Matlab Workshop 9/22/2018

Useful links The help links on this page include 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

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

Acquiring Matlab www.yale.edu/software Free for Yale students

Launching Matlab Click “MATLAB 7” from the start menu (on Unix systems: type “matlab” to enter interactive mode)

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.

Tips 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

Entering Matrices Matrices can be Entered manually A = [1 2 3 ; 4 5 6 ; 7 8 9] Generated by built-in functions Loaded from a file

Matrix operations: + addition - subtraction * multiplication ^ power ‘ transpose \ left division, / division x = A \ b is the solution of A * x = b x = b / A is the solution of x * A = b To make ‘*’ , ‘^’, ‘\’ and ‘/’ apply element-by-element, we precede the operators by ‘.’

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)

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

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))

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) = [ ]

Suppressing Output: C = randn(5,1); 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);

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

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.

Scripts Scripts: a bunch of code grouped together; doesn’t accept argument or return output. Example open m-file editor type disp(‘Hello’) save as test.m in your current directory

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;

Flow Control: MATLAB has following flow controls: If statement For loops While loops Continue statement Break statement

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

for … end beta=0.925; a=1:1000; for i = 1:1000 betavec(i)=beta^a(i) But you should avoid for loops if possible newbetavec(a)=beta.^a

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

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