Wikipedia

MATLAB

For the geographical region, seeMatlab (Bangladesh).
Not to be confused withMATHLAB.

MATLAB(an abbreviation of "MATrix LABoratory"[22]) is aproprietarymulti-paradigmprogramming languageandnumeric computingenvironment developed byMathWorks.MATLAB allowsmatrixmanipulations, plotting offunctionsand data, implementation ofalgorithms,creation ofuser interfaces,and interfacing with programs written in other languages.

MATLAB (programming language)
Paradigmmulti-paradigm:functional,imperative,procedural,object-oriented,array
Designed byCleve Moler
DeveloperMathWorks
First appearedlate 1970s
Stable release
R2024b[1]Edit this on Wikidata / September 12, 2024;2 months ago(September 12, 2024)
Typing disciplinedynamic,weak
Filename extensions.m,.p,[2].mex*,[3].mat,[4].fig,[5].mlx,[6].mlapp,[7].mltbx,[8].mlappinstall,[9].mlpkginstall[10]
Websitemathworks.com
Majorimplementations
MATLAB Software,GNU Octave,Sysquake
Influenced by
Influenced
MATLAB (software)
Developer(s)MathWorks
Initial release1984;40 years ago(1984)
Stable release
R2024b[1]Edit this on Wikidata / September 12, 2024;2 months ago(September 12, 2024)
Written inC/C++,MATLAB
Operating systemWindows,macOS,andLinux[20][21]
PlatformIA-32,x86-64,ARM64
TypeNumerical computing
LicenseProprietarycommercial software
Websitemathworks.com

Although MATLAB is intended primarily for numeric computing, an optional toolbox uses theMuPADsymbolic engineallowing access tosymbolic computingabilities. An additional package,Simulink,adds graphical multi-domain simulation andmodel-based designfordynamicandembedded systems.

As of 2020,MATLAB has more than four million users worldwide.[23]They come from various backgrounds ofengineering,science,andeconomics.As of 2017,more than 5000 global colleges and universities use MATLAB to support instruction and research.[24]

History

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Origins

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MATLAB was invented by mathematician and computer programmerCleve Moler.[25]The idea for MATLAB was based on his 1960s PhD thesis.[25]Moler became a math professor at theUniversity of New Mexicoand started developing MATLAB for his students[25]as a hobby.[26]He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor,George Forsythe.[25]This was followed byFortrancode for linear equations in 1971.[25]

Before version 1.0, MATLAB "was not a programming language; it was a simple interactive matrix calculator. There were no programs, no toolboxes, no graphics. And noODEsorFFTs."[27]

The first early version of MATLAB was completed in the late 1970s.[25]The software was disclosed to the public for the first time in February 1979 at theNaval Postgraduate Schoolin California.[26]Early versions of MATLAB were simplematrix calculatorswith 71 pre-built functions.[28]At the time, MATLAB was distributed for free[29][30]to universities.[31]Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.[32]: 5 

In the 1980s, Cleve Moler metJohn N. Little.They decided to reprogram MATLAB in C and market it for the IBM desktops that were replacing mainframe computers at the time.[25]John Little and programmer Steve Bangert re-programmed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.[26]

Since 1993 an open source alternative,GNU Octave(mostly compatible with matlab) andscilab(similar to matlab) have been available.

Commercial development

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MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference inLas Vegas.[25][26]MathWorks,Inc. was founded to develop the software[30]and the MATLAB programming language was released.[28]The first MATLAB sale was the following year, whenNick Trefethenfrom theMassachusetts Institute of Technologybought ten copies.[26][33]

By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use.[26]The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks.[29]Many of the toolboxes were developed as a result ofStanfordstudents that used MATLAB in academia, then brought the software with them to the private sector.[26]

Over time, MATLAB was re-written for early operating systems created byDigital Equipment Corporation,VAX,Sun Microsystems,and for Unix PCs.[26][28]Version 3 was released in 1987.[34]The first MATLAB compiler was developed byStephen C. Johnsonin the 1990s.[28]

