MATLAB (matrix laboratory) is a multiparadigm numerical computing environment. A proprietary programming language 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, including C, C++, C#, Java, Fortran and Python.
Although MATLAB is intended primarily for numerical 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 2017, MATLAB has roughly 1 million users across industry and academia.^{[7]} MATLAB users come from various backgrounds of engineering, science, and economics.
Cleve Moler, the chairman of the computer science department at the University of New Mexico, started developing MATLAB in the late 1970s.^{[8]} He designed it to give his students access to LINPACK and EISPACK without them having to learn Fortran. It soon spread to other universities and found a strong audience within the applied mathematics community. Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. Recognizing its commercial potential, he joined with Moler and Steve Bangert. They rewrote MATLAB in C and founded MathWorks in 1984 to continue its development. These rewritten libraries were known as JACKPAC.^{[9]} In 2000, MATLAB was rewritten to use a newer set of libraries for matrix manipulation, LAPACK.^{[10]}
MATLAB was first adopted by researchers and practitioners in control engineering, Little's specialty, but quickly spread to many other domains. It is now also used in education, in particular the teaching of linear algebra, numerical analysis, and is popular amongst scientists involved in image processing.^{[8]}
The MATLAB application is built around the MATLAB scripting language. Common usage of the MATLAB application involves using the Command Window as an interactive mathematical shell or executing text files containing MATLAB code.^{[11]}
Variables are defined using the assignment operator, =
. MATLAB is a weakly typed programming language because types are implicitly converted.^{[12]} 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,^{[13]} 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
>> y = x + 0
y =
104 97 116
>> 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 to avoid exceeding) 9 (the terminator value).
>> array = 1:3:9
array =
1 4 7
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 incrementer.
Indexing is onebased,^{[14]} which is the usual convention for matrices in mathematics, although not for some 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 prime to the matrix.
>> 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 MATLAB functions can accept matrices and will apply themselves to 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 often produces code that is faster to execute. This 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 has structure data types.^{[15]} 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^{[16]} (field lookups by name, field manipulations, etc.). Unfortunately, MATLAB JIT does not support MATLAB structures, therefore just a simple bundling of various variables into a structure will come at a cost.^{[17]}
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. Functions are often case sensitive. ^{[18]}
MATLAB supports elements of lambda calculus by introducing function handles,^{[19]} or function references, which are implemented either in .m files or anonymous^{[20]}/nested functions.^{[21]}
MATLAB supports objectoriented programming including classes, inheritance, virtual dispatch, packages, passbyvalue semantics, and passbyreference semantics.^{[22]} 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).^{[23]}
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.
An example of a simple class is provided below.
classdef hello
methods
function greet(this)
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 supports developing applications with graphical user interface (GUI) features. MATLAB includes GUIDE^{[24]} (GUI development environment) for graphically designing GUIs.^{[25]} It also 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:
A MATLAB program can produce threedimensional graphics using the functions surf, plot3 or mesh.
[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:  
In MATLAB, graphical user interfaces can be programmed with the GUI design environment (GUIDE) tool.^{[26]}
MATLAB can call functions and subroutines written in the programming languages C or Fortran.^{[27]} A wrapper function is created allowing MATLAB data types to be passed and returned. The dynamically loadable object files created by compiling such functions are termed "MEXfiles" (for MATLAB executable).^{[28]}^{[29]} Since 2014 increasing twoway interfacing with Python is being added.^{[30]}^{[31]}
Libraries written in Perl, Java, ActiveX or .NET can be directly called from MATLAB,^{[32]}^{[33]} 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^{[34]} which is sold separately by MathWorks, or using an undocumented mechanism called JMI (JavatoMATLAB Interface),^{[35]}^{[36]} (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.^{[37]}
As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.^{[38]}^{[39]}
Libraries also exist to import and export MathML.^{[40]}
MATLAB is a proprietary product of MathWorks, so users are subject to vendor lockin.^{[7]}^{[41]} Although MATLAB Builder products can deploy MATLAB functions as library files which can be used with .NET^{[42]} or Java^{[43]} application building environment, future development will still be tied to the MATLAB language.
Each toolbox is purchased separately. If an evaluation license is requested, the MathWorks sales department requires detailed information about the project for which MATLAB is to be evaluated. If granted (which it often is), the evaluation license is valid for two to four weeks. A student version of MATLAB is available as is a homeuse license for MATLAB, Simulink, and a subset of Mathwork's Toolboxes at substantially reduced prices.
It has been reported that European Union (EU) competition regulators are investigating whether MathWorks refused to sell licenses to a competitor.^{[44]} The regulators dropped the investigation after the complainant withdrew their accusation and no evidence of wrongdoing was found.^{[45]}
MATLAB has a number of competitors.^{[46]} Commercial competitors include Mathematica, TK Solver, Maple, and IDL. There are also free open source alternatives to MATLAB, in particular GNU Octave, Scilab, FreeMat, and SageMath, which are intended to be mostly compatible with the MATLAB language; the Julia programming language also initially used MATLABlike syntax. Among other languages that treat arrays as basic entities (array programming languages) are APL, Fortran 90 and higher, SLang, as well as the statistical languages R and S. There are also libraries to add similar functionality to existing languages, such as IT++ for C++, Perl Data Language for Perl, ILNumerics for .NET, NumPy/SciPy/matplotlib for Python, SciLua/Torch for Lua, SciRuby for Ruby, and Numeric.js for JavaScript.
GNU Octave is unique from other alternatives because it treats incompatibility with MATLAB as a bug (see MATLAB Compatibility of GNU Octave), therefore, making GNU Octave a superset of the MATLAB language.
Version^{[47]}  Release name  Number  Bundled JVM  Year  Release date  Notes 

