Introduction to Matlab

Introduction to Matlab 332:202 Discrete Mathematics Spring 2007

Contents • What is Matlab • Matlab basic • Advanced usage of Matlab - plots - loops - working with m files - advanced functions

Contents • What is Matlab • Matlab basic • Advanced usage of Matlab

What is Matlab • Matrixlaboratory • easy to learn • robust • powerful functions

Get Help • Help - help - help function name (help abs)

Basic Math Operations • To compute a math expression composed of numbers and mathematics operators • + addition • - subtraction • * multiplication • / division • ^ power • Compute (2+3-9)*7^2/4 • =-49

General Math Expressions • To compute a math expression composed of numbers, variables and mathematics operators • Define all variables • The others are the same • E.g. x=3;y=6;x+y=? It is equivalent to 3+6

Exercise in Class(1) • 5 minutes • x=123;y=234;z=345 • Write the command expression and get the result: 1) the sum of x and y 2) subtract y from z 3) the multiplication of x and z • Answer 1) x+y=357;2)z-y=111;3)x*z=42435

Vectors and Matrices • Arrays are represented by some elements within brackets • The elements of each row is separated by at least one space • The separation of rows is by semicolons • E.g. [2 3;1 2]

How to Retrieve Elements of Matrix 1 x=[1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 16] What is the difference between x(2),x(1,2),x(:,2),x(2,:),x(1:2,2)?

How to Retrieve Elements of Matrix 2 • Index begins from 1, not 0 • For matrix x: • x(i) is the ith element, counted along the column • x(i,j) is the element at the ith row and jth column • x(:,j) is all the elements at the jth column • x(i,:) is all the elements at the ith row • x(i1:i2,j) is those elements at the jth column, begins from index i1 to i2

Vector and Matrix Operations • +,-,*,/ are used in operations between matrices • .*,./,.^ are used in operations between matrix elements • Pay attention to the dimensions of vectors and matrices

Exercise in Class(2) • 10 mins • x=[1 2;3 4];y=[5 6;7 8]; • z1=[1 2 3];z2=[4 5 6]; 1)Sum of x and y 2) Product of x and y 3)Bitwise product of x and y 4) Bitwise division of z1 over z2 5) Bitwise division of z1 over z2, but for the first two elements only (both the expression and result) Answer:1) [6 8;10 12]; 2) [19 22;43 50]; 3) [5 12;21 32];4)[0.25 0.4 0.5]; 5) z1(1:2)./z2(1:2)=[0.25 0.4]

Matrix Transpose • More operators other than +,-,*,/,^ • Matrix transpose:’(apostrophe)

Plot • plot(y) plots the columns of y versus their index • plot(x,y) plots vector y versus vector x • plot(x,y,s) plots vector y versus vector x, and s is a character string which states the line properties • plot(X1,Y1,S1,X2,Y2,S2,X3,Y3,S3,...) combines the plots defined by the (X,Y,S) triples, where the X's and Y's are vectors or matrices and the S's are strings.

Color Options - Yellow - ‘y’ • Magenta - ‘m’ • Cyan - ‘c’ • Red - ‘r’ • Green - ‘g’ • Blue - ‘b’ • Black - ‘k’

Line Styles - solid line (default) -- dashed line : dotted line -. dash-dot line

Line Markings • + - plus sign • o - circle • * - asterisk • . - Point • x - cross • s - square • d - diamond • ^ - upward pointing triangle • v - downward pointing triangle • > - right pointing triangle • < - left pointing triangle • p - five-pointed star (pentagram) • h - six-pointed star (hexagram) • Combined use of color, line style, and line marking : ‘r+:’

Example 1)t=0:0.1:4*pi; x=sin(t); plot(x);plot(t,x); plot(t,x,’r’); plot(t,x, 'c+:’); 2)x=1:1:10;y=2*x; plot(x,y,'r-');

Exercise in Class 3 • 15 mins • Write a short program which plots 2 lines in a graph. Two cycles of sin wave and cos wave. • Useful function: plot, sin, cos • t=0:0.1:4*pi; x=sin(t);y=cos(t); • plot(t,x,'r+-',t,y,'bo-.');

Grid • Grid or GRID ON adds major grid lines to the current axes. • GRID OFF removes major and minor grid lines from the current axes.