In 2000, MathWorks added a Fortran-based library for linear algebra in MATLAB 6, replacing the software's original LINPACK and EISPACK subroutines that were in C.[28]MATLAB's Parallel Computing Toolbox was released at the 2004 Supercomputing Conference and support for graphics processing units (GPUs) was added to it in 2010.[28]

Recent history

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Some especially large changes to the software were made with version 8 in 2012.[35]The user interface was reworked[citation needed]andSimulink's functionality was expanded.[36]By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.[28]

Syntax

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The MATLAB application is built around the MATLAB programming language. Common usage of the MATLAB application involves using the "Command Window" as an interactive mathematicalshellor executing text files containing MATLAB code.[37]

"Hello, world!" example

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An example of a"Hello, world!" programexists in MATLAB. 

disp('Hello, world!')

It displays like so: 

Hello, world!

Variables

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Variables are defined using the assignment operator,=.MATLAB is aweakly typedprogramming language because types are implicitly converted.[38]It is an inferred typed language because variables can be assigned without declaring their type, except if they are to be treated as symbolic objects,[39]and that their type can change. Values can come fromconstants,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 and matrices

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A simple array is defined using the colon syntax:initial:increment:terminator.For instance: 

>>array=1:2:9
array =
1 3 5 7 9

defines a variable namedarray(or assigns a new value to an existing variable with the namearray) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (theinitialvalue), increments with each step from the previous value by 2 (theincrementvalue), and stops once it reaches (or is about to exceed) 9 (theterminatorvalue).

Theincrementvalue 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 namedarian array with the values 1, 2, 3, 4, and 5, since the default value of 1 is used as the increment.

Indexingis one-based,[40]which is the usual convention formatricesin mathematics, unlike zero-based indexing commonly used in other programming languages such as C, C++, and Java.

Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to separate the rows. 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 as2:4,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 squareidentity matrixof sizencan be generated using the functioneye,and matrices of any size with zeros or ones can be generated with the functionszerosandones,respectively. 

>>eye(3,3)
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

Transposinga vector or a matrix is done either by the functiontransposeor by adding dot-prime after the matrix (without the dot, prime will performconjugate transposefor complex arrays): 

>>A=[1;2],B=A.',C=transpose(A)
A =
1
2
B =
1 2
C =
1 2

>>D=[0,3;1,5],D.'
D =
0 3
1 5
ans =
0 1
3 5

Most functions accept arrays as input and operate element-wise on each element. For example,mod(2*J,n)will multiply every element inJby 2, and then reduce each element modulon.MATLAB does include standardforandwhileloops, but (as in other similar applications such asAPLandR), using thevectorizednotation is encouraged and is often faster to execute. The following code, excerpted from the functionmagic.m,creates amagic squareMfor odd values ofn(MATLAB functionmeshgridis used here to generate square matricesIandJcontaining⁠⁠): 

[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;

Structures

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MATLAB supports structure data types.[41]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[42](field look-ups by name, field manipulations, etc.).

Functions

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When creating a MATLAB function, the name of the file should match the name of the first function in the file. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores. Variables and functions are case sensitive.[43] 

rgbImage=imread('ecg.png');
grayImage=rgb2gray(rgbImage);% for non-indexed images
level=graythresh(grayImage);% threshold for converting image to binary,
binaryImage=im2bw(grayImage,level);
% Extract the individual red, green, and blue color channels.
redChannel=rgbImage(:,:,1);
greenChannel=rgbImage(:,:,2);
blueChannel=rgbImage(:,:,3);
% Make the black parts pure red.
redChannel(~binaryImage)=255;
greenChannel(~binaryImage)=0;
blueChannel(~binaryImage)=0;
% Now recombine to form the output image.
rgbImageOut=cat(3,redChannel,greenChannel,blueChannel);
imshow(rgbImageOut);

Function handles

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MATLAB supports elements oflambda calculusby introducing function handles,[44]or function references, which are implemented either in.m files or anonymous[45]/nested functions.[46]

Classes and object-oriented programming

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MATLAB supportsobject-oriented programmingincluding classes,inheritance,virtual dispatch, packages,pass-by-valuesemantics, andpass-by-referencesemantics.[47]However, the syntax and calling conventions are significantly different from other languages. MATLAB has value classes and reference classes, depending on whether the class hashandleas a super-class (for reference classes) or not (for value classes).[48]

Method call behavior is different between value and reference classes. For example, a call to a method: 

object.method();

can alter any member ofobjectonly ifobjectis an instance of a reference class, otherwise value class methods must return a new instance if it needs to modify the object.

