MATLAB (matrix laboratory) is a numerical computing environment and fourth-generation 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++, Java, and Fortran.

Although MATLAB is intended primarily for numerical computing, an optional toolbox uses the MuPAD symbolic engine, allowing access to symbolic computing capabilities. An additional package, Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic and embedded systems.

In 2004, MATLAB had around one million users across industry and academia. MATLAB users come from various backgrounds of engineering, science, and economics. MATLAB is widely used in academic and research institutions as well as industrial enterprises

## History

Cleve Moler, the chairman of the computer science department at the University of New Mexico, started developing MATLAB in the late 1970s. 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. In 2000, MATLAB was rewritten to use a newer set of libraries for matrix manipulation, LAPACK.

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 and numerical analysis, and is popular amongst scientists involved in image processing.

## Syntax

The MATLAB application is built around the MATLAB language, and most use of MATLAB involves typing MATLAB code into the Command Window (as an interactive mathematical shell), or executing text files containing MATLAB codes, including scripts and/or functions.

### Variables

Variables are defined using the assignment operator, `=`. MATLAB is a weakly typed programming language because types are implicitly converted. It is a dynamically 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 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```

### Vectors/matrices

A simple array is defined using the colon syntax: init`:`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 init 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 one-based, 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)
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```

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;```

### Structures

MATLAB has 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.). Unfortunately, MATLAB JIT does not support MATLAB structures, therefore just a simple bundling of various variables into a structure will come at a cost.[citation needed]

### Function handles

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

### Classes

Although MATLAB has classes, 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.

## Graphics and graphical user interface programming

MATLAB supports developing applications with graphical user interface features. MATLAB includes GUIDE (GUI development environment) for graphically designing GUIs. It also 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 sine function: A MATLAB program can produce three-dimensional 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 two-dimensional unnormalized sinc function: This code produces a surface 3D plot of the two-dimensional unnormalized sinc function:  In MATLAB, graphical user interfaces can be programmed with the GUI design environment (GUIDE) tool.

