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{{Infobox_Software | name = MATLAB
| logo = [[Image:Matlab.jpg|100px]]
| screenshot = [[Image:Matlab7.4.png|300px]]
| caption = This is a screenshot showing MATLAB 7.4 running on [[Windows XP]] pro 64 bit with a QR decomposition.
| developer = [[The MathWorks]]
| latest_release_version = R2007a
| latest_release_date = March 1, 2007
| operating_system = [[Cross-platform]] [http://www.mathworks.com/products/matlab/requirements.html (list)]
| genre = [[List of numerical analysis software|Technical computing]]
| license = [[Proprietary software|Proprietary]]
| website = [http://www.mathworks.com/products/matlab/ MATLAB product page]
}}

'''MATLAB''' is a [[Numerical analysis|numerical computing]] environment and [[programming language]]. Created by ''[[The MathWorks]]'', MATLAB allows easy [[matrix (mathematics)|matrix]] manipulation, plotting of [[function (mathematics)|function]]s and data, implementation of [[algorithm]]s, creation of [[user interface]]s, and interfacing with programs in other languages. Although it specializes in numerical computing, an optional toolbox interfaces with the [[Maple (software)|Maple]] symbolic engine, allowing it to be part of a full [[computer algebra system]].

As of [[2004]], MATLAB was used by more than one million people in industry and academia.<ref>Richard Goering, "Matlab edges closer to electronic design automation world," ''EE Times'', 10/04/2004 [http://www.eetimes.com/news/design/showArticle.jhtml?articleID=49400392 online]</ref> 

== History ==
Short for "'''mat'''rix '''lab'''oratory", MATLAB was invented in the late [[1970s]] by [[Cleve Moler]], then chairman of the [[computer science]] department at the [[University of New Mexico]].  He designed it to give his students access to [[LINPACK]] and [[EISPACK]] without having to learn [[Fortran]].  It soon spread to other universities and found a strong audience within the [[applied mathematics]] community.  [[John N. Little|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 (programming language)|C]] and founded [[The MathWorks]] in [[1984]] to continue its development.  These rewritten libraries were known as JACKPAC.

MATLAB was first adopted by [[control engineering|control design engineers]], 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 with image processing.<ref>{{cite web | url = http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html | title = The Origins of Matlab | author = Cleve Moler, the creator of MATLAB | accessmonthday = April 15 | accessyear = 2007 | year = 2004 | month = December }}</ref>

== Syntax ==
{{Unreferenced|date=April 2007}}

MATLAB is built around the MATLAB language, sometimes called ''M-code'' or simply ''M''.  The simplest way to execute M-code is to type it in at the prompt, <code>>> </code>, in the Command Window, one of the elements of the MATLAB Desktop.  In this way, MATLAB can be used as an interactive mathematical [[shell (computing)|shell]].  Sequences of commands can be saved in a text file, typically using the MATLAB Editor, as a [[Shell script|script]] or encapsulated into a [[Functional programming|function]], extending the commands available.<ref>[http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html MATLAB technical documentation]</ref>

=== Variables ===

Variables are defined with the assignment operator, <code>=</code>.  MATLAB is [[Type system#Static and dynamic typing|dynamically typed]], meaning that variables can be assigned without declaring their type, and that their type can change.  Values can come from [[constant]]s, from computation involving values of other variables, or from the output of a function.  For example:
<pre>
>> x = 17
x =
    17
>> x = 'hat'
x =
hat
>> x = 3*4
x =
    12
>> y = 3*sin(x)
y =
   -1.6097
</pre>

=== Vectors/Matrices ===

MATLAB is a "Matrix Laboratory", and as such it provides many convenient ways for creating matrices of various dimensions. In the MATLAB vernacular, a ''vector'' refers to a one dimensional (1×''N'' or ''N''×1) matrix, commonly referred to as an array in other programming languages. A ''matrix'' generally refers to a multi-dimensional matrix, that is, a matrix with more than one dimension, for instance, an ''N''×''M'', an ''N''×''M''×''L'', etc., where ''N'', ''M'', and ''L'' are greater than 1. In other languages, such a matrix might be referred to as an array of arrays, or array of arrays of arrays, etc.

