MATLAB

MATLAB (an abbreviation of "MATrix LABoratory"<ref>Template:Cite web</ref>) 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.

Template:As of, MATLAB has more than four million users worldwide.<ref name="mathworksCompanyOverview">Template:Cite web</ref> They come from various backgrounds of engineering, science, and economics. Template:As of, more than 5000 global colleges and universities use MATLAB to support instruction and research.<ref>Template:Cite web</ref>

History

Origins

MATLAB was invented by mathematician and computer programmer Cleve Moler.<ref name="Chonacky Winch 2005 pp. 9–10">Template:Cite journal</ref> The idea for MATLAB was based on his 1960s PhD thesis.<ref name="Chonacky Winch 2005 pp. 9–10" /> Moler became a math professor at the University of New Mexico and started developing MATLAB for his students<ref name="Chonacky Winch 2005 pp. 9–10" /> as a hobby.<ref name="hobby" /> He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe.<ref name="Chonacky Winch 2005 pp. 9–10" /> This was followed by Fortran code for linear equations in 1971.<ref name="Chonacky Winch 2005 pp. 9–10" />

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."<ref>Template:Cite web</ref>

The first early version of MATLAB was completed in the late 1970s.<ref name="Chonacky Winch 2005 pp. 9–10" /> The software was disclosed to the public for the first time in February 1979 at the Naval Postgraduate School in California.<ref name="hobby">Template:Cite journal</ref> Early versions of MATLAB were simple matrix calculators with 71 pre-built functions.<ref name="Moler Little pp. 1–67">Template:Cite journal</ref> At the time, MATLAB was distributed for free<ref name="Xue Press 2020 p. 21">Template:Cite book</ref><ref name="Press 2008 p. 6">Template:Cite book</ref> to universities.<ref name="Woodford Phillips 2011 p. 1">Template:Cite book</ref> Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.<ref name="Tranquillo 2011 p.">Template:Cite book</ref>Template:RP

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.<ref name="Chonacky Winch 2005 pp. 9–10" /> John Little and programmer Steve Bangert re-programmed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.<ref name="hobby" />

Commercial development

MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference in Las Vegas.<ref name="Chonacky Winch 2005 pp. 9–10" /><ref name="hobby" /> MathWorks, Inc. was founded to develop the software<ref name="Press 2008 p. 6"/> and the MATLAB programming language was released.<ref name="Moler Little pp. 1–67" /> The first MATLAB sale was the following year, when Nick Trefethen from the Massachusetts Institute of Technology bought ten copies.<ref name="hobby" /><ref name="LoTurco 2020">Template:Cite web</ref>

By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use.<ref name="hobby" /> The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks.<ref name="Xue Press 2020 p. 21" /> 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.<ref name="hobby" />

Over time, MATLAB was re-written for early operating systems created by Digital Equipment Corporation, VAX, Sun Microsystems, and for Unix PCs.<ref name="hobby" /><ref name="Moler Little pp. 1–67" /> Version 3 was released in 1987.<ref name="Gatto Rizzoli 1993 pp. 85–88">Template:Cite journal</ref> The first MATLAB compiler was developed by Stephen C. Johnson in the 1990s.<ref name="Moler Little pp. 1–67" />

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.<ref name="Moler Little pp. 1–67" /> 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.<ref name="Moler Little pp. 1–67" />

Recent history

Some especially large changes to the software were made with version 8 in 2012.<ref name="Cho Martinez 2014 p.">Template:Cite book</ref> The user interface was reworkedTemplate:Fact and Simulink's functionality was expanded.<ref name="Xue Chen 2013 p. 17">Template:Cite book</ref>

By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.<ref name="Moler Little pp. 1–67" />

Release history

For a complete list of changes of both MATLAB an official toolboxes, check MATLAB previous releases.<ref>Template:Cite web</ref>

Versions of the MATLAB product family

Name of release	MATLAB	Simulink, Stateflow (MATLAB attachments)	Year
Volume 8	5.0		1996
Volume 9	5.1		1997
R9.1	5.1.1		1997
R10	5.2		1998
R10.1	5.2.1		1998
R11	5.3		1999
R11.1	5.3.1		1999
R12	6.0		2000
R12.1	6.1		2001
R13	6.5		2002
R13SP1	6.5.1		2003
R13SP2	6.5.2
R14	7	6.0	2004
R14SP1	7.0.1	6.1
R14SP2	7.0.4	6.2	2005
R14SP3	7.1	6.3
R2006a	7.2	6.4	2006
R2006b	7.3	6.5
R2007a	7.4	6.6	2007
R2007b	7.5	7.0
R2008a	7.6	7.1	2008
R2008b	7.7	7.2
R2009a	7.8	7.3	2009
R2009b	7.9	7.4
R2010a	7.10	7.5	2010
R2010b	7.11	7.6
R2011a	7.12	7.7	2011
R2011b	7.13	7.8
R2012a	7.14	7.9	2012
R2012b	8.0	8.0
R2013a	8.1	8.1	2013
R2013b	8.2	8.2
R2014a	8.3	8.3	2014
R2014b	8.4	8.4
R2015a	8.5	8.5	2015
R2015b	8.6	8.6
R2016a	9.0	8.7	2016
R2016b	9.1	8.8
R2017a	9.2	8.9	2017
R2017b	9.3	9.0
R2018a	9.4	9.1	2018
R2018b	9.5	9.2
R2019a	9.6	9.3	2019
R2019b	9.7	10.0
R2020a	9.8	10.1	2020
R2020b	9.9	10.2
R2021a	9.10	10.3	2021
R2021b	9.11	10.4
R2022a	9.12	10.5	2022
R2022b	9.13	10.6
R2023a	9.14	10.7	2023
R2023b	23.2	23.2
R2024a	24.1	24.1	2024
R2024b	24.2	24.2

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.<ref>Template:Cite web</ref>

"Hello, world!" example

An example of a "Hello, world!" program exists in MATLAB.

