# Software:MATLAB

Short description: Numerical computing environment and programming language
Paradigm multi-paradigm: functional, imperative, procedural, object-oriented, array Cleve Moler MathWorks late 1970s dynamic, weak .m, .p,[1] .mex*,[2] .mat,[3] .fig,[4] .mlx,[5] .mlapp,[6] .mltbx,[7] .mlappinstall,[8] .mlpkginstall[9] mathworks.com MATLAB Programming at Wikibooks
Developer(s) L-shaped membrane logo[18] MathWorks 1984; 38 years ago C/C++, MATLAB Windows, macOS, and Linux[19][20] IA-32, x86-64 Numerical computing Proprietary commercial software mathworks.com

MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm 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.

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 multi-domain simulation and model-based design for dynamic and embedded systems.

As of 2020, MATLAB has more than 4 million users worldwide.[21] They come from various backgrounds of engineering, science, and economics.

## History

### Origins

MATLAB was invented by mathematician and computer programmer Cleve Moler.[22] The idea for MATLAB was based on his 1960s PhD thesis.[22] Moler became a math professor at the University of New Mexico and started developing MATLAB for his students[22] as a hobby.[23] He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe.[22] This was followed by Fortran code for linear equations in 1971.[22]

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."[24]

The first early version of MATLAB was completed in the late 1970s.[22] The software was disclosed to the public for the first time in February 1979 at the Naval Postgraduate School in California.[23] Early versions of MATLAB were simple matrix calculators with 71 pre-built functions.[25] At the time, MATLAB was distributed for free[26][27] to universities.[28] Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.[29]: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.[22] John Little and programmer Steve Bangert re-programmed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.[23]

### Commercial development

MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference in Las Vegas.[22][23] MathWorks, Inc. was founded to develop the software[27] and the MATLAB programming language was released.[25] The first MATLAB sale was the following year, when Nick Trefethen from the Massachusetts Institute of Technology bought ten copies.[23][30]

By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use.[23] The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks.[26] 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.[23]

Over time, MATLAB was re-written for early operating systems created by Digital Equipment Corporation, VAX, Sun Microsystems, and for Unix PCs.[23][25] Version 3 was released in 1987.[31] The first MATLAB compiler was developed by Stephen C. Johnson in the 1990s.[25]

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.[25] 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.[25]

### Recent history

Some especially large changes to the software were made with version 8 in 2012.[32] The user interface was reworked and Simulink's functionality was expanded.[33] By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.[25]

## Features

MATLAB combines a desktop environment tuned for iterative analysis and design processes with a programming language that expresses matrix and array mathematics directly. It includes the Live Editor for creating scripts that combine code, output, and formatted text in an executable notebook. It allows to extend its functions and developments of all kinds of discipline through a set of characteristics called toolbox.

### Toolbox

• 5G Toolbox: Simulate, analyze, and test 5G communications systems
• Aerospace Toolbox: Analyze and visualize aerospace vehicle motion using reference standards and models
• Antenna Toolbox: Design, analyze, and visualize antenna elements and antenna arrays
• Audio Toolbox: Design and analyze speech, acoustic, and audio processing systems
• Communications Toolbox: Design and simulate the physical layer of communications systems
• Deep Learning Toolbox: Design, train, and analyze deep learning networks
• DSP System Toolbox: Design and simulate streaming signal processing systems
• Financial Toolbox: Analyze financial data and develop financial models
• LTE Toolbox: Simulate, analyze, and test the physical layer of LTE and LTE-Advanced wireless communications systems
• GPU Coder: Generate CUDA code for NVIDIA GPUs
• MATLAB Compiler: Build standalone executables and web apps from MATLAB programs
• RF PCB Toolbox: Perform electromagnetic analysis of printed circuit boards
• Satellite Communications Toolbox: Simulate, analyze, and test satellite communications systems and links
• SerDes Toolbox: Design SerDes systems and generate IBIS-AMI models for high-speed digital interconnects
• Signal Integrity Toolbox: Simulate and analyze high-speed serial and parallel links
• Signal Processing Toolbox: Perform signal processing and analysis
• Statistics and Machine Learning Toolbox: Analyze and model data using statistics and machine learning
• Symbolic Math Toolbox: Perform symbolic math computations
• Wavelet Toolbox: Analyze and synthesize signals and images using wavelets

In addition to these, you can develop applications for all kinds of industries, with more than 100 Toolboxes for Matlab and Simulink.[34]

## Syntax

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.[35]

### Variables

Variables are defined using the assignment operator, =. MATLAB is a weakly typed programming language because types are implicitly converted.[36] 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,[37] 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

### 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.

Indexing is one-based,[38] which is the usual convention for matrices 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 [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 dot-prime 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 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 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;

### Structures

MATLAB supports structure data types.[39] 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[40] (field look-ups by name, field manipulations, etc.).

