Introduction toIntroduction to

Matlab WorkshopMatlab Workshop

Matthew Johnson, EconomicsMatthew Johnson, Economics

October 17, 2008October 17, 2008

04/21/23 1

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Getting HelpGetting Help

Useful links: Useful links: http://statlab.stat.yale.edu/help/FAQ/matlab_FAQ.jsp The The help links on this page include help links on this page include Mathworks’ Getting Started (the official Mathworks’ Getting Started (the official online documentation of Matlab) Kermit online documentation of Matlab) Kermit Sigmon’s MATLAB Primer (a very good Sigmon’s MATLAB Primer (a very good beginner manual); University of Utah’s beginner manual); University of Utah’s MATLAB Tutorial and some others. MATLAB Tutorial and some others.

MATLAB’s online help manualMATLAB’s online help manualStatlab ConsultantsStatlab Consultants

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What is MATLAB?What is MATLAB?

MATLAB is a matrix-based tool for MATLAB is a matrix-based tool for numerical computations. It’s very numerical computations. It’s very powerful and easy to use.powerful and easy to use.

Both programming language and Both programming language and interactive environmentinteractive environment

Very fast native functions; very slow Very fast native functions; very slow when processing loopswhen processing loops

Lots of available toolboxesLots of available toolboxes

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Acquiring MatlabAcquiring Matlab

www.yale.edu/software Free for Yale studentsFree for Yale students Installed on all Statlab computersInstalled on all Statlab computers

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Launching MatlabLaunching Matlab

Double-click the “MATLAB R2008a” Double-click the “MATLAB R2008a” icon on the desktopicon on the desktop

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The InterfaceThe Interface Main Window: Input/OutputMain Window: Input/Output Workspace: consists of the Workspace: consists of the

variables you create during a variables you create during a MATLAB session;MATLAB session;

Command History: double Command History: double click them to evaluate them;click them to evaluate them;

Current Directory browser: Current Directory browser: shows you where you are.shows you where you are.

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Interface (continued)Interface (continued)

Can use Matlab as a calculatorCan use Matlab as a calculator Type “help” for a list of all help Type “help” for a list of all help

topicstopics help abs gives the syntax and help abs gives the syntax and

information about the absolute value information about the absolute value commandcommand

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Entering MatricesEntering Matrices

Matrices can be :Matrices can be : Entered manuallyEntered manually

A = [1 2 3 ; 4 5 6 ; 7 8 9] A = [1 2 3 ; 4 5 6 ; 7 8 9] Generated by built-in functionsGenerated by built-in functions Loaded from a fileLoaded from a file

File>Import DataFile>Import Data

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Matrix operations:Matrix operations: + addition+ addition - subtraction- subtraction * multiplication * multiplication ^ power^ power ‘ ‘ transposetranspose To make operations apply element-To make operations apply element-

by-element, we precede the by-element, we precede the operators by ‘.’operators by ‘.’

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Subscripts:Subscripts:

Subscripts: the element in row i and Subscripts: the element in row i and column j of A is denoted by A(i, j). column j of A is denoted by A(i, j).

i,j can also be vectors of indices or i,j can also be vectors of indices or logical arrays:logical arrays:A=4*[1 2 3 4 5 6 7 8 9]’A=4*[1 2 3 4 5 6 7 8 9]’b=A>18; c=[5 6 7 8 9]’b=A>18; c=[5 6 7 8 9]’

A(b), A(c)A(b), A(c)

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The Colon Operator ‘:’ The Colon Operator ‘:’

The colon ‘:’ is one of MATLAB ’s most The colon ‘:’ is one of MATLAB ’s most important operators. It has many important operators. It has many formats:formats:

Subscript expressions involving colons Subscript expressions involving colons refer to portions of a matrix: refer to portions of a matrix: A(5:9) is the fifth to the ninth elements A(5:9) is the fifth to the ninth elements of A.of A.

[0:0.2:3] is a row vector containing [0:0.2:3] is a row vector containing integers from 0 to 3, in increments of 0.2integers from 0 to 3, in increments of 0.2

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Matrices and Random Matrices and Random Numbers:Numbers:

Four functions that generate basic matrices:Four functions that generate basic matrices: Zeros: all zeros.Zeros: all zeros. A = zeros(1,3)A = zeros(1,3) Ones: all ones.Ones: all ones. A = ones(2,4)A = ones(2,4) Rand: elements are U[0,1] random variables Rand: elements are U[0,1] random variables

A = rand(3,5)A = rand(3,5) Randn: elements are standard-normal Randn: elements are standard-normal

random variablesrandom variables A = randn(2,5)A = randn(2,5) Be careful: Matlab always sets the same Be careful: Matlab always sets the same

seed.seed.Get ‘more random’ numbers by typing Get ‘more random’ numbers by typing rand('state', sum(100*clock))rand('state', sum(100*clock))

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A=eye(3)A=eye(3) gives a 3-by-3 identity matrix gives a 3-by-3 identity matrix sparse(m,n):sparse(m,n): same as same as zeros(m,n),zeros(m,n), use if use if

most elements are zeros.most elements are zeros. Concatenation: join small (compatible) Concatenation: join small (compatible)

matrices to make bigger ones:matrices to make bigger ones:

B = [A A-2; A*2 A/4]B = [A A-2; A*2 A/4] Deleting rows and columns: Deleting rows and columns: B(:,2) = [ ]B(:,2) = [ ]

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Suppressing Output:Suppressing Output:

If you simply type a statement and press If you simply type a statement and press Enter, Enter, MATLAB automatically displays MATLAB automatically displays the results on screen. If you end the line the results on screen. If you end the line with a semicolon ‘;’, MATLAB performs with a semicolon ‘;’, MATLAB performs the computation but does not display any the computation but does not display any result.result.

