions.^{[52]}^{[53]} Since 2014 increasing twoway interfacing with Python was being added.^{[54]}^{[55]}
Libraries written in Perl, Java, ActiveX or .NET can be directly called from MATLAB,^{[56]}^{[57]} and many MATLAB libraries (for example XML or SQL 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^{[58]} which is sold separately by MathWorks, or using an undocumented mechanism called JMI (JavatoMATLAB Interface),^{[59]}^{[60]} (which should not be confused with the unrelated Java Metadata Interface that is also called JMI). Official MATLAB API for Java was added in 2016.^{[61]}
As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.^{[62]}^{[63]}
Libraries also exist to import and export MathML.^{[64]}
While MATLAB is the most popular commercial numerical computation software package,^{[65]} other alternatives are available, such as the open source computation language GNU Octave, the statistics programming language R, the computing environment Maple and the computational language Julia.^{[65]}^{[66]}
In 2020, MATLAB withdrew services from two Chinese universities as a result of US sanctions. The universities said this will be responded to by increased use of opensource alternatives and by developing domestic alternatives.^{[67]}
MATLAB is updated twice per year.^{[68]}^{: 517 }^{[35]} In addition to new features and other improvements, each release has new bug fixes and smaller changes.^{[69]}
Version^{[70]}  Release name  Number  Bundled JVM  Year  Release date  Notes 

1.0  1984  
2  1986  
3  1987  First Matlab toolbox introduced; support for ordinary differential equations added.^{[27]}^{: 81 }  
3.5  1990  Ran on DOS, Lowest requirement is an Intel 8088; Math Processor is supported, however had compatibility issues with NEC v20 + Intel 8087 combination.  
4  1992  Ran on Windows 3.1x and Macintosh.  
4.2c  1994  Ran on Windows 3.1x; needed a math coprocessor.  
5.0  Volume 8  1996  December 1996  Unified releases across all platforms.  
5.1  Volume 9  1997  May 1997  
5.1.1  R9.1  
5.2  R10  1998  March 1998  Last version working on classic Macs.  
5.2.1  R10.1  
5.3  R11  1999  January 1999  
5.3.1  R11.1  November 1999  
6.0  R12  12  1.1.8  2000  November 2000  First release with bundled Java virtual machine (JVM). 
6.1  R12.1  1.3.0  2001  June 2001  Last release for Windows 95.  
6.5  R13  13  1.3.1  2002  July 2002  
6.5.1  R13SP1  2003  
6.5.2  R13SP2  Last release for Windows 98, Windows ME, IBM/AIX, Alpha/TRU64, and SGI/IRIX.^{[71]}  
7  R14  14  1.4.2  2004  June 2004  Introduced anonymous and nested functions;^{[72]} reintroduced for Mac (under Mac OS X). 
7.0.1  R14SP1  October 2004  
R14SP1+  2004  November 2004  Parallel Computing Toolbox introduced.^{[27]}^{: 4 }^{[73]}^{: 3 }  
7.0.4  R14SP2  1.5.0  2005  March 7, 2005  Support added for memorymapped files.^{[74]}  
7.1  R14SP3  1.5.0  September 1, 2005  First 64bit version available for Windows XP 64bit.  
7.2  R2006a  15  1.5.0  2006  March 1, 2006  
7.3  R2006b  16  1.5.0  September 1, 2006  HDF5based MATfile support added.  
7.4  R2007a  17  1.5.0_07  2007  March 1, 2007  New bsxfun function added to apply elementbyelement binary operation with singleton expansion enabled.^{[75]} 
7.5  R2007b  18  1.6.0  September 1, 2007  Last release for Windows 2000 and PowerPC Mac; License Server support for Windows Vista;^{[76]} new internal format for Pcode.  
7.6  R2008a  19  1.6.0  2008  March 1, 2008  Major enhancements to objectoriented programming abilities with a new class definition syntax;^{[77]} ability to manage namespaces with packages.^{[78]} 
7.7  R2008b  20  1.6.0_04  October 9, 2008  Last release for processors w/o SSE2; New Map data structure;^{[79]} upgrades to random number generators.^{[80]}  
7.8  R2009a  21  1.6.0_04  2009  March 6, 2009  First release for Microsoft 32bit & 64bit Windows 7; new external interface to .NET Framework.^{[81]} 
7.9  R2009b  22  1.6.0_12  September 4, 2009  First release for Intel 64bit Mac, and last for Solaris SPARC; new use for the tilde operator (~ ) to ignore arguments in function calls.^{[82]}^{[83]}  
7.9.1  R2009bSP1  1.6.0_12  2010  April 1, 2010  Bug fixes.  
7.10  R2010a  23  1.6.0_12  March 5, 2010  Last release for Intel 32bit Mac.  
7.11  R2010b  24  1.6.0_17  September 3, 2010  Added support for enumerations;^{[84]} added features for running MATLAB code on NVIDIA CUDAbased GPUs.^{[85]}  
7.11.1  R2010bSP1  1.6.0_17  2011  March 17, 2011  Bug fixes and updates.  
7.11.2  R2010bSP2  1.6.0_17  April 5, 2012^{[86]}  Bug fixes.  
7.12  R2011a  25  1.6.0_17  April 8, 2011  New rng function to control random number generation.^{[87]}^{[88]}^{[89]}  
7.13  R2011b  26  1.6.0_17  September 1, 2011  Added ability to access/change parts of variables directly in MATfiles, without loading into memory;^{[90]} increased maximum local workers with Parallel Computing Toolbox from 8 to 12.^{[91]}  
7.14  R2012a  27  1.6.0_17  2012  March 1, 2012  Last version with 32bit Linux support.^{[92]} 
8  R2012b  28  1.6.0_17  September 11, 2012  First release with Toolstrip interface;^{[93]} MATLAB Apps introduced;^{[94]} redesigned documentation system.  
8.1  R2013a  29  1.6.0_17  2013  March 7, 2013  New unit testing framework.^{[95]} 
8.2  R2013b  30  1.7.0_11  September 6, 2013^{[96]}  Built in Java Runtime Environment (JRE) updated to version 7;^{[97]} New table data type.^{[98]}  
8.3  R2014a  31  1.7.0_11  2014  March 7, 2014^{[99]}  Simplified compiler setup for building MEXfiles; USB Webcams support in core MATLAB; number of local workers no longer limited to 12 with Parallel Computing Toolbox. 
8.4  R2014b  32  1.7.0_11  October 3, 2014  New classbased graphics engine (a.k.a. HG2);^{[100]} tabbing function in GUI;^{[101]} improved user toolbox packaging and help files;^{[102]} new objects for timedate manipulations;^{[103]} GitSubversion integration in IDE;^{[104]} big data abilities with MapReduce (scalable to Hadoop);^{[105]} new py package for using Python from inside MATLAB;^{[106]} new engine interface to call MATLAB from Python;^{[107]} several new and improved functions: webread (RESTful web services with JSON/XML support), tcpclient (socketbased connections), histcounts , histogram , animatedline , and others.
 