## Object-oriented programming

MATLAB’s support for object-oriented programming includes classes, inheritance, virtual dispatch, packages, pass-by-value semantics, and pass-by-reference semantics.

```classdef hello
methods
function doit(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.doit;
Hello!```

## Interfacing with other languages

MATLAB can call functions and subroutines written in the C programming language or Fortran. 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 “MEX-files” (for MATLAB executable).

Libraries written in Perl, Java, ActiveX or .NET can be directly called from MATLAB, 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 which is sold separately by MathWorks, or using an undocumented mechanism called JMI (Java-to-MATLAB Interface), (which should not be confused with the unrelated Java Metadata Interface that is also called JMI).

As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.

Libraries also exist to import and export MathML.

MATLAB is a proprietary product of MathWorks, so users are subject to vendor lock-in. Although MATLAB Builder product can deploy MATLAB functions as library files which can be used with .NET or Java 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. Overall the process of acquiring a license is expensive in terms of money and time[citation needed]. If granted (which it often is), the evaluation license is valid for two to four weeks. A student version of MATLAB is also available.

It has been reported that EU competition regulators are investigating whether MathWorks refused to sell licenses to a competitor.

## Alternatives

See also: list of numerical analysis software and comparison of numerical analysis software

MATLAB has a number of competitors. Commercial competitors include Mathematica, Maple, and IDL. There are also free open source alternatives to MATLAB, in particular GNU Octave, FreeMat, and Scilab which are intended to be mostly compatible with the MATLAB language. Among other languages that treat arrays as basic entities (array programming languages) are APL, Fortran 90 and higher, Julia, S-Lang, 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, and SciPy for Python.

GNU Octave stands out as it treats incompatibility with MATLAB as a bug (see GNU Octave#Matlab), therefore it aims to provide a software clone.

## Release history

Version 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 MS-DOS but required at least a 386 processor. Version 3.5m required math coprocessor
MATLAB 4 1992
MATLAB 4.2c 1994 Ran on Windows 3.1. Required 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
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
MATLAB 7 R14 14 1.4.2 2004 June, 2004
MATLAB 7.0.1 R14SP1 October, 2004
MATLAB 7.0.4 R14SP2 1.5.0 2005 March 7, 2005
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 HDF5-based MAT-file support
MATLAB 7.4 R2007a 17 1.5.0_07 2007 March 1, 2007
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
MATLAB 7.6 R2008a 19 1.6.0 2008 March 1, 2008 New Class-Definition Syntax.
MATLAB 7.7 R2008b 20 1.6.0_04 October 9, 2008
MATLAB 7.8 R2009a 21 1.6.0_04 2009 March 6, 2009 First release for 32-bit & 64-bit Microsoft Windows 7.
MATLAB 7.9 R2009b 22 1.6.0_12 September 4, 2009 First release for Intel 64-bit Mac, and last for Solaris SPARC.
MATLAB 7.9.1 R2009bSP1 1.6.0_12 2010 April 1, 2010
MATLAB 7.10 R2010a 23 1.6.0_12 March 5, 2010 Last release for Intel 32-bit Mac.
MATLAB 7.11 R2010b 24 1.6.0_17 September 3, 2010
MATLAB 7.11.1 R2010bSP1 1.6.0_17 2011 March 17, 2011
MATLAB 7.12 R2011a 25 1.6.0_17 April 8, 2011
MATLAB 7.13 R2011b 26 1.6.0_17 September 1, 2011
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. MATLAB Apps. Redesigned documentation system.
MATLAB 8.1 R2013a 29 1.6.0_17 2013 March 7, 2013 New unit testing framework.
MATLAB 8.2 R2013b 30 1.7.0_11 September 6, 2013 New table data type.

The number (or Release number) is the version reported by Concurrent License Manager program FlexLM.

## File extensions

### MATLAB

.fig
MATLAB figure
.m
MATLAB code (function, script, or class)
.mat
MATLAB data (binary file for storing variables)
.mex… (.mexw32, .mexw64, .mexglx, …)
MATLAB executable MEX-files (platform specific, e.g. “.mexmac” for the Mac, “.mexglx” for Linux, etc.)
.p
MATLAB content-obscured .m file (P-code)
.mlappinstall
MATLAB packaged App Installer

.mdl
.mdlp