### Functions

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.[41] gbImage = imread('ecg.png'); grayImage = rgb2gray(rgbImage); % for non-indexed 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);

### Function handles

MATLAB supports elements of lambda calculus by introducing function handles,[42] or function references, which are implemented either in .m files or anonymous[43]/nested functions.[44]

### Classes and object-oriented programming

MATLAB supports object-oriented programming including classes, inheritance, virtual dispatch, packages, pass-by-value semantics, and pass-by-reference semantics.[45] 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).[46]

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

<graph>{ "version": 2, "width": 400, "height": 200, "data": [ { "name": "table", "values": [ { "x": 3, "y": 1 }, { "x": 1, "y": 3 }, { "x": 2, "y": 2 }, { "x": 3, "y": 4 } ] } ], "scales": [ { "name": "x", "type": "ordinal", "range": "width", "zero": false, "domain": { "data": "table", "field": "x" } }, { "name": "y", "type": "linear", "range": "height", "nice": true, "domain": { "data": "table", "field": "y" } } ], "axes": [ { "type": "x", "scale": "x" }, { "type": "y", "scale": "y" } ], "marks": [ { "type": "rect", "from": { "data": "table" }, "properties": { "enter": { "x": { "scale": "x", "field": "x" }, "y": { "scale": "y", "field": "y" }, "y2": { "scale": "y", "value": 0 }, "fill": { "value": "steelblue" }, "width": { "scale": "x", "band": "true", "offset": -1 } } } } ] }</graph>

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 sine function:

MATLAB supports three-dimensional 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 two-dimensional unnormalized sinc function: This code produces a surface 3D plot of the two-dimensional unnormalized sinc function:

MATLAB supports developing graphical user interface (GUI) applications.[47] UIs can be generated either programmatically or using visual design environments such as GUIDE and App Designer.[48][49]

## MATLAB and other languages

MATLAB can call functions and subroutines written in the programming languages C or Fortran.[50] 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.[51][52] Since 2014 increasing two-way interfacing with Python was being added.[53][54]

Libraries written in Perl, Java, ActiveX or .NET can be directly called from MATLAB,[55][56] 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[57] which is sold separately by MathWorks, or using an undocumented mechanism called JMI (Java-to-MATLAB Interface),[58][59] (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.[60]

As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.[61][62]

Libraries also exist to import and export MathML.[63]

While MATLAB is the most popular commercial numerical computation software package,[64] 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.[64][65]

## 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.[66]

## Release history

MATLAB is updated twice per year.[67]:517[33] In addition to new features and other improvements, each release has new bug fixes and smaller changes.[68]