An example of a simple class is provided below: 

classdefHello
methods
functiongreet(obj)
disp('Hello!')
end
end
end

When put into a file namedhello.m,this can be executed with the following commands: 

>>x=Hello();
>>x.greet();
Hello!

Graphics and graphical user interface programming

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MATLAB has tightly integrated graph-plotting features. For example, the functionplotcan be used to produce a graph from two vectorsxandy.The code: 

x=0:pi/100:2*pi;
y=sin(x);
plot(x,y)

produces the following figure of thesine function:

MATLAB supports three-dimensional graphics as well: 

[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([-1010-1010-0.31])
xlabel('{\bfx}')
ylabel('{\bfy}')
zlabel('{\bfsinc} ({\bfR})')
hiddenoff

[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([-1010-1010-0.31])
xlabel('{\bfx}')
ylabel('{\bfy}')
zlabel('{\bfsinc} ({\bfR})')
This code produces awireframe3D plot of the two-dimensional unnormalizedsinc function: This code produces asurface3D plot of the two-dimensional unnormalizedsinc function:

MATLAB supports developinggraphical user interface(GUI) applications.[49]UIs can be generated either programmatically or using visual design environments such asGUIDEandApp Designer.[50][51]

MATLAB and other languages

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MATLAB can call functions and subroutines written in the programming languagesCorFortran.[52]A wrapper function is created allowing MATLAB data types to be passed and returned.MEX files(MATLAB executables) are the dynamically loadable object files created by compiling such functions.[53][54]Since 2014 increasing two-way interfacing withPythonwas being added.[55][56]

Libraries written inPerl,Java,ActiveXor.NETcan be directly called from MATLAB,[57][58]and many MATLAB libraries (for exampleXMLorSQLsupport) are implemented as wrappers around Java or ActiveX libraries. Calling MATLAB from Java is more complicated, but can be done with a MATLAB toolbox[59]which is sold separately byMathWorks,or using an undocumented mechanism called JMI (Java-to-MATLAB Interface),[60][61](which should not be confused with the unrelatedJava Metadata Interfacethat is also called JMI). Official MATLAB API for Java was added in 2016.[62]

As alternatives to theMuPADbased Symbolic Math Toolbox available from MathWorks, MATLAB can be connected toMapleorMathematica.[63][64]

Libraries also exist to import and exportMathML.[65]

Relations to US sanctions

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In 2020, MATLAB withdrew services from two Chinese universities as a result of US sanctions. The universities said this will be responded to by increased use of open-source alternatives and by developing domestic alternatives.[66]