.slx
Simulink Model (SLX format)
.slxp
Simulink Protected Model (SLX format)

.ssc
Simscape Model

.mn
.mu
.xvc, .xvz

### Third-party

.jkt
GPU Cache file generated by Jacket for MATLAB (AccelerEyes)
.mum
MATLAB CAPE-OPEN Unit Operation Model File (AmsterCHEM)

## Easter eggs

Several easter eggs exist in MATLAB. These include hidden pictures, and random inside jokes. For example, typing in “spy” will generate a picture of the spies from Spy vs Spy. “Spy” was changed to an image of a dog in recent releases (R2011B). 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 – some appear and some disappear.

• List of numerical analysis software
• Comparison of numerical analysis software

## Notes

1. ^ “System Requirements and Platform Availability”. MathWorks. Retrieved 2013-08-14.
2. ^ a b Richard Goering, “Matlab edges closer to electronic design automation world,” EE Times, 10/04/2004
3. ^ a b Cleve Moler (December 2004). “The Origins of MATLAB”. Retrieved April 15, 2007.
4. ^ “MATLAB Programming Language”. Altius Directory. Retrieved 2010-12-17.
5. ^ Cleve Moler (January 2000). “MATLAB Incorporates LAPACK”. Cleve’s Corner. MathWorks. Retrieved December 20, 2008.
6. ^ “MATLAB Documentation”. MathWorks. Retrieved 2013-08-14.
7. ^ “Comparing MATLAB with Other OO Languages”. MATLAB. MathWorks. Retrieved 14 August 2013.
8. ^ “Create Symbolic Variables and Expressions”. Symbolic Math Toolbox. MathWorks. Retrieved 14 August 2013.
9. ^ “Matrix Indexing”. MathWorks. Retrieved 14 August 2013.
10. ^ “Structures”. MathWorks. Retrieved 14 August 2013.
11. ^ “Generate Field Names from Variables”. MathWorks. Retrieved 14 August 2013.
12. ^ “Function Handles”. MathWorks. Retrieved 14 August 2013.
13. ^ “Anonymous Functions”. MathWorks. Retrieved 14 August 2013.
14. ^ “Nested Functions”. MathWorks.
15. ^ “Comparing Handle and Value Classes”. MathWorks.
16. ^ “Introduction to GUIDE”. MathWorks. Retrieved 14 August 2013.
17. ^ “MATLAB GUI”. MathWorks. 2011-04-30. Retrieved 2013-08-14.
18. ^ Smith, S. T. (2006). Matlab: Advanced GUI Development. Dog Ear Publishing. ISBN 978-1-59858-181-2.
19. ^ “Object-Oriented Programming”. MathWorks. Retrieved 2013-08-14.
20. ^ “Application Programming Interfaces to MATLAB”. MathWorks. Retrieved 14 August 2013.
21. ^ “Create MEX-Files”. MathWorks. Retrieved 14 August 2013.
22. ^ Spielman, Dan (2004-02-10). “Connecting C and Matlab”. Yale University, Computer Science Department. Retrieved 2008-05-20.
23. ^ “External Programming Language Interfaces”. MathWorks. Retrieved 14 August 2013.
24. ^ “Call Perl script using appropriate operating system executable”. MathWorks. Retrieved 7 November 2013.
25. ^ “MATLAB Builder JA”. MathWorks. Retrieved 2010-06-07.
26. ^ Yair Altman (2010-04-14). “Java-to-Matlab Interface”. Undocumented Matlab. Retrieved 2010-06-07.
27. ^ Joshua Kaplan. “matlabcontrol JMI”.
28. ^ Roger Germundsson from Wolfram Research (1998-09-30). “MaMa: Calling MATLAB from Mathematica with MathLink”. Wolfram Library Archive.
29. ^ rsmenon, szhorvat (2013). “MATLink: Communicate with MATLAB from Mathematica”. Retrieved 14 August 2013.
30. ^ Michael Weitzel (2006-09-01). “MathML import/export”. MathWorks – File Exchange. Retrieved 2013-08-14.
31. ^ Jan Stafford (21 May 2003). “The Wrong Choice: Locked in by license restrictions”. SearchOpenSource.com. Retrieved 14 August 2013.
32. ^ “MATLAB Builder NE”. MathWorks. Retrieved 14 August 2013.
33. ^ “MATLAB Builder JA”. MathWorks. Retrieved 14 August 2013.
34. ^ “MathWorks Software Licenses Probed by EU Antitrust Regulators”. Bloomberg news. 2012-03-01.
35. ^ Stefan Steinhaus (February 24, 2008). “Comparison of mathematical programs for data analysis”.
36. ^ Cleve Moler (January 2006). “The Growth of MATLAB and The MathWorks over Two Decades”. News & Notes Newsletter. MathWorks. Retrieved 14 August 2013.
37. ^ “Do MATLAB versions prior to R2007a run under Windows Vista?”. MathWorks. 2010-09-03. Retrieved 2011-02-08.
38. ^ “OOP Compatibility with Previous Versions”. MathWorks. Retrieved March 11, 2013.
39. ^ Loren Shure (September 2012). “The MATLAB R2012b Desktop – Part 1: Introduction to the Toolstrip”.
40. ^ “MATLAB Apps”. MathWorks. Retrieved August 14, 2013.
41. ^ “MATLAB Unit Testing Framework”. MathWorks. Retrieved August 14, 2013.
42. ^ “MathWorks Announces Release 2013b of the MATLAB and Simulink Product Families”. MathWorks. September 2013.
