MATLAB

MATLAB (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.

, MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research.

History

Origins

MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis.

The first early version of MATLAB was completed in the late 1970s. Early versions of MATLAB were simple matrix calculators with 71 pre-built functions. At the time, MATLAB was distributed for free to universities. Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.

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.

By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use. The first MATLAB compiler was developed by Stephen C. Johnson in the 1990s. The user interface was reworked and Simulink's functionality was expanded.

By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.

{|class="sortable wikitable"

|+ 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

| rowspan=2|2003

!R13SP2

|6.5.2

!R14

|6.0

| rowspan=2|2004

!R14SP1

|7.0.1

|6.1

!R14SP2

|7.0.4

|6.2

| rowspan=2|2005

!R14SP3

|7.1

|6.3

!R2006a

|7.2

|6.4

| rowspan=2|2006

!R2006b

|7.3

|6.5

!R2007a

|7.4

|6.6

| rowspan=2|2007

!R2007b

|7.5

|7.0

!R2008a

|7.6

|7.1

| rowspan=2|2008

!R2008b

|7.7

|7.2

!R2009a

|7.8

|7.3

| rowspan=2|2009

!R2009b

|7.9

|7.4

!R2010a

|7.10

|7.5

| rowspan=2|2010

!R2010b

|7.11

|7.6

!R2011a

|7.12

|7.7

| rowspan=2|2011

!R2011b

|7.13

|7.8

!R2012a

|7.14

|7.9

|rowspan=2|2012

!R2012b

|8.0

!R2013a

|8.1

|rowspan=2|2013

!R2013b

|8.2

!R2014a

|8.3

|rowspan=2|2014

!R2014b

|8.4

!R2015a

|8.5

|rowspan=2|2015

!R2015b

|8.6

!R2016a

|9.0

|8.7

| rowspan="2" |2016

!R2016b

|9.1

|8.8

!R2017a

|9.2

|8.9

| rowspan="2" |2017

!R2017b

|9.3

|9.0

!R2018a

|9.4

|9.1

| rowspan="2" |2018

!R2018b

|9.5

|9.2

!R2019a

|9.6

|9.3

| rowspan="2" |2019

!R2019b

|9.7

|10.0

!R2020a

|9.8

|10.1

| rowspan="2" |2020

!R2020b

|9.9

|10.2

!R2021a

|9.10

|10.3

| rowspan="2" |2021

!R2021b

|9.11

|10.4

!R2022a

|9.12

|10.5

| rowspan="2" |2022

!R2022b

|9.13

|10.6

!R2023a

|9.14

|10.7

| rowspan="2" |2023

!R2023b

|23.2

!R2024a

|24.1

| rowspan="2" |2024

!R2024b

|24.2

!R2025a

|25.1

| rowspan="2" |2025

!R2025b

|25.2

!R2026a

|26.1

| rowspan="1" |2026

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.

"Hello, world!" example

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

disp('Hello, world!')

</syntaxhighlight>

It displays like so:

Hello, world!

</syntaxhighlight>

Variables

Variables are defined using the assignment operator, <code>=</code>.

MATLAB is a weakly typed programming language because types are implicitly converted. 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, 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 =

>> 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<code>:</code>increment<code>:</code>terminator. For instance:

>> array = 1:2:9

array =

1 3 5 7 9

</syntaxhighlight>

defines a variable named <code>array</code> (or assigns a new value to an existing variable with the name <code>array</code>) 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

</syntaxhighlight>

assigns to the variable named <code>ari</code> 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, 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 <code>[]</code>. Parentheses <code>()</code> 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 =

</syntaxhighlight>

Sets of indices can be specified by expressions such as <code>2:4</code>, which evaluates to <code>[2, 3, 4]</code>. 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

</syntaxhighlight>

A square identity matrix of size n can be generated using the function <code>eye</code>, and matrices of any size with zeros or ones can be generated with the functions <code>zeros</code> and <code>ones</code>, respectively.

>> eye(3,3)

ans =

1 0 0

0 1 0

0 0 1

>> zeros(2,3)

ans =

0 0 0

>> ones(2,3)

ans =

1 1 1

</syntaxhighlight>

Transposing a vector or a matrix is done either by the function <code>transpose</code> 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 =

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, <code>mod(2*J,n)</code> will multiply every element in J by 2, and then reduce each element modulo n. MATLAB does include standard <code>for</code> and <code>while</code> 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 <code>meshgrid</code> is used here to generate square matrices and containing ):

[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. 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.).

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.

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 and object-oriented programming

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

Method call behavior is different between value and reference classes. For example, a call to a method:

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:

classdef Hello

methods

function greet(obj)

disp('Hello!')

end

</syntaxhighlight>

When put into a file named <code>hello.m</code>, this can be executed with the following commands:

>> 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:

x = 0:pi/100:2*pi;

y = sin(x);

plot(x,y)

</syntaxhighlight>

produces the following figure of the sine function:

350px

MATLAB supports three-dimensional graphics as well:

| valign="top" |<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>

| valign="top" |<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:

| style="text-align:center;"|File:MATLAB mesh sinc3D.svg

| style="text-align:center;"|File:MATLAB surf sinc3D.svg

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

MATLAB and other languages

MATLAB can call functions and subroutines written in the programming languages C or Fortran. 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. Since 2014 increasing two-way interfacing with Python was being added.

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). Official MATLAB API for Java was added in 2016.

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.

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.

Notes

External links

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MATLAB documentation

History

Origins

Syntax

"Hello, world!" example

Variables

Vectors and matrices

Structures

Functions

Function handles

Classes and object-oriented programming

Graphics and graphical user interface programming

MATLAB and other languages

Relations to US sanctions

See also

Notes

Further reading

External links