MATLAB

MATLAB

File:MATLAB-R2008a-for-Linux.png MATLAB R2008a screenshot
Developer(s)	The MathWorks
Stable release	R2010a / March 5, 2010 (2010-03-05)
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
Designed by	Cleve Moler
Developer	The MathWorks
First appeared	late 1970s
Preview release	R2020a Prerelease [±]
Typing discipline	dynamic
OS	Cross-platform
Website	www.mathworks.com/products/matlab.html,%20https://de.mathworks.com/products/matlab.html

MATLAB stands for "Matrix Laboratory" and is a numerical computing environment and fourth-generation programming language. Developed by The 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++, 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, MathWorks claimed that MATLAB was used by more than one million people across the industry and the academic world. MATLAB users come from various backgrounds of engineering, science, and economics. Among these users are Massachusetts Institute of Technology, RWTH Aachen University, ABB Group, Boeing, Ford Motor, Halliburton, Lockheed Martin, Motorola, NASA, Novartis, Pfizer, Philips, Toyota, and UniCredit Bank.

History

MATLAB was created 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. 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

MATLAB, the application, is built around the MATLAB language. The simplest way to execute MATLAB 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 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.

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;

Semicolon

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, a references to functions, which are implemented either in .m files or anonymous/nested functions.

Classes

MATLAB supports classes, however the syntax and calling conventions are significantly different than in other languagues, because MATLAB does not have reference data types. For example, a call to a method

object.method();

cannot normally alter any variables of object variable. To create an impression that the method alters the state of variable, MATLAB toolboxes use evalin() command, which has its own restrictions.

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

Interactions 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.

As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.

Limitations

MATLAB is a proprietary product of The 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.

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.

Mathematical matrix functions generally accept an optional argument to specify a direction, while others, like plot, do not, and so 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. A workaround can be constructed to create an ancillary frequency labeling array with element values equal to the index less 1 that would be used instead of the index, or the MATLAB programmer can remember to subtract 1 from the index obtained from functions that return an index such as find(), min(), max().

MATLAB built-in datatypes are always passed by value. Therefore, all input parameters to a function are usually copied (later MATLAB releases introduced lazy copy where if an input parameters are not being altered, a copy is not being made, however this has certain restrictions). Instances of user-defined classes are also copied and passed by value as the default, however user-defined classes can be made to exhibit reference behavior by inheriting from the abstract handle class. Variables of such classes store a reference to the instance. An alternative to using references is global variables, however MATLAB JIT does not support globals, as well as structures, therefore the code performance will degrade.

The MATLAB editor does not have code completion, references searches, or refactoring. Since MATLAB is weakly typed, these tools would be hard, if not impossible, to provide in future releases since it is unknown which methods of an object can be called without knowing its type. Without code completion, there is a tendency to use short cryptic names for variables, function and methods, making code hard to read. Without code completion or reference searches it can take a long time to text search for what functions and methods can be called in a given context. Without refactoring, it is time consuming and error prone to change variable, method, or function names, or to modify an API.

Productivity of a development team working on a large software project in MATLAB will likely be several times slower and result in a higher defect rate than development in a language and IDE with type checking, code completion, reference search, refactoring tools, and unit testing support.

It is very difficult to employ agile programming practices, such as Extreme Programming, in MATLAB due to the lack of refactoring tools.

MATLAB lacks any native support for GPU acceleration such as OpenCL, Microsoft's DirectCompute, or nVidia's CUDA.

Alternatives

MATLAB has a number of competitors.

Its main competitor is the commercial software package Mathematica.

There are 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 is one web / cloud based alternative - Monkey Analytics - which provides a modern web interface on top of GNU Octave or Python (including matplotlib, NumPy, SciPy and more).

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

See also: list of numerical analysis software and comparison of numerical analysis software

Release history

Version	Release name	Year	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
MATLAB 7.1	R14SP3
MATLAB 7.2	R2006a	2006
MATLAB 7.3	R2006b
MATLAB 7.4	R2007a	2007
MATLAB 7.5	R2007b		This is the last release for Windows 2000, and the last release for PowerPC Mac.
MATLAB 7.6	R2008a	2008
MATLAB 7.7	R2008b
MATLAB 7.8	R2009a	2009	This is the first release for 32-bit & 64-bit Windows 7.
MATLAB 7.9	R2009b		This is the first release for Intel 64-bit Mac, and the last release for Solaris SPARC.
MATLAB 7.10	R2010a	2010	This is the last release for Intel 32-bit Mac.

Notes

• 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.

External links

• MATLAB overview, at The MathWorks website
• System Requirements - Platform Roadmap, at "The MathWorks" website.
• MATLAB at Curlie
• comp.soft-sys.matlab
• LiteratePrograms (MATLAB)
• Official blogs
• Examples for the MEX interface to access R&S measurement instruments
• Comparison of mathematical programs for data analysis ScientificWeb
• Physical Modeling in MATLAB, by Allen B. Downey, Green Tea Press.