Example: C = randn(5,1) v.s. Example: C = randn(5,1) v.s.

C = randn(5,1);C = randn(5,1);

Aside: You can run Matlab Aside: You can run Matlab remotely!remotely!

Available to anyone with a Yale pantheon Available to anyone with a Yale pantheon accountaccount

You need the following (free) softwareYou need the following (free) software Xming (available from Xming (available from

http://sourceforge.net/projects/xming)http://sourceforge.net/projects/xming) SSH (available from SSH (available from www.yale.edu/software))

Useful if you don’t want to have Matlab Useful if you don’t want to have Matlab take up memory/processing power on take up memory/processing power on you computeryou computer

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Aside: You can run Matlab Aside: You can run Matlab remotely!remotely!

Instructions:Instructions: Start Xming (it will run in the background)Start Xming (it will run in the background) Log in to eli.yale.edu through SSHLog in to eli.yale.edu through SSH

In SSH click on Edit, then click Settings, then In SSH click on Edit, then click Settings, then click Tunnelingclick Tunneling

Check the box at the bottom that says “Tunnel X11 Check the box at the bottom that says “Tunnel X11 Connections” and click OKConnections” and click OK

You’re all set! Type “matlab &” in SSH to You’re all set! Type “matlab &” in SSH to run the programrun the program

Note that this is an older version of matlabNote that this is an older version of matlab

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Functions: Functions: MATLAB provides a large number of MATLAB provides a large number of

standard elementary mathematical standard elementary mathematical functions, including functions, including abs, sqrt, exp, sinabs, sqrt, exp, sin. .

For a list of the elementary mathematical For a list of the elementary mathematical functions, type:functions, type:

help elfunhelp elfun For a list of more advanced mathematical For a list of more advanced mathematical

and matrix functions, typeand matrix functions, type

help specfunhelp specfun

help elmathelp elmat

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Programming with Programming with MATLAB: MATLAB:

Files that contain code in the Files that contain code in the MATLAB language are called M-files. MATLAB language are called M-files. You can create M-files using the You can create M-files using the matlab editor, then use them as you matlab editor, then use them as you would any other MATLAB functions would any other MATLAB functions or commands. There are two types or commands. There are two types of M-files: Scripts and Functions.of M-files: Scripts and Functions.

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ScriptsScripts Scripts: a bunch of code grouped Scripts: a bunch of code grouped

together; doesn’t accept argument or together; doesn’t accept argument or return output.return output.

You should do most of your work using You should do most of your work using scripts!scripts!

Example:Example: open m-file editoropen m-file editor type type disp(‘Hello’)disp(‘Hello’) type disp(‘World’)type disp(‘World’) save as test.m in your current directorysave as test.m in your current directory type “test” in Matlabtype “test” in Matlab

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Functions:Functions:

Functions are M-files that can accept Functions are M-files that can accept input arguments and return output input arguments and return output arguments. The name of the M-file arguments. The name of the M-file and of the function should be the and of the function should be the same. same.

For example, save this as area.m:For example, save this as area.m:function ar = area(radius)function ar = area(radius)ar=pi*radius^2;ar=pi*radius^2;

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Flow Control:Flow Control:

MATLAB has following flow controls:MATLAB has following flow controls: If statementIf statement For loopsFor loops While loopsWhile loops

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if … elseif … else … endif … elseif … else … end

if A > B 'greater' elseif A < B 'less' else 'equal'end

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for … endfor … endbeta=0.925;a=1:100000;for i = 1:100000 betavec(i)=beta^a(i);endbetavec But you should avoid for loops if possiblenewbetavec=beta.^a

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GraphicsGraphics: plot: plot

x = [0 : .01 : 2*pi];x = [0 : .01 : 2*pi];

y = sin(x);y = sin(x);

plot(x,y)plot(x,y)

y2 = sin(x-.25)y2 = sin(x-.25)

y3 = sin(x-.5)y3 = sin(x-.5)

plot(x,y,x,y2,x,y3)plot(x,y,x,y2,x,y3)

Cool Graphs!Cool Graphs!

[x,y] = meshgrid([-2:.2:2]);[x,y] = meshgrid([-2:.2:2]); Z = x.*exp(-x.^2-y.^2); Z = x.*exp(-x.^2-y.^2); surf(x,y,Z,gradient(Z)) surf(x,y,Z,gradient(Z))

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Learn from othersLearn from others

There are lots of Matlab functions There are lots of Matlab functions already out there:already out there:

Google them!Google them! http://www.mathworks.com/matlabc

entral/ James LeSage’s econometrics James LeSage’s econometrics

toolbox:toolbox:http://www.spatial-econometrics.com/