Introduction to Matlab Workshop Matthew Johnson, Economics October 17, /13/20151

2 Getting Help Useful links: 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. MATLAB is a matrix-based tool for numerical computations. It’s very powerful and easy to use. Both programming language and interactive environment Both programming language and interactive environment Very fast native functions; very slow when processing loops Very fast native functions; very slow when processing loops Lots of available toolboxes Lots of available toolboxes

4 Acquiring Matlab Free for Yale students Free for Yale students Installed on all Statlab computers Installed on all Statlab computers

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

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

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

8 Entering Matrices Matrices can be :  Entered manually A = [1 2 3 ; ; 7 8 9]  Generated by built-in functions  Loaded from a file  File>Import Data

9 Matrix operations: + addition + addition - subtraction - subtraction * multiplication * multiplication ^ power ^ power ‘ transpose ‘ transpose To make operations apply element-by-element, we precede the operators by ‘.’ 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). 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*[ ]’ b=A>18; c=[ ]’ i,j can also be vectors of indices or logical arrays: A=4*[ ]’ b=A>18; c=[ ]’ A(b), A(c) A(b), A(c)

11 The Colon Operator ‘:’ 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: 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 [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) Zeros: all zeros. A = zeros(1,3) Ones: all ones. A = ones(2,4) Ones: all ones. A = ones(2,4) Rand: elements are U[0,1] random variables A = rand(3,5) Rand: elements are U[0,1] random variables A = rand(3,5) Randn: elements are standard-normal random variables A = randn(2,5) 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)) 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 A=eye(3) gives a 3-by-3 identity matrix sparse(m,n): same as zeros(m,n), use if most elements are zeros. sparse(m,n): same as zeros(m,n), use if most elements are zeros. Concatenation: join small (compatible) matrices to make bigger ones: Concatenation: join small (compatible) matrices to make bigger ones: B = [A A-2; A*2 A/4] Deleting rows and columns: Deleting rows and columns: B(:,2) = [ ] 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. Example: C = randn(5,1) v.s. C = randn(5,1); C = randn(5,1);

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

Aside: You can run Matlab 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 SSH Log in to eli.yale.edu through SSH In SSH click on Edit, then click Settings, then click Tunneling 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 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 You’re all set! Type “matlab &” in SSH to run the program Note that this is an older version of matlab Note that this is an older version of matlab 16

17 Functions: MATLAB provides a large number of standard elementary mathematical functions, including abs, sqrt, exp, sin. MATLAB provides a large number of standard elementary mathematical functions, including abs, sqrt, exp, sin. For a list of the elementary mathematical functions, type: For a list of the elementary mathematical functions, type: help elfun help elfun For a list of more advanced mathematical and matrix functions, type 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. 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. Scripts: a bunch of code grouped together; doesn’t accept argument or return output. You should do most of your work using scripts! You should do most of your work using scripts! Example: Example: open m-file editor open m-file editor type disp(‘Hello’) type disp(‘Hello’) type disp(‘World’) type disp(‘World’) save as test.m in your current directory save as test.m in your current directory type “test” in Matlab 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. 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; 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 If statement For loops For loops While 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: 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)

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)) 25

26 Learn from others There are lots of Matlab functions already out there: There are lots of Matlab functions already out there: Google them! Google them! James LeSage’s econometrics toolbox: James LeSage’s econometrics toolbox: