MATLAB
MATLAB R2008a running on Ubuntu Linux 7. Ubuntu Kubuntu Edubuntu Xubuntu Gobuntu --> Ubuntu 10 to train and test a Support Vector Machine via calling a C program SVM Light. Support vector machines ( SVMs) are a set of related Supervised learning methods used for classification and regression.
Developed by	The MathWorks
Latest release	R2008a / March 1, 2008 (2008-03-01); 101 days ago
OS	Cross-platform[1]
Genre	Technical computing
License	Proprietary
Website	MATLAB product page

MATLAB is a numerical computing environment and programming language. A software developer is a person or organization concerned with facets of the software development process wider than design and coding a somewhat broader scope of The MathWorks, Inc is a privately held mid-size multi-national Corporation which specializes in technical computing software. A software release is the distribution whether public or private of an initial or new and upgraded version of a Computer software product Events 86 BC - Lucius Cornelius Sulla, at the head of a Roman Republic army enters in Athens, removing the Tyrant 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common An operating system (commonly abbreviated OS and O/S) is the software component of a Computer system that is responsible for the management and coordination In computing cross-platform (also known as multi-platform) is a term used to refer to Computer software or computing methods and concepts that are implemented Computer software can be organized into categories based on common function type or field of use Listed here are a number of computer programs used for performing numerical calculations acslX is a software application for modeling and evaluating the performance A software license (or software licence in commonwealth usage is a Legal instrument governing the usage or redistribution of copyright protected software Proprietary software is Computer software on which the producer has set restrictions on use private modification copying, or republishing. A website (alternatively web site or Web site, a back-construction from the Proper noun World Wide Web) is a collection of Web pages A programming paradigm is a fundamental style of Computer programming. In Computer science, imperative programming is a Programming paradigm that describes computation in terms of statements that change a program state This article is about the Decade 1970-1979 For the Year 1970 see 1970. Cleve Barry Moler is a mathematician and computer programmer specializing in Numerical analysis. A software developer is a person or organization concerned with facets of the software development process wider than design and coding a somewhat broader scope of The MathWorks, Inc is a privately held mid-size multi-national Corporation which specializes in technical computing software. In Computer science, a type system defines how a Programming language classifies values and expressions into '''types''', how it can In Computer science, a type system defines how a Programming language classifies values and expressions into '''types''', how it can An operating system (commonly abbreviated OS and O/S) is the software component of a Computer system that is responsible for the management and coordination In computing cross-platform (also known as multi-platform) is a term used to refer to Computer software or computing methods and concepts that are implemented Numerical analysis is the study of Algorithms for the problems of continuous mathematics (as distinguished from Discrete mathematics) A programming language is an Artificial language that can be used to write programs which control the behavior of a machine particularly a Computer. Created by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. The MathWorks, Inc is a privately held mid-size multi-national Corporation which specializes in technical computing software. In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation The user interface (or Human Computer Interface) is the aggregate of means by which people&mdash the users '&mdash interact with the System Although it is numeric only, an optional toolbox interfaces with the Maple symbolic engine, allowing access to computer algebra capabilities. Maple is a general-purpose commercial Computer algebra system. A computer algebra system ( CAS) is a software program that facilitates Symbolic mathematics.

As of 2004, MathWorks has claimed that MATLAB is used by more than one million people across industry and the academic world. "MMIV" redirects here For the Modest Mouse album see " Baron von Bullshit Rides Again " ^[2]

History

Short for "matrix laboratory", MATLAB was invented in the late 1970s by Cleve Moler, then chairman of the computer science department at the University of New Mexico. This article is about the Decade 1970-1979 For the Year 1970 see 1970. Cleve Barry Moler is a mathematician and computer programmer specializing in Numerical analysis. Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their The University of New Mexico ( UNM) is a Public University in Albuquerque, New Mexico. ^[3] He designed it to give his students access to LINPACK and EISPACK without having to learn Fortran. LINPACK is a software library for performing numerical Linear algebra on digital computers EISPACK is a Software library for Numerical computation of Eigenvalues and Eigenvectors of matrices written in FORTRAN. Fortran (previously FORTRAN) is a general-purpose, procedural, imperative Programming language that is especially suited to It soon spread to other universities and found a strong audience within the applied mathematics community. Applied mathematics is a branch of Mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. John N ( Jack) Little is the president and co-founder of The MathWorks, and co-author of the company's first product MATLAB, rewritten in Leland Stanford Junior University, commonly known as Stanford University or simply Stanford, is a private Research university located in Year 1983 ( MCMLXXXIII) was a Common year starting on Saturday (link displays the 1983 Gregorian calendar) Recognizing its commercial potential, he joined with Moler and Steve Bangert. They rewrote MATLAB in C and founded The MathWorks in 1984 to continue its development. tags please moot on the talk page first! --> In Computing, C is a general-purpose cross-platform block structured The MathWorks, Inc is a privately held mid-size multi-national Corporation which specializes in technical computing software. Year 1984 ( MCMLXXXIV) was a Leap year starting on Sunday (link displays the 1984 Gregorian calendar) These rewritten libraries were known as JACKPAC.

