Introduction to Matlab

Introduction to Matlab Tutorial for CS4MN3/SE3X03 Wen Yu McMaster University

Matlab Overview • Matlabis a commercial "Matrix Laboratory" package which operates as an interactive programming environment • Matlab is installed in Moore - sshmoore - change to working directory - matlab - quit or exit

Entering matrices • On the interactive window A = [1 2 3 A = [1,2,3; 4,5,6; 7,8,9] 4 5 6 7 8 9 ] • From Files - data files: load data.ext - script files: data.m • Built-in statements and functions: rand(2,3) • From blocks: B = [A, zeros(3,2); zeros(2,3), eye(2)]

Operations • Matrix operations: +, -, *, ^, ‘, \, / - x = A\b is the solution of A x = b - x = b/A is the solution of x A = b - b/A = (A’\b’)’ • Array operations (entry-wise): .*, .^, .\, ./ - [1,2,3,4].*[1,2,3,4] = [1,2,3,4].^2 = [1,4,9,16]

Statements, Expressions, and Variables • Matlab is an expression language • variable = expression, or simply expression • Expressions are assigned to default variable ans • A statement is terminated with (;), (,) or carriage return • A statement can be placed in several lines • Several statements can be placed in one line

Control Statement • for i = m:k:n statements end • whilerelation statements end • ifrelation statements end

Relations • Relational operators: <, >, <=, >=, ==, ~= • Logical operators: &, |, ~ • A relation between matrices is true if the relation of each entry is true • any(any(A ~= B)) returns true if any entry of A and B is not equal

Submatrices and Colon Notation • 1:5 gives [1 2 3 4 5] • 0.2:0.2:1.2 gives [0.2, 0.4, 0.6, 0.8, 1.0, 1.2] • 5:-1:1 gives [5 4 3 2 1] • B(1:4,3) first four entries of the third column • B(:,3) the third column • B(1:4,:) first four rows • C=B, B(:,[2 4 5]) = C(:,1:3) • B(:,[2,4]) = B(:,[2,4])*[1 2;3 4]

M-files • A script file consists of a sequence of normal MATLAB statements • Variables in a script file are global • Function files provide extensibility to MATLAB • Variables in a function file are by default local • function [out1, out2, …] = fname(in1, in2, …) • A comment line begins with the % symbol

Text • s = 'This is a string‘ • disp(‘This message is hereby displayed') • error('Sorry, the matrix must be symmetric') • iter = input('Enter the number of iterations: ') • fprintf(1,‘This is a string, too.’)

Output Format. • format short fixed point with 4 decimal places (the default) • format long fixed point with 14 decimal places • format short e scientific notation with 4 decimal places • format long e scientific notation with 15 decimal places • format rat approximation by ratio of small integers • format hex hexadecimal format • format bank fixed dollars and cents • Format compact suppress most blank lines

Graphics Polar plot: t=0:.01:2*pi; polar(t,abs(sin(2*t).*cos(2*t))); Line plot: x=0:0.05:5;,y=sin(x.^2);,plot(x,y); Stem plot: x = 0:0.1:4;, y = sin(x.^2).*exp(-x); stem(x,y)

Graphics – cond. Surface plot: z=peaks(25);, surf(z);, colormap(jet); Mesh plot: z=peaks(25);, mesh(z); Contour plot: z=peaks(25);,contour(z,16); Quiver plot:

Titles, Axes labeled, and Text • title graph title • xlabel x-axis label • ylabel y-axis label • text position text at specified coordinates

Axis • axis([xmin,xmax,ymin,ymax]) set axis scaling to prescribed limits • axis(axis) freezes scaling for subsequent graphs • axis auto returns to auto-scaling • v = axis returns vector v showing current scaling • axis square same scale on both axes • axis equal same scale and tic marks on both axes • axis off turns off axis scaling and tic marks • axis on turns on axis scaling and tic marks

Line- and Mark-types • Linetypes: solid (-), dashed (--). dotted (:), dashdot (-.) • Marktypes: point (.), plus (+), star (*), circle (o), x-mark (x)

Other Useful Command for Graphics • figurecreates an empty figure window • hold on freezes the current graphics screen • hold off releases the hold • print-deps -f3 filename saves to filename.eps the graphics figure 3 • saveas(gcf, ‘plot2.eps’) save current figure as graphics file.

References • MATLAB Primer, Kermit Sigmon, Department of Mathematics, University of Florida • Introduction to Matlab, Joanna Waniek • Matlab Tutorial, Prof. Matthias Hein • Introduction to MATLAB, Markus Kuhn, University of Cambridge

Introduction to Matlab