MATLAB provides a simple way to define simple arrays using the syntax: ''init''<code>:</code>''increment''<code>:</code>''terminator''. For instance:
<pre>
>> array = 1:2:9
array =
     1     3     5     7     9
</pre>
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 ''init'' value, and each value increments from the previous value by 2 (the ''increment'' value), and stops once it reaches but not exceeding 9 (9 being the value of the terminator).
<pre>
>> array = 1:3:9
array =
     1     4     7
</pre>
the ''increment'' value can actually be left out of this syntax (along with one of the colons), to use a default value of 1.
<pre>
>> ari = 1:5
ari =
     1     2     3     4     5
</pre>
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 incrementer.

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 []. Elements and subarrays are accessed using parenthesis ().
<pre>
>> 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

>> A(2:4,3:4)

ans =

    11     8
     7    12
    14     1

</pre>
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.
<pre>
>> 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
</pre>

=== Semicolon ===

In many other languages, the semicolon is required to terminate commands. In MATLAB the semicolon is optional. If a statement is not terminated with a semicolon, then the result of the statement is displayed. A statement that does not explicitly return a result, for instance 'clc', will behave the same whether or not a semicolon is included. <ref>The MathWorks, ''[http://www.mathworks.com/access/helpdesk/help/techdoc/ref/specialcharacters.html MATLAB Function Reference]'', accessed [[12 October]], [[2006]].</ref>

=== Graphics ===

Function ''plot'' can be used to produce a graph from two vectors ''x'' and ''y''. The code:
<pre>
x = 0:pi/100:2*pi;
y = sin(x);
plot(x,y)
</pre>
produces the following figure of the [[sine wave|sine function]]:

[[Image:Matlab plot sin.svg|350px]]

Three dimensional graphics can be produced using the functions ''surf'', ''plot3'' or ''mesh''.
<pre>
[X,Y] = meshgrid(-8:.5:8);
R = sqrt(X.^2 + Y.^2)+eps;
Z = sin(R)./R;
surf(X,Y,Z)
</pre>
This code produces the figure of a two-dimensional [[sinc function]].

[[Image:Matlab plot sinc.png|350px]]

== Code snippets ==

This code, excerpted from the function ''magic.m'', creates a [[magic square]] ''M'' for odd values of ''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;

Note that this code performs operations on vectors and matrices without the use of "for" loops. Idiomatic MATLAB programs usually operate on whole arrays at a time. The MESHGRID utility function above creates arrays like these:

<pre>
J =

     1     2     3
     1     2     3
     1     2     3

I =

     1     1     1
     2     2     2
     3     3     3
</pre>

Most scalar functions can also be used on arrays, and will apply themselves in parallel to each element. Thus mod(2*J,n) will (scalar) multiply the entire J array with 2, before reducing each element modulo ''n''.

MATLAB does include standard "for" and "while" loops, but using MATLAB's vectorized notation often produces code that is easier to read and faster to execute.

Most commonly used functions are already included in MATLAB, and the same magic square could be obtained by using the ''magic'' function.

<pre>
magic(n)
</pre>

== Limitations ==
{{Unreferenced|date=April 2007}}
MATLAB is a [[proprietary software|proprietary]] product of The MathWorks, so users are subject to [[vendor lock-in]].  Some [[list of numerical analysis software|other source languages]], however, are partially compatible and provide a migration path.

The language shows a mixed heritage with a sometimes erratic syntax.  For example, MATLAB uses parentheses, e.g. <code>y = f(x)</code>, for both indexing into an array and calling a function.  Although this ambiguous syntax can facilitate a switch between a [[subroutine|procedure]] and a [[lookup table]], both of which correspond to mathematical [[Function (mathematics)|functions]], a careful reading of the code may be required to establish the intent.