8.5  R2015a  33  1.7.0_60  2015  March 5, 2015  
8.5  R2015aSP1  1.7.0_60  October 14, 2015  Last release supporting Windows XP and Windows Vista.  
8.6  R2015b  34  1.7.0_60  September 3, 2015  New MATLAB execution engine (a.k.a. LXE);^{[108]} graph and digraph classes to work with graphs and networks;^{[109]} MinGWw64 as supported compiler on Windows;^{[110]} last version with 32bit support.
 
9.0  R2016a  35  1.7.0_60  2016  March 3, 2016  Released Live Scripts: interactive documents that combine text, code, and output (in the style of Literate programming);^{[111]} App Designer introduced: a new development environment for building apps (with new kind of UI figures, axes, and components);^{[112]} pause execution of running programs using a Pause Button. 
9.1  R2016b  36  1.7.0_60  September 15, 2016  Added ability to define local functions in scripts;^{[113]} automatic expansion of dimensions (previously provided via explicit call to bsxfun ); tall arrays for Big data;^{[114]} new string type;^{[115]} new functions to encode/decode JSON;^{[116]} official MATLAB Engine API for Java.^{[61]}  
9.2  R2017a  37  1.7.0_60  2017  March 9, 2017  Released MATLAB Online: cloudbased MATLAB desktop accessed in a web browser;^{[117]} doublequoted strings; new memoize function for Memoization; expanded object properties validation;^{[118]} mocking framework for unit testing;^{[119]} MEX targets 64bit by default; new heatmap function for creating heatmap charts.^{[120]} 
9.3  R2017b  38  1.8.0_121  September 21, 2017  Introduced a GPU Coder that converts MATLAB code to CUDA code for Nvidia.^{[121]}  
9.4  R2018a  39  1.8.0_144  2018  March 15, 2018^{[122]}  Improvements to the Live editor; introduction of the C++ MEX interface; ability to customize tab completion; web applications.^{[123]} 
9.5  R2018b  40  1.8.0_152  September 12, 2018  Added support for cloud providers, such as Amazon Web Services; Neural Network Toolbox replaced with Deep Learning Toolbox.^{[124]}  
9.6  R2019a  41  1.8.0_181  2019  March 20, 2019  Released MATLAB Projects; added state machine programming with Stateflow.^{[125]} 
9.7  R2019b  42  1.8.0_202  September 11, 2019  Introduction of 'arguments' block for input validation; enabling of dot indexing into function outputs; introduction of Live Editor Tasks.^{[126]}  
9.8  R2020a  43  2020  March 19, 2020  Removal of Mupad notebook; improved support for AMD CPUs (AVX2);^{[127]} default UTF8 encoding for MATLAB code files;^{[128]} ability to create standalone applications with Simulink.^{[129]}  
9.9  R2020b  44  September 17, 2020  Improved support for AMD CPUs (AVX2);^{[127]} online version of Simulink.^{[130]}  
9.10  R2021a  45  2021  March 11, 2021  
9.11  R2021b  46  September 22, 2021  
9.12.0  R2022a  47  2022  March 9, 2022  
9.13  R2022b  48  September 15, 2022  Introduced "Dictionaries" (associative arrays). Can now call MATLAB from .NET applications. 
The number (or release number) is the version reported by Concurrent License Manager program FLEXlm. For a complete list of changes of both MATLAB and official toolboxes, consult the MATLAB release notes.^{[131]}
So APL, Speakeasy, LINPACK, EISPACK, and PL0 were the predecessors to MATLAB.
Versions of MATLAB prior to R2012a are fully supported on 32bit Linux. After R2012a, MATLAB is no longer supported on 32bit Linux.