Introduction to Matlab Workshop

1. Introduction toMatlab Workshop Matthew Johnson, Economics October 17, 2008

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

3. What is MATLAB? • MATLAB is a matrix-based tool for numerical computations. It’s very powerful and easy to use. • Both programming language and interactive environment • Very fast native functions; very slow when processing loops • Lots of available toolboxes

4. Acquiring Matlab • www.yale.edu/software • Free for Yale students • Installed on all Statlab computers

5. Launching Matlab • Double-click the “MATLAB R2008a” icon on the desktop

6. The Interface • Main Window: Input/Output • Workspace: consists of the variables you create during a MATLAB session; • Command History: double click them to evaluate them; • Current Directory browser: shows you where you are.

7. Interface (continued) • Can use Matlab as a calculator • Type “help” for a list of all help topics • help abs gives the syntax and information about the absolute value command

8. Entering Matrices Matrices can be : • Entered manuallyA = [1 2 3 ; 4 5 6 ; 7 8 9] • Generated by built-in functions • Loaded from a file • File>Import Data

9. Matrix operations: • + addition • - subtraction • * multiplication • ^ power • ‘ transpose • To make operations apply element-by-element, we precede the operators by ‘.’

10. Subscripts: • Subscripts: the element in row i and column j of A is denoted by A(i, j). • i,j can also be vectors of indices or logical arrays:A=4*[1 2 3 4 5 6 7 8 9]’b=A>18; c=[5 6 7 8 9]’ • A(b), A(c)

11. The Colon Operator ‘:’ The colon ‘:’ is one of MATLAB ’s most important operators. It has many formats: • Subscript expressions involving colons refer to portions of a matrix: A(5:9) is the fifth to the ninth elements of A. • [0:0.2:3] is a row vector containing integers from 0 to 3, in increments of 0.2

12. Matrices and Random Numbers: Four functions that generate basic matrices: • Zeros: all zeros. A = zeros(1,3) • Ones: all ones. A = ones(2,4) • Rand: elements are U[0,1] random variables A = rand(3,5) • Randn: elements are standard-normal random variables A = randn(2,5) • Be careful: Matlab always sets the same seed.Get ‘more random’ numbers by typing rand('state', sum(100*clock))

13. A=eye(3) gives a 3-by-3 identity matrix • sparse(m,n): same as zeros(m,n), use if most elements are zeros. • Concatenation: join small (compatible) matrices to make bigger ones: B = [A A-2; A*2 A/4] • Deleting rows and columns: B(:,2) = [ ]

14. Suppressing Output: If you simply type a statement and press Enter, MATLAB automatically displays the results on screen. If you end the line with a semicolon ‘;’, MATLAB performs the computation but does not display any result. • Example: C = randn(5,1) v.s. C = randn(5,1);

15. Aside: You can run Matlab remotely! • Available to anyone with a Yale pantheon account • You need the following (free) software • Xming (available from http://sourceforge.net/projects/xming) • SSH (available from www.yale.edu/software) • Useful if you don’t want to have Matlab take up memory/processing power on you computer

16. Aside: You can run Matlab remotely! • Instructions: • Start Xming (it will run in the background) • Log in to eli.yale.edu through SSH • In SSH click on Edit, then click Settings, then click Tunneling • Check the box at the bottom that says “Tunnel X11 Connections” and click OK • You’re all set! Type “matlab &” in SSH to run the program • Note that this is an older version of matlab

17. Functions: • MATLAB provides a large number of standard elementary mathematical functions, including abs, sqrt, exp, sin. • For a list of the elementary mathematical functions, type: help elfun • For a list of more advanced mathematical and matrix functions, type help specfun help elmat

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

19. Scripts • Scripts: a bunch of code grouped together; doesn’t accept argument or return output. • You should do most of your work using scripts! • Example: • open m-file editor • type disp(‘Hello’) • type disp(‘World’) • save as test.m in your current directory • type “test” in Matlab

20. Functions: • Functions are M-files that can accept input arguments and return output arguments. The name of the M-file and of the function should be the same. • For example, save this as area.m:function ar = area(radius)ar=pi*radius^2;

21. Flow Control: MATLAB has following flow controls: • If statement • For loops • While loops

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

23. for … end beta=0.925; a=1:100000; for i = 1:100000 betavec(i)=beta^a(i); end betavec • But you should avoid for loops if possible newbetavec=beta.^a

24. Graphics: plot x = [0 : .01 : 2*pi]; y = sin(x); plot(x,y) y2 = sin(x-.25) y3 = sin(x-.5) plot(x,y,x,y2,x,y3)

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

26. Learn from others • There are lots of Matlab functions already out there: • Google them! • http://www.mathworks.com/matlabcentral/ • James LeSage’s econometrics toolbox:http://www.spatial-econometrics.com/