See also

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Notes

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  1. ^ab"MathWorks Announces Release 2024b of MATLAB and Simulink".RetrievedSeptember 15,2024.
  2. ^"Protect Your Source Code".MathWorks.RetrievedNovember 1,2019.
  3. ^"MEX Platform Compatibility".MathWorks.RetrievedNovember 1,2019.
  4. ^"MAT-File Versions".MathWorks.RetrievedNovember 1,2019.
  5. ^"Save Figure to Reopen in MATLAB Later".MathWorks.RetrievedNovember 1,2019.
  6. ^"Live Code File Format (.mlx)".MathWorks.RetrievedNovember 1,2019.
  7. ^"MATLAB App Designer".MathWorks.RetrievedNovember 1,2019.
  8. ^"Toolbox Distribution".MathWorks.RetrievedNovember 1,2019.
  9. ^"MATLAB App Installer File".MathWorks.RetrievedNovember 1,2019.
  10. ^"Support Package Installation".MathWorks.RetrievedNovember 1,2019.
  11. ^"An interview with CLEVE MOLER Conducted by Thomas Haigh On 8 and 9 March, 2004 Santa Barbara, California"(PDF).Computer History Museum. Archived fromthe original(PDF)on December 27, 2014.RetrievedDecember 6,2016.So APL, Speakeasy, LINPACK, EISPACK, and PL0 were the predecessors to MATLAB.
  12. ^Bezanson, Jeff; Karpinski, Stefan; Shah, Viral; Edelman, Alan (February 14, 2012)."Why We Created Julia".Julia Language.RetrievedDecember 1,2016.
  13. ^Eaton, John W. (May 21, 2001)."Octave: Past, Present, and Future"(PDF).Texas-Wisconsin Modeling and Control Consortium.Archived fromthe original(PDF)on August 9, 2017.RetrievedDecember 1,2016.
  14. ^"History".Scilab. Archived fromthe originalon December 1, 2016.RetrievedDecember 1,2016.
  15. ^S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.
  16. ^Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis.Society for Industrial and Applied Mathematics.
  17. ^Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic.Acta Numerica,19, 287–449.
  18. ^Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).
  19. ^"The L-Shaped Membrane".MathWorks. 2003.RetrievedFebruary 7,2014.
  20. ^"System Requirements and Platform Availability".MathWorks.RetrievedAugust 14,2013.
  21. ^"Platform Road Map for MATLAB and Simulink Product Families".de.mathworks.com.RetrievedDecember 22,2021.
  22. ^"Matrices and Arrays - MATLAB & Simulink".www.mathworks.com.RetrievedMay 21,2022.
  23. ^The MathWorks (February 2020)."Company Overview"(PDF).
  24. ^"Current number of matlab users worldwide".Mathworks.November 9, 2017.RetrievedApril 26,2023.
  25. ^abcdefghChonacky, N.; Winch, D. (2005). "Reviews of Maple, Mathematica, and Matlab: Coming Soon to a Publication Near You".Computing in Science & Engineering.7(2). Institute of Electrical and Electronics Engineers (IEEE): 9–10.Bibcode:2005CSE.....7b...9C.doi:10.1109/mcse.2005.39.ISSN1521-9615.S2CID29660034.
  26. ^abcdefghHaigh, Thomas."Cleve Moler: Mathematical Software Pioneer and Creator of Matlab"(PDF).IEEE Annals of the History of Computing.IEEE Computer Society.
  27. ^"A Brief History of MATLAB".www.mathworks.com.RetrievedSeptember 4,2021.
  28. ^abcdefgMoler, Cleve; Little, Jack (June 12, 2020)."A history of MATLAB".Proceedings of the ACM on Programming Languages.4(HOPL). Association for Computing Machinery (ACM): 1–67.doi:10.1145/3386331.ISSN2475-1421.
  29. ^abXue, D.; Press, T.U. (2020).MATLAB Programming: Mathematical Problem Solutions.De Gruyter STEM. De Gruyter. p. 21.ISBN978-3-11-066370-9.RetrievedSeptember 16,2020.
  30. ^abPress, CRC (2008).Solving Applied Mathematical Problems with MATLAB.CRC Press. p. 6.ISBN978-1-4200-8251-7.RetrievedSeptember 16,2020.
  31. ^Woodford, C.; Phillips, C. (2011).Numerical Methods with Worked Examples: Matlab Edition.SpringerLink: Bücher. Springer Netherlands. p. 1.ISBN978-94-007-1366-6.RetrievedSeptember 16,2020.
