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# MATLAB

MATLAB is a numerical computing environment and programming language. 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. Although it is numeric only, an optional toolbox interfaces with the Maple symbolic engine, allowing access to computer algebra capabilities.

As of 2004, MathWorks has claimed that MATLAB is used by more than one million people across industry and the academic world.

## 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. 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 The MathWorks in 1984 to continue its development. 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. 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

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. 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 dynamically typed, meaning that 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 >> 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 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 1. Arrays with more than two dimensions are referred to as multidimensional arrays.

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, which is the usual convention for matrices in mathematics. 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. >> 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;

### 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.

### 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: align="center"

## 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. 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. 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.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.

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. 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. While `sum` and many similar functions accept an optional argument to specify a direction, others, like `plot`, 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). 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.

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. 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. 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.

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. 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.

## Release history

Date - release name - version :

• 2008, R2008a, 7.6
• 2007, R2007b, 7.5
• 2007, R2007a, 7.4
• 2006, R2006b, 7.3
• 2006, R2006a, 7.2
• 2005, R14SP3, 7.1
• 2005, R14SP2, 7.0.4
• 2004, R14SP1, 7.0.1
• 2004, R14, 7
• 2003, R13SP2, 6.5.2
• 2003, R13SP1, 6.5.1
• 2002, R13. 6.5
• 2001, R12.1, 6.1
• 2000, R12, 6.0
• 1999, R11.1, 5.3.1
• 1999, R11, 5.3
• 1998, R10.1, 5.2.1
• 1998, R10, 5.2
• 1997, R9.1, 5.1.1
• 1997, R9, 5.1
• 1996, R8, 5.0
• 1994, R7, 4.2c
• 1992, R?, 4
• 1990, R?, 3.5
• 1987, R?, 3
• 1986, R?, 2
• 1984, R?, 1.0