Introduction to MatlabStatLab Workshop

Yale UniversityMaximiliano Appendino, Economics

October 18th, 2013

What is Matlab?Matlab is a matrix-based tool for numerical

computationsPowerful Easy to use

Programming language Interactive environmentLots of available toolboxes

Getting HelpUseful links:

http://statlab.stat.yale.edu/help/FAQ/matlab_FAQ.jspMathworks' Getting Started Matlab CenterKermit Sigmon’s Matlab PrimerMany others

Google your questionMatlab’s help

OnlineStatlab Consultants: Max Perez Leon,

Zhentao Shi

Acquiring MatlabITS Software Library & Resources:

http://www.yale.edu/its/software/Free for students: Matlab R2013aAvailable in Statlab locations

The Center for Science and Social Science Information 219 Prospect St, Basement Kline Biology Tower

Rosenkranz Hall 115 Prospect St, Room 01

Launching MatlabDouble-click the “MATLAB R2013a” icon on

the desktopOr click the start bottom, type MATLAB and

enterUsual Interface:

Command WindowWorkplace

.MAT filesCommand historyCurrent Folder

InterfaceCan be used as a calculator“help” gives you a list of all topics

“help topic” informs you about the particular topic

Example:>> help>> help stats>> help normcdf

Entering MatricesEntered manually:

>> A = [1 2 3 4; 5 6 7 8; 9 10 11 12]

Generate it by built-in functions

Loaded from a file .MAT or Menu File Import Data…

Matrix Operation+ addition- subtraction* multiplication^ power‘ transposeElement-by-element: preceded the operators

by .Subscripts:

>> B = A(2,3)

Matrix OperationMatrix Multiplication

>> [1 2; 3 4]*[1 2; 3 4] [7 10; 15 22]

Element-by-element Multiplication>> [1 2; 3 4].*[1 2; 3 4]

[1 4;9 16]

The Colon Operator : One of Matlab’s most important operators:

Portions of a matrix:>> C = A(:,3)>> D = A(1,:)>> E = A(1:2,1:3)

Create matrices using increments:>> F = [1:0.1:1.5]’ >> G = [1:0.1:1.5; 1:0.5:3.5]

Matrix Generation FunctionsZeros:

>> zeros(3,3)Ones:

>> ones(3,3)Identity:

>> eye(3)More on matrices and linear algebra:

>> help elmat>> help matfun

Random MatricesPseudo-Random numbers:

Change the seed:>> rng('shuffle')>> rng(15)

U[0,1] random variable:>> RU = rand(3,4)

Normal random variable:>> RN = randn(4,3)

Matrix manipulationConcatenation:

>> A2 = [A A.^2; A./2 A]Deleting rows and columns:

>> A2(:,7:8) = []Adding rows and columns:

>> A2 = [1:2:11;A2]Knowing the size:

>> sizeA2 = size(A2)

Suppressing OutputIf you simply type a statement and press

Enter Matlab automatically displays the results on the Command Window

If you end the line with a semicolon ; Matlab performs the computation but does not display any result>> H = rand(2,2)>> H = rand(2,2);>> H

FunctionsMatlab provides a large number of standard

elementary mathematical functions:>> abs(-10)>> sqrt(9)>> x = [0:0.1:2*pi];>> y = sin(y);

Look for the ones you need: Google>> help

GraphicsMatlab generate 2-dimensional plots easily:

>> plot(x,y)

>> y2 = y + 0.25;>> y3 = y + 0.50;>> plot(x,y,x,y2,x,y3)

With a friendly interface to edit them

GraphicsAlso 3-dimensional ones:

First we need to generate a grid:>> [X,Y] = meshgrid([-2:.2:2]);

Second we can calculate the function to graph:>> Z = X.*exp(-X.^2-Y.^2);

Finally the graph:>> surf(X,Y,Z)

ProgrammingM-files contain Matlab code.m is their extensionMatlab editorCan be used as any command or function as

long as they are in the “Current Folder”Two types:

ScriptsFunctions

ScriptsA list of code grouped together

It does not accept argument or return outputUse them to register your workExample:

File New Scriptdisp(‘Hello’)File Save test.m>> test

FunctionsFunctions are M-files that can accept input

arguments and return output arguments. The M-file and the function should have the

same nameExample:

function ar = area(radius)ar = pi*radius.^2;File Save area.m>> area(2)

Flow ControlMatlab has the standard flow controls

If statements

For loops

While loops

If statementa = 10;b = 11;

if a > bdisp('greater‘)

elseif a < bdisp('less‘)

elsedisp('equal‘)

end

>> [a==b]

For loopsbetavec = zeros(100,1);beta = 0.925;a = [1:100];for i = 1:100

betavec(i)=beta^a(i);endplot(betavec)But you should avoid for loops if possible:

>> newbetavec=beta.^a

While loopsThe previous example would be:betavec = zeros(100,1);beta = 0.925;a = [1:100];i = 1;while i < 101

betavec(i)=beta^a(i);i = i + 1;

endplot(betavec)

Solving problemsCheck if somebody else has already solved it

Matlab itselfAnybody using Matlab

Solve it by yourselfUse Matlab’s matrix processing capacity as

much as you canBe organized with your code

Thank you!

Questions, Comments,

Problems to solve?