  32. ^Tranquillo, J.V. (2011).MATLAB for Engineering and the Life Sciences.Synthesis digital library of engineering and computer science. Morgan & Claypool Publishers.ISBN978-1-60845-710-6.RetrievedSeptember 17,2020.
  33. ^LoTurco, Lori (January 28, 2020)."Accelerating the pace of engineering".MIT News.Massachusetts Institute of Technology.RetrievedSeptember 16,2020.
  34. ^Gatto, Marino; Rizzoli, Andrea (1993). "Review of MATLAB, Version 4.0".Natural Resource Modeling.7(1). Wiley: 85–88.Bibcode:1993NRM.....7...85G.doi:10.1111/j.1939-7445.1993.tb00141.x.ISSN0890-8575.
  35. ^Cho, M.J.; Martinez, W.L. (2014).Statistics in MATLAB: A Primer.Chapman & Hall/CRC Computer Science & Data Analysis. CRC Press.ISBN978-1-4665-9657-3.RetrievedSeptember 17,2020.
  36. ^Xue, D.; Chen, Y. (2013).System Simulation Techniques with MATLAB and Simulink.No Longer used. Wiley. p. 17.ISBN978-1-118-69437-4.RetrievedOctober 15,2020.
  37. ^"MATLAB Documentation".MathWorks.RetrievedAugust 14,2013.
  38. ^"Comparing MATLAB with Other OO Languages".MATLAB.MathWorks.RetrievedAugust 14,2013.
  39. ^"Create Symbolic Variables and Expressions".Symbolic Math Toolbox.MathWorks.RetrievedAugust 14,2013.
  40. ^"Matrix Indexing".MathWorks.RetrievedAugust 14,2013.
  41. ^"Structures".MathWorks.RetrievedAugust 14,2013.
  42. ^"Generate Field Names from Variables".MathWorks.RetrievedAugust 14,2013.
  43. ^"Case and Space Sensitivity".MathWorks.RetrievedNovember 1,2019.
  44. ^"Function Handles".MathWorks.RetrievedAugust 14,2013.
  45. ^"Anonymous Functions".MathWorks.RetrievedAugust 14,2013.
  46. ^"Nested Functions".MathWorks.
  47. ^"Object-Oriented Programming".MathWorks.RetrievedAugust 14,2013.
  48. ^"Comparing Handle and Value Classes".MathWorks.
  49. ^"MATLAB GUI".MathWorks. April 30, 2011.RetrievedAugust 14,2013.
  50. ^"Create a Simple GUIDE GUI".MathWorks.RetrievedAugust 14,2014.
  51. ^"MATLAB App Designer".MathWorks.RetrievedNovember 1,2019.
  52. ^"Application Programming Interfaces to MATLAB".MathWorks. Archived fromthe originalon September 15, 2017.RetrievedAugust 14,2013.
  53. ^"Create MEX-Files".MathWorks. Archived fromthe originalon March 3, 2014.RetrievedAugust 14,2013.
  54. ^Spielman, Dan (February 10, 2004)."Connecting C and Matlab".Yale University, Computer Science Department.RetrievedMay 20,2008.
  55. ^"MATLAB Engine for Python".MathWorks.RetrievedJune 13,2015.
  56. ^"Call Python Libraries".MathWorks.RetrievedJune 13,2015.
  57. ^"External Programming Language Interfaces".MathWorks. Archived fromthe originalon March 11, 2014.RetrievedAugust 14,2013.
  58. ^"Call Perl script using appropriate operating system executable".MathWorks.RetrievedNovember 7,2013.
  59. ^"MATLAB Builder JA".MathWorks.RetrievedJune 7,2010.
  60. ^Altman, Yair (April 14, 2010)."Java-to-Matlab Interface".Undocumented Matlab. Archived fromthe originalon September 5, 2015.RetrievedJune 7,2010.
  61. ^Kaplan, Joshua."matlabcontrol JMI".
  62. ^"MATLAB Engine API for Java".MathWorks.RetrievedSeptember 15,2016.
  63. ^Germundsson, Roger (September 30, 1998)."MaMa: Calling MATLAB from Mathematica with MathLink".Wolfram Research.Wolfram Library Archive.
  64. ^rsmenon; szhorvat (2013)."MATLink: Communicate with MATLAB from Mathematica".RetrievedAugust 14,2013.
  65. ^Weitzel, Michael (September 1, 2006)."MathML import/export".MathWorks - File Exchange. Archived fromthe originalon February 25, 2011.RetrievedAugust 14,2013.
  66. ^"US military ban locks two Chinese universities out of popular software".South China Morning Post.June 12, 2020.RetrievedNovember 6,2020.

Further reading

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