MATLAB 1.0  1984  
MATLAB 2  1986  
MATLAB 3  1987  
MATLAB 3.5  1990  Ran on DOS but needed at least a 386 processor; version 3.5m needed math coprocessor  
MATLAB 4  1992  Ran on Macintosh  
MATLAB 4.2c  1994  Ran on Windows 3.1x, needed a math coprocessor  
MATLAB 5.0  Volume 8  1996  December, 1996  Unified releases across all platforms  
MATLAB 5.1  Volume 9  1997  May, 1997  
MATLAB 5.1.1  R9.1  
MATLAB 5.2  R10  1998  March, 1998  Last version working on classic Mac's  
MATLAB 5.2.1  R10.1  
MATLAB 5.3  R11  1999  January, 1999  
MATLAB 5.3.1  R11.1  November, 1999  
MATLAB 6.0  R12  12  1.1.8  2000  November, 2000  First release with bundled Java virtual machine (JVM) 
MATLAB 6.1  R12.1  1.3.0  2001  June, 2001  
MATLAB 6.5  R13  13  1.3.1  2002  July, 2002  
MATLAB 6.5.1  R13SP1  2003  
MATLAB 6.5.2  R13SP2  Last release for IBM/AIX, Alpha/TRU64, and SGI/IRIX^{[48]}  
MATLAB 7  R14  14  1.4.2  2004  June, 2004  Introduced anonymous and nested functions^{[49]} Reintroduced for Mac (under Mac OS X) 
MATLAB 7.0.1  R14SP1  October, 2004  
MATLAB 7.0.4  R14SP2  1.5.0  2005  March 7, 2005  Support for memorymapped files^{[50]}  
MATLAB 7.1  R14SP3  1.5.0  September 1, 2005  
MATLAB 7.2  R2006a  15  1.5.0  2006  March 1, 2006  
MATLAB 7.3  R2006b  16  1.5.0  September 1, 2006  HDF5based MATfile support  
MATLAB 7.4  R2007a  17  1.5.0_07  2007  March 1, 2007  New bsxfun function to apply elementbyelement binary operation with singleton expansion enabled^{[51]} 
MATLAB 7.5  R2007b  18  1.6.0  September 1, 2007  Last release for Windows 2000 and PowerPC Mac; License Server support for Windows Vista;^{[52]} new internal format for Pcode  
MATLAB 7.6  R2008a  19  1.6.0  2008  March 1, 2008  Major enhancements to objectoriented programming abilities with a new class definition syntax,^{[53]} and ability to manage namespaces with packages^{[54]} 
MATLAB 7.7  R2008b  20  1.6.0_04  October 9, 2008  New Map data structure:^{[55]} upgrades to random number generators^{[56]}  
MATLAB 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^{[57]} 
MATLAB 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^{[58]}^{[59]} 