Comment Functions • xlabel('text') adds text beside the x-axis on the current axis • ylabel('text') adds text beside the y-axis on the current axis • title('text') adds text at the top of the current axis • legend(string1,string2,string3, ...) puts a legend on the current plot using the specified strings as labels • text(x,y,'string') adds the text in the quotes to location (X,Y) on the current axes

Axis • AXIS Control axis scaling and appearance. • AXIS([XMIN XMAX YMIN YMAX]) sets scaling for the x- and y-axes on the current plot. • AXIS OFF turns off all axis labeling, tick marks and background. • AXIS ON turns axis labeling, tick marks and background back on.

Exercise in Class 4 • 15 mins • Write a short program which plots 2 lines in a graph. Two cycles of sin wave and cos wave. • Use as many functions as you can: plot, sin, cos, grid, xlabel, ylabel, grid, title, legend, text, axis • t=0:0.1:4*pi; • x=sin(t); • y=cos(t); • plot(t,x,'r+-',t,y,'bo-.'); • grid on; • xlabel('The Time'); • ylabel('The Amplitude'); • title('Sin Wave and Cos Wave'); • legend('Sin','Cos','Location','Best'); • axis([0,4*pi,-2,2]); • grid on; • text(3/4*pi,sin(3/4*pi),'\leftarrow Sin'); • text(9/4*pi,cos(9/4*pi),'\leftarrow Cos');

Plots and Graphs – Con’t • HOLD ON holds the current plot and all axis properties so that subsequent graphing commands add to the existing graph. • HOLD OFF returns to the default mode whereby PLOT commands erase the previous plots and reset all axis properties before drawing new plots. • Figure or figure ( );

Save Figures • Save manually • Use Function Print - print filename directs the output to the PostScript file designated by filename - print -dformat filename exports the figure to the specified file using the specified graphics format, (such as TIFF). e.g. print –dmeta filename print -deps filename

Exercise in Class 5 • 5 mins • Generate a figure, and save it as ps file and emf file, respectively

Plots and Graphs – Con’t One example, different views • Plot3() x=-1:0.1:1; y=-1:0.1:1; z=x.^2+y.^2; plot3(x,y,z); • Mesh(); contour(); meshc(); meshz(); Surf(); [x,y]=meshgrid(-1:0.1:1); z=x.^2+y.^2; mesh(x,y,z); • H = SUBPLOT(m,n,p), or SUBPLOT(mnp), breaks the Figure window into an m-by-n matrix of small axes, selects the p-th axes for the current plot, and returns the axis handle. The axes are counted along the top row of the Figure window, then the second row, etc.

Basic Control Statements-for • for, end for variable=expression statement; end expression: initial value: increment: end value for i=1:5 for j=1:4 A(i,j)=1/(i+j-1); end end;

Exercise in Class 6 • 10 mins • Write a for program to compute 0.5+1+1.5+2+…+50 • x=0; • for i=0.5:0.5:50 • x=x+i; • end

Basic Control Statements-while • while, end while expression statement; end expression: a logical statement which is connected by ==,<,<=,>,>=,~=. x=1; while x<5 x=x+1; end

Exercise in Class 7 • 10 mins • Write a while program to compute 0.5+1+1.5+2+…+50 • i=0.5;x=0; • while i<=50 • x=x+i; • i=i+0.5; • end

Basic Control Statements-if • if, elseif, end IF expression statements ELSEIF expression statements ELSE statements END

M Files • Put a bunch of commands in an .m file. • Run the file under the command window. • The using of ‘;’. • Write a function as an .m file. - file name is the function name - the first line defines the function function myresutl=myfunction(a, b); - the comment lines (start with %) follow the first line is shown when asking for help

Exercise in Class • 10 mins • Write a m file to compute 0.5+1+1.5+2+…+50 • Run it

Useful Links • www.mathworks.com • Google

Introduction to Matlab