Many functions have a different behavior with matrix and vector arguments. Since vectors are matrices of one row or one column, this can give unexpected results. For instance, function <code>sum(A)</code> where <code>A</code> is a matrix gives a row vector containing the sum of each column of <code>A</code>, and <code>sum(v)</code> where <code>v</code> is a column or row vector gives the sum of its elements; hence the programmer must be careful if the matrix argument of <code>sum</code> can degenerate into a single-row array. While <code>sum</code> and many similar functions accept an optional argument to specify a direction, others, like <code>plot</code>, do not, and require additional checks. There are other cases where MATLAB's interpretation of code may not be consistently what the user intended (e.g. how spaces are handled inside brackets as separators where it makes sense but not where it doesn't, or backslash [[escape character|escape]] sequences which are interpreted by some functions like <code>fprintf</code> but not directly by the language parser because it wouldn't be convenient for Windows directories). What might be considered as a convenience for commands typed interactively where the user can check that MATLAB does what the user wants may be less supportive of the need to construct [[reusability|reusable code]].

Though other [[datatype]]s are available, the default is a [[matrix (mathematics)|matrix]] of [[Double precision|double]]s.  This array type does not include a way to attach attributes such as engineering units or sampling rates. Although time and date markers were added in R14SP3 with the time series object, [[sample rate]] is still lacking. Such attributes can be managed by the user via structures or other methods.

[[Array#Indices into arrays|Array indexing]] is one-based which is the common convention for [[matrix (mathematics)|matrices]] in mathematics, but does not accommodate the indexing convention of sequences that have zero or negative indices.  For instance, in MATLAB the [[Discrete Fourier transform|DFT]] (or [[Fast Fourier transform|FFT]]) is defined with the [[DC component]] at index 1 instead of index 0, which is not consistent with the standard definition of the DFT.  This one-based indexing convention is [[Hard coding|hard coded]] into MATLAB, making it impossible for a user to define their own zero-based or negative indexed arrays to concisely model an idea having non-positive indices.

MATLAB doesn't support [[reference (computer science)|reference]]s, which makes it difficult to implement data structures that contain indirections, such as open hash tables, linked lists, trees, and various other common computer science data structures. In addition, since the language is consistently call-by-value, it means that functions that modify array or object values must return these through output parameters and the caller must assign those modified values for the change to be persistent.

== See also ==
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Please do not add any links to other individual languages. See [[Talk:MATLAB#DADiSP]].
For discussion on references to (GNU) Octave see [[Talk:MATLAB#Octave]]
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MATLAB add-ons:
* [[Simulink]] is a graphical block diagramming tool for modeling, simulating and analyzing multi-domain dynamic systems.
* [[Stateflow]] is a simulation tool for event-driven systems.

Application areas:
* [[MATLAB image processing]]

Similar products, some of which are free and/or partially compatible:
* The MATLAB ''language'' is an [[Array programming|array programming language]].  
* The MATLAB ''software'' is a numerical analysis [[integrated development environment|IDE]]. See [[List of numerical analysis software]] for an exhaustive list.
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Please do not add any links to other individual languages. See [[Talk:MATLAB#DADiSP]].
For discussion on references to (GNU) Octave see [[Talk:MATLAB#Octave]]
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==References==

{{reflist}}

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Additional sources:

* {{cite book |last=Gilat |first=Amos |authorlink= |coauthors= |title=MATLAB: An Introduction with Applications 2nd Edition |year=2004 |publisher=John Wiley & Sons |location= |id=ISBN 0-471-69420-7 }}

==External links==
{{wikibookspar|Programming|MATLAB}}
* [http://www.mathworks.com/products/matlab/ MATLAB overview], at ''The MathWorks'' website
* [http://www.cyclismo.org/tutorial/matlab/ A tutorial for beginners]
* [http://www.mathworks.com/matlabcentral/ MATLAB Central the MATLAB user community]
* [http://dmoz.org/Science/Math/Software/MATLAB/ The MATLAB category at the Open Directory Project]
* [http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html Information about the history of and inspiration for MATLAB, written by Cleve Moler]
* [news://comp.soft-sys.matlab comp.soft-sys.matlab]
* [http://xtargets.com/snippets Share MATLAB code snippets online]
* [http://en.literateprograms.org/Category:Programming_language:Matlab LiteratePrograms (MATLAB)]
* [http://www.math.tu-berlin.de/~ehrhardt/matlab_alternatives.html Free Alternatives to MATLAB]

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