MATLAB 7.9.1  R2009bSP1  1.6.0_12  2010  April 1, 2010  bug fixes.  
MATLAB 7.10  R2010a  23  1.6.0_12  March 5, 2010  Last release for Intel 32bit Mac  
MATLAB 7.11  R2010b  24  1.6.0_17  September 3, 2010  Add support for enumerations^{[60]}  
MATLAB 7.11.1  R2010bSP1  1.6.0_17  2011  March 17, 2011  bug fixes and updates  
MATLAB 7.11.2  R2010bSP2  1.6.0_17  April 5, 2012^{[61]}  bug fixes  
MATLAB 7.12  R2011a  25  1.6.0_17  April 8, 2011  New rng function to control random number generation^{[62]}^{[63]}^{[64]} 

MATLAB 7.13  R2011b  26  1.6.0_17  September 1, 2011  Accesschange parts of variables directly in MATfiles, without loading into memory;^{[65]} increased maximum local workers with Parallel Computing Toolbox from 8 to 12^{[66]}  
MATLAB 7.14  R2012a  27  1.6.0_17  2012  March 1, 2012  
MATLAB 8  R2012b  28  1.6.0_17  September 11, 2012  First release with Toolstrip interface;^{[67]} MATLAB Apps.^{[68]} redesigned documentation system  
MATLAB 8.1  R2013a  29  1.6.0_17  2013  March 7, 2013  New unit testing framework^{[69]} 
MATLAB 8.2  R2013b  30  1.7.0_11  September 6, 2013^{[70]}  New table data type^{[71]}  
MATLAB 8.3  R2014a  31  1.7.0_11  2014  March 7, 2014^{[72]}  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 
MATLAB 8.4  R2014b  32  1.7.0_11  October 3, 2014  New classbased graphics engine (a.k.a. HG2);^{[73]} tabbing function in GUI;^{[74]} improved user toolbox packaging and help files;^{[75]} new objects for timedate manipulations;^{[76]} GitSubversion integration in IDE;^{[77]} big data abilities with MapReduce (scalable to Hadoop);^{[78]} new py package for using Python from inside MATLAB,^{[79]} new engine interface to call MATLAB from Python;^{[80]} several new and improved functions: webread (RESTful web services with JSON/XML support), tcpclient (socketbased connections), histcounts , histogram , animatedline , and others 

MATLAB 8.5  R2015a  33  1.7.0_60  2015  March 5, 2015  Last release supporting Windows XP and Windows Vista 
MATLAB 8.5  R2015aSP1  1.7.0_60  October 14, 2015  
MATLAB 8.6  R2015b  34  1.7.0_60  September 3, 2015  New MATLAB execution engine (a.k.a. LXE);^{[81]} graph and digraph classes to work with graphs and networks;^{[82]} MinGWw64 as supported compiler on Windows;^{[83]} Last version with 32bit support 

MATLAB 9.0  R2016a  35  1.7.0_60  2016  March 3, 2016  Live Scripts: interactive documents that combine text, code, and output (in the style of Literate programming);^{[84]} App Designer: a new development environment for building apps (with new kind of UI figures, axes, and components);^{[85]} pause execution of running programs using a Pause Button 
MATLAB 9.1  R2016b  36  1.7.0_60  September 15, 2016  define local functions in scripts;^{[86]} automatic expansion of dimensions (previously provided via explicit call to bsxfun ); tall arrays for Big data;^{[87]} new string type;^{[88]} new functions to encode/decode JSON;^{[89]} official MATLAB Engine API for Java^{[37]} 

MATLAB 9.2  R2017a  37  1.7.0_60  2017  March 9, 2017  MATLAB Online: cloudbased MATLAB desktop accessed in a web browser;^{[90]} doublequoted strings; new memoize function for Memoization; expanded object properties validation;^{[91]} mocking framework for unit testing;^{[92]} MEX targets 64bit by default; new heatmap function for creating heatmap charts^{[93]} 
MATLAB 9.3  R2017b  38  1.8.0_121  September 21, 2017  
MATLAB 9.4  R2018a  1.8.0_144  2018  March 15, 2018^{[94]} 
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.^{[95]}
Several easter eggs exist in MATLAB.^{[109]} These include hidden pictures,^{[110]} and jokes. For example, typing in "spy" used to generate a picture of the spies from Spy vs Spy, but now displays an image of a dog. Typing in "why" randomly outputs a philosophical answer. Other commands include "penny", "toilet", "image", and "life". Not every Easter egg appears in every version of MATLAB.
So APL, Speakeasy, LINPACK, EISPACK, and PL0 were the predecessors to MATLAB.
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