43. ^ “MATLAB Tables”. MathWorks. Retrieved 14 September 2013.
44. ^ “Introducing MEX-Files”. MathWorks. Retrieved 14 August 2013.
45. ^ “Binary MEX-File Extensions”. MathWorks. Retrieved 14 August 2013.
46. ^ “Protect Your Source Code”. MathWorks. Retrieved 14 August 2013.
47. ^ “MATLAB App Installer File”. MathWorks. Retrieved 14 August 2013.
48. ^ “Simscape”. MathWorks. Retrieved 14 August 2013.
49. ^ “What MATLAB Easter eggs do you know?”. MathWorks – MATLAB Answers. 2011-02-25. Retrieved 2013-08-14.
50. ^ Steve Eddins (2006-10-17). “The Story Behind the MATLAB Default Image”. Retrieved 14 August 2013.

## References

• Gilat, Amos (2004). MATLAB: An Introduction with Applications 2nd Edition. John Wiley & Sons. ISBN 978-0-471-69420-5.
• Quarteroni, Alfio; Fausto Saleri (2006). Scientific Computing with MATLAB and Octave. Springer. ISBN 978-3-540-32612-0.
• Ferreira, A.J.M. (2009). MATLAB Codes for Finite Element Analysis. Springer. ISBN 978-1-4020-9199-5.
• Lynch, Stephen (2004). Dynamical Systems with Applications using MATLAB. Birkhäuser. ISBN 978-0-8176-4321-8. Wikibooks has a book on the topic of: MATLAB Programming Wikimedia Commons has media related to MATLAB.
• Hazewinkel, Michiel, ed. (2001), “Linear algebra software packages”, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
• MATLAB overview, at the MathWorks website
• Platform Road Map, at the MathWorks website.
• System Requirements, at the MathWorks website.
• MATLAB Central File Exchange – Library of over 18,000 user-contributed MATLAB files and toolboxes, mostly distributed under BSD License.
• MATLAB at the Open Directory Project
• MATLAB Central Newsreader – a web-based newsgroups reader hosted by MathWorks for comp.soft-sys.matlab
• LiteratePrograms (MATLAB)
• MATLAB Central Blogs
• Physical Modeling in MATLAB by Allen B. Downey, Green Tea Press, PDF, ISBN 978-0-615-18550-7. An introduction to MATLAB.
• Writing Fast MATLAB Code by Pascal Getreuer
• Calling MATLAB from Java: MatlabControl JMI Wrapper, The MatlabJava Server, MatlabControl
• International Online Workshop on MATLAB and Simulink by WorldServe Education
• MATLAB tag on Stack Overflow.
• MATLAB Answers – a collaborative environment for finding the best answers to your questions about MATLAB, Simulink, and related products.
• Cody – a MATLAB Central game that challenges and expands your knowledge of MATLAB.
• MATLAB Online Programming Contest
• Trendy – a MATLAB based web service for tracking and plotting trends.

MathWorks was founded in Portola Valley, California, by Jack Little (President & CEO), Cleve Moler (Chief Scientist), and Steve Bangert (now inactive) on December 7, 1984. Its flagship product, MATLAB, made its public debut at the IEEE Conference on Decision and Control in Las Vegas, Nevada that same year. The company sold its first order, 10 copies of MATLAB, for \$500 to the Massachusetts Institute of Technology (MIT) in February 1985.

In 1986, MathWorks relocated to Massachusetts and following a decade of growth, settled into its current headquarters on Apple Hill Drive in the town of Natick in July 1999. By that time, the company had grown to nearly 1,000 people. The company started its global expansion in 1997, with an office in the United Kingdom. The years that followed saw opening of offices in Spain, Germany, France, The Netherlands, and Switzerland in 2000; an office in Italy in 2002; and locations in South Korea and Sweden in 2004. An office in China opened in 2007, India in 2008 and the company established a direct presence in Japan in 2009. In 2007, MathWorks acquired Polyspace Technologies  and started including the Polyspace products in their MATLAB releases in 2008. In 2008, MathWorks acquired SciFace Software GmbH & Co. KG, makers of MuPAD, and started including MuPAD in their Symbolic Math Toolbox, replacing the existing Maple engine. MathWorks also expanded its main campus in Massachusetts with the purchase of a 150,000-square-foot (14,000 m2) office building at Apple Hill in July 2008, followed by the purchase of another 170,000-square-foot (16,000 m2) building in the same complex in December 2009. In April 2013, the company again expanded its footprint in Natick by an additional 500,000-square-foot (46,000 m2) with the purchase of the former headquarters of Boston Scientific.

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