MATLAB was first adopted by control design engineers, Little's specialty, but quickly spread to many other domains. Control engineering is the Engineering discipline that focuses on mathematical modeling of Systems of a diverse nature analyzing their dynamic behavior 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. Linear algebra is the branch of Mathematics concerned with Numerical analysis is the study of Algorithms for the problems of continuous mathematics (as distinguished from Discrete mathematics) Image processing is any form of Signal processing for which the input is an image such as photographs or frames of video the output of image processing can be either an image ^[3]

Syntax

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, >> , in the Command Window, one of the elements of the MATLAB Desktop. In this way, MATLAB can be used as an interactive mathematical shell. In computing a shell is a piece of software that provides an interface for users 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. A shell script is a script written for the shell, or Command line interpreter, of an Operating system. In Computer science, functional programming is a Programming paradigm that treats Computation as the evaluation of mathematical functions and ^[4]

Variables

Variables are defined with the assignment operator, =. MATLAB is dynamically typed, meaning that variables can be assigned without declaring their type, and that their type can change. In Computer science, a type system defines how a Programming language classifies values and expressions into '''types''', how it can Values can come from constants, from computation involving values of other variables, or from the output of a function. A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation. 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/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, or simply as a multidimensional array.

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, 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).

>> 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^[5], which is the usual convention for matrices in mathematics. In Computer science an array is a Data structure consisting of a group of elements that are accessed by indexing. In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally This is atypical for programming languages, whose arrays more often start with zero.

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
 
>> 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. In Linear algebra, the identity matrix or unit matrix of size n is the n -by- n Square matrix with ones on the Main

>> 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). In Recreational mathematics, a magic square of order n is an arrangement of n ² numbers usually distinct Integers in a square, such

[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;

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. ^[6]

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:

Limitations

For a long time there was criticism that because MATLAB is a proprietary product of The MathWorks, users are subject to vendor lock-in. In Mathematics, the sinc function, denoted by \scriptstyle\mathrm{sinc}(x\ and sometimes as \scriptstyle\mathrm{Sa}(x\ has two definitions sometimes In Mathematics, the sinc function, denoted by \scriptstyle\mathrm{sinc}(x\ and sometimes as \scriptstyle\mathrm{Sa}(x\ has two definitions sometimes The word proprietary indicates that a party or proprietor exercises private Ownership, control or use over an item of Property. In Economics, vendor lock-in, also known as proprietary lock-in, or customer lock-in, makes a customer dependent on a vendor for products ^{[7] [8]} Recently an additional tool called the MATLAB Builder under the Application Deployment tools section has been provided to deploy MATLAB functions as library files which can be used with .NET or Java application building environment. Java refers to a number of Computer software products and specifications from Sun Microsystems that together provide a system for developing Application software But the drawback is that the computer where the application has to be deployed needs MCR (MATLAB Component Runtime) for the MATLAB files to function normally. MCR can be distributed freely with library files generated by the MATLAB compiler.

MATLAB, like Fortran, Visual Basic and Ada, uses parentheses, e. Fortran (previously FORTRAN) is a general-purpose, procedural, imperative Programming language that is especially suited to Visual Basic ( VB) is the third-generation event-driven programming language and associated development environment (IDE from Ada is a structured, Statically typed, imperative, and object-oriented high-level computer Programming language g. y = f(x), for both indexing into an array and calling a function. Although this syntax can facilitate a switch between a procedure and a lookup table, both of which correspond to mathematical functions, a careful reading of the code may be required to establish the intent. In Computer science, a subroutine ( function, method, procedure, or subprogram) is a portion of code within a larger In Computer science, a lookup table is a Data structure, usually an Array or Associative array, often used to replace a runtime computation with The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function

MATLAB lacks a package system, like those found in modern languages such as Java and Python, where classes can be resolved unambiguously, e. g. Java's java. lang. System. out. println(). In MATLAB, all functions share the global namespace, and precedence of functions with the same name is determined by the order in which they appear in the user's MATLAB path and other subtle rules. ^[9] As such, two users may experience different results when executing what otherwise appears to be the same code when their paths are different.

