Introduction to MATLAB Morris Law Jan 5, 2013

Outline Matlab software Entering matrix Matrix function and manipulation Matlab graphics Matlab programming: writing M-file and functions Function input & output Control flow

MATLAB software Multi-platforms (Windows, Linux, MacOSX) Technical computing Script language Variables are all matrices Expandable by adding toolboxes

Entering matrix Explicit listing M-file External data files Stored the above statement in ex1.m. Run the M-file, i.e. >> ex1 External data files >> load A.dat Built-in statements and functions >> B = eye(3)

Matrix function and manipulation ones(3), zeros(3), eyes(3) magic(4), hilb(5), rand(4,3) size(A), eig(A), det(A), inv(A), diag(A) sum(A), prod(A), mean(A), max(A), std(A)

Exercise on Matrix functions Try A = [1 2 3; 4 5 6; 7 0 9] x = ones(3) y = eye(3) z = zeros(3) d = diag(A) det(A) inv(A) rank(A) eig(A)

Exercise on Matrix functions m = magic(4) sum(m) sum(m’) sum(diag(m)) r = rand(4,3) size(r)

Matrix elements >> x = [-1.3, sqrt(3), (1+2+3)*4/5 ]; -1.3000 >> x(5)= abs(x(1)) x = -1.3000 1.7321 4.8000 0 1.3000 >> y = 1:5 y = 1 2 3 4 5 xy = [x;y] xy = -1.3000 1.7321 4.8000 0 1.3000 1.0000 2.0000 3.0000 4.0000 5.0000

Matrix elements (cont) >> B = [A;r]; >> C = [A,zeros(size(A));ones(size(A)),A] C = 1 2 3 0 0 0 4 5 6 0 0 0 7 8 9 0 0 0 1 1 1 1 2 3 1 1 1 4 5 6 1 1 1 7 8 9 >> D = C(1:3,:) >> D = C(:,3:4)

Matrix Arithmetic Additions (+) Subtraction (-) Multiplication (*) Right division (/) Solve A = xb by x = A/b Left division (\) Solve Ax = b by x = A\b Power (^)

Element-by-Element Operation Using Period (.) x = [1,2,3]; y = [4 5 6]; >> x .* y ans 4 10 18 >> x ./ y 0.25 0.4 0.5 >> x .\ y 4 2.5 2 >> x .^ y ans 1 32 729 >> x .^ 2 1 4 9 >> 2 .^ [x y] 2 4 8 16 32 64

MATLAB graphics If y is a vector, plot(y) produced a linear graph plot(x,y) produces a graph of y versus x t = 0: pi/10: 2*pi; x = sin(t) Y1 = sin(t+.25); Y2 = sin(t+.50); plot(x,y1,’r-’,x,y2,’g--’) Title(‘Phase Shift’) xlabel(‘x=sin(t)’); ylabel(‘y1=sin(t+)’);

MATLAB graphics – 3D mesh The following commands draw a mesh x = [-pi:0.1:pi]; y=x; [X,Y]=meshgrid(x,y); Z = sin(X).* sin(Y) + cos(X).*cos(Y); mesh(Z);

MATLAB programming Two kinds of MATLAB program 1. Script or M-file sequence of Matlab statements without input and output variables are global 2. Functions with input and output defined as function [out1, out2, … outN]= funcname(in1, in2, … inN) variables are local

Writing scripts / M-files Use Matlab M-file editor, save the following as fibo.m % An M-file to calculate Fibonacci numbers f = [1 1]; i=1; while f(i) + f(i+1) < 1000 f(i+2) = f(i) + f(i+1); i=i+1; end plot(f); At the Matlab command prompt, type the following to run >> fibo

Writing script – another example looptest.m % Fill b with square roots of 1 to 1000 using a for loop clear; tic; for i= 1:1000 b(i) = sqrt(i); end t=toc; disp([‘Time taken for loop method is ‘, num2str(t)]); % Fill b with square roots of 1 to 1000 using a vector a = 1:1000; b = sqrt(a); disp([‘Time taken for vector method is ‘, num2str(t)]); Run the program with >> looptest

MATLAB function MATLAB functions allow input and output variables function y = stat(x) % mean average [ m n ] = size(x); if m == 1 m = n; end y = sum(x) / m; If z is a vector, z = 1:99, type >> mean(z) ans 50

Control flow If and break statement For Loops While Loops or for v = expression statements end While Loops while expression If and break statement if expression, break, end or if expression statements [elseif expression statements] [else expression end

General Purpose commands (1/5) Managing commands and functions demo run demo help on line documentation Info information about MATLAB and MathWorks lookfor keyword search through the help entries path control MATLAB's search path type list M-file what directory listing of M-, MAT- and MEX-files which locate functions and files

General Purpose commands (2/5) Managing variables and the workspace clear clear variables and functions from memory disp display matrix or text length length of vector load retrieve variables from disk pack consolidate workspace memory save save workspace variables to disk size size of matrix who list current variables whos list current variables, long form

General Purpose commands (3/5) Working with files and the operating system cd change current working directory delete delete file diary save text of MATLAB session dir directory listing getenv get environment value ! execute operating system command

General Purpose commands (4/5) Controlling the command window clc clear command window echo echo commands inside script files format set output format home send cursor home more control paged output in command window

General Purpose commands (5/5) Starting and quitting from MATLAB matlabrc master startup M-file quit terminate MATLAB startup M-file executed when MATLAB is invoked

Search for documentation helpdesk http://www.mathworks.com

Reference Booklet on Introduction to MATLAB MATLAB primer (version 3)