MATLAB

MATLAB

File:MATLAB-R2008a-for-Linux.png MATLAB R2008a screenshot
Developer(s)	MathWorks
Stable release	R2011a / April 8, 2011 (2011-04-08)
Preview release	R2020a Prerelease [±]
Written in	C, Java
Operating system	Cross-platform
Type	Technical computing
License	Proprietary
Website	MATLAB product page

MATLAB

Paradigm	multi-paradigm: imperative, procedural, object-oriented, array
Designed by	Cleve Moler
Developer	MathWorks
First appeared	late 1970s
Preview release	R2020a Prerelease [±]
Typing discipline	dynamic, weak
OS	Cross-platform
Website	www.mathworks.com/products/matlab.html,%20https://de.mathworks.com/products/matlab.html

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

MATLAB was created in the late 1970s by Cleve Moler, the 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. 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 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.

Syntax

The MATLAB application is built around the MATLAB language. The simplest way to execute MATLAB code is to type it in the Command Window, which is one of the elements of the MATLAB Desktop. When code is entered in the Command Window, MATLAB can be used as an interactive mathematical shell. Sequences of commands can be saved in a text file, typically using the MATLAB Editor, as a script or encapsulated into a function, extending the commands available.

Variables

Variables are defined with the assignment operator, =. MATLAB is a weakly dynamically typed programming language. It is a weakly typed 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

MATLAB has several functions for rounding fractional values to integers:

• round(X): round to nearest integer, trailing 5 rounds to the nearest integer away from zero. For example, round(2.5) returns 3; round(-2.5) returns -3.
• fix(X): round to nearest integer toward zero (truncate). For example, fix(2.7) returns 2; fix(-2.7) returns -2
• floor(X): round to the nearest integer toward minus infinity (round to the nearest integer less than or equal to X). For example, floor(2.7) returns 2; floor(-2.3) returns -3.
• ceil(X): round to the nearest integer toward positive infinity (round to the nearest integer greater than or equal to X); for example, ceil(2.3) returns 3; ceil(-2.7) returns -2

Vectors/matrices

MATLAB is a "Matrix Laboratory", and as such it provides many convenient ways for creating vectors, matrices, and multi-dimensional arrays. 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 2-dimensional array, i.e. an m×n array where m and n are greater than or equal to 1. Arrays with more than two dimensions are referred to as multidimensional arrays. Arrays are among the fundamental types and several standard functions natively support array operations which are optimized to work without explicit loops. Therefore the MATLAB language is also an example of array programming language.

MATLAB provides a simple way to define simple arrays using the 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.

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 using MATLAB's vectorized notation often produces code that is easier to read and 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;

Semicolons

Unlike many other languages, where the semicolon is used to terminate commands, in MATLAB the semicolon serves to suppress the output of the line that it concludes (it serves a similar purpose in Mathematica.)

Graphics

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:

Three-dimensional graphics can be produced 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:

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

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.

Secondary programming

MATLAB also carries secondary programming which incorporates the MATLAB standard code into a more user friendly way to represent a function or system.

Classes

MATLAB supports classes, however the syntax and calling conventions are significantly different than in other languages. MATLAB supports value classes and reference classes, depending if the class has handle as super-class (for reference classes) or not (for value classes).

Depending if a class is declared as value or reference, method call behavior is different. For example, a call to a method

object.method();

can alter any variables of object variable only for reference classes.

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 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 MATLAB extension, 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.

License

MATLAB is a proprietary product of MathWorks, so users are subject to vendor lock-in. Although MATLAB Builder 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.

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, IDL by ITT Visual Information Solutions and Metlynx.

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 (but not the MATLAB desktop environment).

Among other languages that treat arrays as basic entities (array programming languages) are APL and J, Fortran 95 and 2003, as well as the statistical language S (the main implementations of S are S-PLUS and the popular open source language R).

There are also several libraries to add similar functionality to existing languages, such as Itpp for C++, Perl Data Language for Perl and SciPy together with NumPy and Matplotlib for Python.

Release history

Version	Release name	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	R7	1994		Ran on Windows 3.1. Required a math coprocessor
MATLAB 5.0	R8	1996
MATLAB 5.1	R9	1997
MATLAB 5.1.1	R9.1
MATLAB 5.2	R10	1998
MATLAB 5.2.1	R10.1
MATLAB 5.3	R11	1999
MATLAB 5.3.1	R11.1
MATLAB 6.0	R12	2000
MATLAB 6.1	R12.1	2001
MATLAB 6.5	R13	2002
MATLAB 6.5.1	R13SP1	2003
MATLAB 6.5.2	R13SP2
MATLAB 7	R14	2004
MATLAB 7.0.1	R14SP1
MATLAB 7.0.4	R14SP2	2005	March 7, 2005
MATLAB 7.1	R14SP3		September 1, 2005
MATLAB 7.2	R2006a	2006	March 1, 2006
MATLAB 7.3	R2006b		September 1, 2006	HDF5-based MAT-file support
MATLAB 7.4	R2007a	2007	March 1, 2007
MATLAB 7.5	R2007b		September 1, 2007	Last release for Windows 2000 and PowerPC Mac. License Server support for Windows Vista
MATLAB 7.6	R2008a	2008	March 1, 2008
MATLAB 7.7	R2008b		October 9, 2008
MATLAB 7.8	R2009a	2009	March 6, 2009	First release for 32-bit & 64-bit Windows 7.
MATLAB 7.9	R2009b		September 4, 2009	First release for Intel 64-bit Mac, and last for Solaris SPARC.
MATLAB 7.9.1	R2009bSP1	2010	April 1, 2010
MATLAB 7.10	R2010a		March 5, 2010	Last release for Intel 32-bit Mac.
MATLAB 7.11	R2010b		September 3, 2010
MATLAB 7.11.1	R2010bSP1	2011	March 17, 2011
MATLAB 7.12	R2011a		April 8, 2011

File Extensions

Native

.fig

MATLAB Figure

.m

MATLAB function, script, or class

.mat

MATLAB binary file for storing variables

.mex...

MATLAB executable (platform specific, e.g. ".mexmac" for the Mac, ".mexglx" for Linux, etc.)

.p

MATLAB content-obscured .m file (result of pcode() )

Third-party

.jkt

GPU Cache file generated by Jacket for MATLAB (AccelerEyes)

.mum

MATLAB CAPE-OPEN Unit Operation Model File (AmsterCHEM)

See also

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

References

• Gilat, Amos (2004). MATLAB: An Introduction with Applications 2nd Edition. John Wiley & Sons. ISBN 978-0-471-69420-5. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)
• Quarteroni, Alfio (2006). Scientific Computing with MATLAB and Octave. Springer. ISBN 978-3-540-32612-0. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• 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.

External links

• MATLAB overview, at the MathWorks website
• System Requirements - Platform Roadmap, at the MathWorks website.
• MATLAB Central File Exchange - library of over 12,000 MATLAB files and toolboxes, mostly distributed under BSD License.
• MATLAB at Curlie
• comp.soft-sys.matlab
• LiteratePrograms (MATLAB)
• Official blogs
• Examples to remote control R&S instruments from MATLAB
• Comparison of mathematical programs for data analysis ScientificWeb
• 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 P. Getreuer
• Calling Matlab from Java: MatlabControl JMI Wrapper, The MatlabJava Server, MatlabControl
• Calling Matlab from Java: using Java RMI server - JAMAL