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 sum(A) where A is a matrix gives a row vector containing the sum of each column of A, and sum(v) where v is a column or row vector gives the sum of its elements; hence the programmer must be careful if the matrix argument of sum can degenerate into a single-row array. ^[10] While sum and many similar functions accept an optional argument to specify a direction, others, like plot,^[11] 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 sequences which are interpreted by some functions like fprintf but not directly by the language parser because it wouldn't be convenient for Windows directories). In Computing and Telecommunication, an escape character is a single character which in a sequence of characters signifies that what is to follow takes an alternative 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 reusable code. In Computer science and Software engineering, reusability is the likelihood a segment of source code can be used again to add new functionalities with slight or no

Array indexing is one-based which is the common convention for matrices in mathematics, but does not accommodate any indexing convention of sequences that have zero or negative indices. In Computer science an array is a Data structure consisting of a group of elements that are accessed by indexing. In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally For instance, in MATLAB the DFT (or 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 in any literature. In Mathematics, the discrete Fourier transform (DFT is one of the specific forms of Fourier analysis. This one-based indexing convention is hard coded into MATLAB, making it difficult for a user to define their own zero-based or negative indexed arrays to concisely model an idea having non-positive indices. Hard coding (also hard-coding or hardcoding) refers to the software development practice of embedding input or configuration data directly into the Source

Though other datatypes are available, the default is a matrix of doubles. A data type in Programming languages is an attribute of a datum which tells the computer (and the programmer something about the kind of datum it is In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally In Computing, double precision is a Computer numbering format that occupies two adjacent storage locations in computer memory 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. Sampling theorem The Nyquist–Shannon sampling theorem states that perfect reconstruction Such attributes can be managed by the user via structures or other methods.

M-code written for a specific release of MATLAB often does not run with earlier releases. To give just one example: save('x','filename') saves the variable x in a file. The variable can be loaded with load('filename') in the same MATLAB release. However, if saved with MATLAB version 7 or later, it cannot be loaded with MATLAB version 6 or earlier. As workaround, in MATLAB version 7 save('x','filename','-v6') generates a file that can be read with version 6. However, executing save('x','filename','-v6') in version 6 causes an error message.

Calling C and Fortran functions

MATLAB can call functions and subroutines written in C programming language or Fortran. tags please moot on the talk page first! --> In Computing, C is a general-purpose cross-platform block structured 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", although the file name extension depends on the operating system and processor. ^[12][13]

See also

• GNU Octave, a similar free numerical computing environment
• List of numerical analysis software
• Comparison of numerical analysis software

Add-ons

• Simulink, a graphical block diagramming tool for modeling, simulating and analyzing multi-domain dynamic systems. Octave is a free Computer program for performing numerical computations which is mostly compatible with MATLAB. Free software or software libre is Software that can be used studied and modified without restriction and which can be copied and redistributed in modified or unmodified Listed here are a number of computer programs used for performing numerical calculations acslX is a software application for modeling and evaluating the performance The following tables provide a comparison of Numerical analysis software. Simulink, developed by The MathWorks, is a commercial tool for modeling simulating and analyzing multidomain dynamic systems
• Stateflow, a simulation tool for event-driven systems. Stateflow is an interactive design and simulation tool for event-driven systems that was developed by The MathWorks.

References

Further reading

• Gilat, Amos (2004). MATLAB: An Introduction with Applications 2nd Edition. John Wiley & Sons. ISBN 978-0-471-69420-5.  
• Quarteroni, Alfio; Fausto Saleri (2006). Scientific Computing with MATLAB and Octave. Springer. ISBN 978-3-540-32612-0.  

External links

• MATLAB overview, at The MathWorks website
• MATLAB Central the MATLAB user community
• MATLAB at the Open Directory Project
• Information about the history of and inspiration for MATLAB, written by Cleve Moler
• comp.soft-sys.matlab
• Share MATLAB code snippets online
• LiteratePrograms (MATLAB)
• Free Alternatives to MATLAB

Tutorials

• MATLAB Tutorials and Matlab Examples, MATLAB Forum
• A tutorial for beginners
• Blinkdagger: A Matlab Blog with Useful Tips and Tutorials by Quan Quach and Daniel Sutoyo
• Another tutorial
• MATLAB tutorial links
• Writing Fast MATLAB Code, by Pascal Getreuer

Official blogs

• Loren on the Art of MATLAB by Loren Shure
• Doug's Pick of the Week by Doug Hull
• Steve on Image Processing by Steve Eddins
• Inside the MATLAB Desktop by The Desktop Team
• Seth on Simulink by Seth Popinchalk