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️Mon Oct 04 2004

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MATLAB

MATLAB R2007a running on Windows XP pro 64-bit with a QR decomposition.
Developer:	The MathWorks
Latest release:	R2007b / September 1, 2007
OS:	Cross-platform^[1]
Genre:	Technical computing
License:	Proprietary
Website:	MATLAB product page

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 specializes in numerical computing, an optional toolbox interfaces with the 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.^[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. 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.^[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. 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.^[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. Values can come from constants, from computation involving values of other variables, or from the output of a function. For example: <source lang="matlab"> >> x = 17 x =

>> x = 'hat' x = hat >> x = 3*4 x =

>> y = 3*sin(x) y =

-1.6097

</source>

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:increment:terminator. For instance: <source lang="matlab"> >> array = 1:2:9 array =

1 3 5 7 9

</source> 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). <source lang="matlab"> >> array = 1:3:9 array =

1 4 7

</source> the increment value can actually be left out of this syntax (along with one of the colons), to use a default value of 1. <source lang="matlab"> >> ari = 1:5 ari =

1 2 3 4 5

</source> 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.

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 (). <source lang="matlab"> >> 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 =

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

11 8
7 12
14 1

</source> 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. <source lang="matlab"> >> 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

</source>

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.

<source lang="matlab"> [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; </source>

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.^[5]

Graphics

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

Three dimensional graphics can be produced using the functions surf, plot3 or mesh. <source lang="matlab"> [X,Y] = meshgrid(-8:.5:8); R = sqrt(X.^2 + Y.^2)+eps; Z = sin(R)./R; surf(X,Y,Z) </source> This code produces the 3D plot of a two-dimensional sinc function of radius.

Limitations

MATLAB is a proprietary product of The MathWorks, so users are subject to vendor lock-in. Some other source languages, however, are partially compatible (like GNU Octave) or provide a simple migration path (like Scilab).

The language has a mixed heritage with a sometimes unconventional syntax. For example, MATLAB uses parentheses, e.g. y = f(x), for both indexing into an array and calling a function. Although this ambiguous 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 has no namespace resolution system like the system found in more modern languages such as Java and Python, where classes are located inside packages which can be unambiguously resolved and provide order, e.g. Java's System.out.println() makes it clear to user precisely which function is being called. 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 environment variable (unless the function in question is the method of a class). Functions are usually not prefixed or otherwise organized logically. As such, two users may experience different results when executing what otherwise appears to be the same code.

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.^[6] While sum and many similar functions accept an optional argument to specify a direction, others, like plot,^[7] 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.

Though other datatypes are available, the default is a matrix of doubles. 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 indexing is one-based which is the common convention for matrices in mathematics, but does not accommodate the 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. 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.

MATLAB doesn't support references,^[8] 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, the language consistently passes function arguments by value, so any values that change must be returned from the function and re-assigned by the caller. This can, however, be circumvented by declaring variables to be global, which permits access to a value within a function.

References

^ http://www.mathworks.com/products/matlab/requirements.html
^ Richard Goering, "Matlab edges closer to electronic design automation world," EE Times, 10/04/2004 online
^ Cleve Moler, the creator of MATLAB (December 2004). The Origins of MATLAB. Retrieved on April 15, 2007.
^ MATLAB technical documentation
^ The MathWorks, MATLAB Function Reference, accessed 12 October, 2006.
^ http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html
^ http://www.mathworks.com/access/helpdesk/help/techdoc/ref/plot.html
^ http://www.mit.edu/~pwb/cssm/matlab-faq.html#passbyref

External links

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