Version[69] Release name Number Bundled JVM Year Release date Notes
MATLAB 1.0 1984
MATLAB 2 1986
MATLAB 3 1987 First Matlab toolbox introduced; support for ordinary differential equations added.[25]:81
MATLAB 3.5 1990 Ran on DOS but needed at least a 386 processor; needed a math coprocessor.
MATLAB 4 1992 Ran on Windows 3.1x and 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 Macs.
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 Last release for Windows 95.
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 Windows 98, Windows ME, IBM/AIX, Alpha/TRU64, and SGI/IRIX.[70]
MATLAB 7 R14 14 1.4.2 2004 June 2004 Introduced anonymous and nested functions;[71] re-introduced for Mac (under Mac OS X).
MATLAB 7.0.1 R14SP1 October 2004
R14SP1+ 2004 November 2004 Parallel Computing Toolbox introduced.[25]:4[72]:3
MATLAB 7.0.4 R14SP2 1.5.0 2005 March 7, 2005 Support added for memory-mapped files.[73]
MATLAB 7.1 R14SP3 1.5.0 September 1, 2005 First 64-bit version available for Windows XP 64-bit.
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 added.
MATLAB 7.4 R2007a 17 1.5.0_07 2007 March 1, 2007 New bsxfun function added to apply element-by-element binary operation with singleton expansion enabled.[74]
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;[75] new internal format for P-code.
MATLAB 7.6 R2008a 19 1.6.0 2008 March 1, 2008 Major enhancements to object-oriented programming abilities with a new class definition syntax;[76] ability to manage namespaces with packages.[77]
MATLAB 7.7 R2008b 20 1.6.0_04 October 9, 2008 Last release for processors w/o SSE2; New Map data structure;[78] upgrades to random number generators.[79]
MATLAB 7.8 R2009a 21 1.6.0_04 2009 March 6, 2009 First release for Microsoft 32-bit & 64-bit Windows 7; new external interface to .NET Framework.[80]
MATLAB 7.9 R2009b 22 1.6.0_12 September 4, 2009 First release for Intel 64-bit Mac, and last for Solaris SPARC; new use for the tilde operator (~) to ignore arguments in function calls.[81][82]
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 32-bit Mac.
MATLAB 7.11 R2010b 24 1.6.0_17 September 3, 2010 Added support for enumerations;[83] added features for running MATLAB code on NVIDIA CUDA-based GPUs.[84]
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[85] Bug fixes.
MATLAB 7.12 R2011a 25 1.6.0_17 April 8, 2011 New rng function to control random number generation.[86][87][88]
MATLAB 7.13 R2011b 26 1.6.0_17 September 1, 2011 Added ability to access/change parts of variables directly in MAT-files, without loading into memory;[89] increased maximum local workers with Parallel Computing Toolbox from 8 to 12.[90]
MATLAB 7.14 R2012a 27 1.6.0_17 2012 March 1, 2012 Last version with 32-bit Linux support.[91]
MATLAB 8 R2012b 28 1.6.0_17 September 11, 2012 First release with Toolstrip interface;[92] MATLAB Apps introduced;[93] redesigned documentation system.
MATLAB 8.1 R2013a 29 1.6.0_17 2013 March 7, 2013 New unit testing framework.[94]
MATLAB 8.2 R2013b 30 1.7.0_11 September 6, 2013[95] Built in Java Runtime Environment (JRE) updated to version 7;[96] New table data type.[97]
MATLAB 8.3 R2014a 31 1.7.0_11 2014 March 7, 2014[98] Simplified compiler setup for building MEX-files; 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 class-based graphics engine (a.k.a. HG2);[99] tabbing function in GUI;[100] improved user toolbox packaging and help files;[101] new objects for time-date manipulations;[102] Git-Subversion integration in IDE;[103] big data abilities with MapReduce (scalable to Hadoop);[104] new py package for using Python from inside MATLAB;[105] new engine interface to call MATLAB from Python;[106] several new and improved functions: webread (RESTful web services with JSON/XML support), tcpclient (socket-based connections), histcounts, histogram, animatedline, and others.
MATLAB 8.5 R2015a 33 1.7.0_60 2015 March 5, 2015
MATLAB 8.5 R2015aSP1 1.7.0_60 October 14, 2015 Last release supporting Windows XP and Windows Vista.
MATLAB 8.6 R2015b 34 1.7.0_60 September 3, 2015 New MATLAB execution engine (a.k.a. LXE);[107] graph and digraph classes to work with graphs and networks;[108] MinGW-w64 as supported compiler on Windows;[109] last version with 32-bit support.
MATLAB 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);[110] App Designer introduced: a new development environment for building apps (with new kind of UI figures, axes, and components);[111] pause execution of running programs using a Pause Button.
MATLAB 9.1 R2016b 36 1.7.0_60 September 15, 2016 Added ability to define local functions in scripts;[112] automatic expansion of dimensions (previously provided via explicit call to bsxfun); tall arrays for Big data;[113] new string type;[114] new functions to encode/decode JSON;[115] official MATLAB Engine API for Java.[60]
MATLAB 9.2 R2017a 37 1.7.0_60 2017 March 9, 2017 Released MATLAB Online: cloud-based MATLAB desktop accessed in a web browser;[116] double-quoted strings; new memoize function for Memoization; expanded object properties validation;[117] mocking framework for unit testing;[118] MEX targets 64-bit by default; new heatmap function for creating heatmap charts.[119]
MATLAB 9.3 R2017b 38 1.8.0_121 September 21, 2017 Introduced a GPU Coder that converts MATLAB code to CUDA code for Nvidia.[120]
MATLAB 9.4 R2018a 39 1.8.0_144 2018 March 15, 2018[121] Improvements to the Live editor; introduction of the C++ MEX interface; ability to customize tab completion; web applications.[122]
MATLAB 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.[123]
MATLAB 9.6 R2019a 41 1.8.0_181 2019 March 20, 2019 Released MATLAB Projects; added state machine programming with Stateflow.[124]
MATLAB 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.[125]
MATLAB 9.8 R2020a 43 2020 March 19, 2020 Removal of Mupad notebook; improved support for AMD CPUs (AVX2);[126] default UTF-8 encoding for MATLAB code files;[127] ability to create stand-alone applications with Simulink.[128]
MATLAB 9.9 R2020b 44 September 17, 2020 Improved support for AMD CPUs (AVX2);[126] online version of Simulink.[129]
MATLAB 9.10 R2021a 45 2021 March 11,2021
MATLAB 9.11 R2021b 46 September 22, 2021
MATLAB 9.12.0 R2022a 2022 March 9, 2022

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.[130]

## Notes

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