<syntaxhighlight lang="matlab"> disp('Hello, world!') </syntaxhighlight>

It displays like so:

<syntaxhighlight lang="output"> Hello, world! </syntaxhighlight>

Variables

Variables are defined using the assignment operator, =.

MATLAB is a weakly typed programming language because types are implicitly converted.<ref>Template:Cite web</ref> 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,<ref>Template:Cite web</ref> 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: <syntaxhighlight lang="matlabsession"> >> 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

</syntaxhighlight>

Vectors and matrices

A simple array is defined using the colon syntax: initial:increment:terminator. For instance: <syntaxhighlight lang="matlabsession"> >> array = 1:2:9 array =

1 3 5 7 9

</syntaxhighlight> 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. <syntaxhighlight lang="matlabsession"> >> ari = 1:5 ari =

1 2 3 4 5

</syntaxhighlight> 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,<ref>Template:Cite web</ref> 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 separate the rows. 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).

<syntaxhighlight lang="matlabsession"> >> 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

</syntaxhighlight>

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: <syntaxhighlight lang="matlabsession"> >> A(2:4,3:4) ans =

11 8
7 12
14 1

</syntaxhighlight> 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. <syntaxhighlight lang="matlabsession"> >> 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

</syntaxhighlight>

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): <syntaxhighlight lang="matlabsession"> >> 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

</syntaxhighlight>

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 APL and 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 Template:Mvar and Template:Mvar containing Template:Tmath):

<syntaxhighlight lang="matlab"> [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; </syntaxhighlight>

Structures

MATLAB supports structure data types.<ref>Template:Cite web</ref> 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<ref>Template:Cite web</ref> (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.<ref>Template:Cite web</ref> Template:Sxhl

Function handles

MATLAB supports elements of lambda calculus by introducing function handles,<ref>Template:Cite web</ref> or function references, which are implemented either in .m files or anonymous<ref>Template:Cite web</ref>/nested functions.<ref>Template:Cite web</ref>

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.<ref>Template:Cite web</ref> 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).<ref>Template:Cite web</ref>

Method call behavior is different between value and reference classes. For example, a call to a method: <syntaxhighlight lang="matlab"> object.method(); </syntaxhighlight> 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:

<syntaxhighlight lang="matlab"> classdef Hello

   methods
       function greet(obj)
           disp('Hello!')
       end
   end

end </syntaxhighlight>

When put into a file named hello.m, this can be executed with the following commands: <syntaxhighlight lang="matlabsession"> >> x = Hello(); >> x.greet(); Hello! </syntaxhighlight>

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: <syntaxhighlight lang="matlab"> x = 0:pi/100:2*pi; y = sin(x); plot(x,y) </syntaxhighlight> produces the following figure of the sine function:

File:Matlab plot sin.svg

MATLAB supports three-dimensional graphics as well:

<syntaxhighlight lang="matlab">[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 </syntaxhighlight>		<syntaxhighlight lang="matlab"> [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})') </syntaxhighlight>
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:
File:MATLAB mesh sinc3D.svg		File:MATLAB surf sinc3D.svg

MATLAB supports developing graphical user interface (GUI) applications.<ref>Template:Cite web</ref> UIs can be generated either programmatically or using visual design environments such as GUIDE and App Designer.<ref>Template:Cite web</ref><ref>Template:Cite web</ref>

MATLAB and other languages

MATLAB can call functions and subroutines written in the programming languages C or Fortran.<ref>Template:Cite web</ref> 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.<ref>Template:Cite web</ref><ref>Template:Cite web</ref> Since 2014 increasing two-way interfacing with Python was being added.<ref>Template:Cite web</ref><ref>Template:Cite web</ref>

Libraries written in Perl, Java, ActiveX or .NET can be directly called from MATLAB,<ref>Template:Cite web</ref><ref>Template:Cite web</ref> 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<ref>Template:Cite web</ref> which is sold separately by MathWorks, or using an undocumented mechanism called JMI (Java-to-MATLAB Interface),<ref>Template:Cite web</ref><ref>Template:Cite web</ref> (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.<ref name="MATLAB Engine API for Java">Template:Cite web</ref>

As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.<ref>Template:Cite web</ref><ref>Template:Cite web</ref>

Libraries also exist to import and export MathML.<ref>Template:Cite web</ref>

Relations to US sanctions

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 open-source alternatives and by developing domestic alternatives.<ref>Template:Cite web</ref>

See also

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

Further reading

• Template:Cite book
• Template:Cite book
• Template:Cite book
• Template:Cite book

External links

• Template:Official website