INTRODUCTION TO MATLAB LAB# 01

Introduction to Matlab What is Matlab? Matlab is a commercial “MATrix LABoratory” package by Mathworks, which operates as an interactive programming environment with graphical output. The MATLAB programming language is exceptionally straight forward since almost every data object is assumed to be an Array. In engineering MATLAB is displacing popular programming languages, due to its interactive interface, reliable algorithmic foundation, fully extensible environment and availability of different tool boxes.

Introduction to MATLAB Entering and Running MATLAB On a system running Microsoft Windows double click on the Matlab icon to launch Matlab. A command window will appear with the prompt >> you are now in MATLAB. Leaving Matlab A MATLAB session may be terminated by simply typing >> quit or by typing >>exit at the MATLAB prompt. Online Help Online help is available from the MATLAB prompt both generally and for specific commands. >> help >> help demo

Desktop Tools (Matlab v7) Command Window type commands Workspace view program variables clear to clear double click on a variable to see it in the Array Editor Command History view past commands save a whole session using diary

Variables MATLAB is case sensitive, that is Variable Assignment: ‘a’ is not the same as ‘A’ MATLAB has built in variables like pi, eps and ans. The variable ans will keep track of the last output which was not assigned to another variable. Variable Assignment: The equality sign is used to assigned values to variables. >> x = 3 y = x ^ 2 Out put can be suppressed by appending a semicolon to the command lines. >> x = 3 ; y = x ^ 2 ;

Variables Active Variables: Removing Variables Who Removing Variables Clear x Clear Saving and Restoring Variables Save filename Load filename

Variable Arithmetic Operator precedence Double Precision Arithmetic 2 + 3 *4 ^ 2 Double Precision Arithmetic Normally the results will be displayed in a shorter form. a = sqrt( 2 ) >> a = 1.4142 Format long b = sqrt ( 2 ) >> b = 1.41421356………. Format short Command Line Editing The arrow keys allow “ command line editing”

Built in Mathematical Functions Functions Meaning Examples Sin sine sin ( pi )=0.0 Cos cosine cos ( pi )=1.0 Tan tangent tan ( pi / 4)=1.0 Exp exponential exp(1.0)=2.7183 log natural log log(2.7183)=1.0 Arguments to trigonometric functions are given in radians. x= pi / 3; sin( x ) ^ 2 + cos ( x ) ^ 2 = ?

Matrices The element within a row of a matrix may be separated by a commas as well as a blank. The elements of a matrix being created are enclosed by brackets. A matrix is entered in “row major order” [i.e. all of the first row, then all of the second row; etc]; Rows are separated by semicolon [or a new line], and the elements of the row may be separated by either a comma or space. The following commands will create a 3 x 3 matrix and assigned it to the variable A. >> A = [1 2 3; 4 5 6; 7 8 9]; or A = [1,2,3;4,5,6;7,8,9] >> A = [ 1 2 3 4 5 6 7 8 9 ]

Matrices The matrix element located in the i-th row and j-th column of A is referred to in the usual way: >> A (1 , 2), A ( 2 , 3) Matrices can be easily modified: A ( 2 , 3 ) = 10; Building Matrices from a Block: Large matrices can be assembled from smaller matrix blocks i.e. C = [A;10 11 12]; [A; A; A] [A, A, A] >> B = [A, zeros(3,2); zeros(2,3), eye( 2 ) ] ?

Built in Matrix Functions Function Description diag return diagonal M.E as a vector eye identity matrix magic magic squares ones matrix of ones rand randomly generated matrix zeros matrix of zeros

Built in Matrix Functions Matrices of Random Entries: >> rand ( 3 ) >> rand ( m , n ) Magic Squares: A magic square is a square matrix which has equal sums along all its rows and columns. >> magic ( 4 ) Matrix of Ones: >> eye ( m , n ) >> eye ( n ) Matrices of Zeros: >> zeros ( m , n ) >> zeros ( n ) Diagonal Matrices: >> diag (A) diag ( diag ( A ) ) ?

Matrix Operations + Addition - Subtraction .* element-by-element mul * Multiplication ^ Power ‘ Transpose / Division * If the sizes of the matrices are incompatible for the matrix operation, an error message will result. .* element-by-element mul ./ element-by-element div .^ element-by-element power .‘ transpose

Matrix Operations Matrix Transpose: >> A’ Matrix Addition / Subtraction: A + B, A – B Matrix Multiplication; A * B , B * A. Round Floating Point Numbers to Integers: >> f = [-.5 .1 .5 ] round (f) ceil (f) floor (f) sum (f) prod (f) Matrix Element Level Operations: The matrix operation of addition and subtraction are already operates on an element by element basis but other operation given above do not. Matlab has a convention in which a dot in front of the operations is used. i.e [1 , 2 , 3 , 4 ] . * [ 1 , 2 , 3 , 4 ] [ 1 , 2 , 3 , 4 ] . ^ 2

Operators (relational, logical) == equal ~= not equal < less than <= less than or equal > greater than >= greater than or equal & AND | OR ~ NOT

Branching Constructs If – end Construct: If - else - end Construct: if < condition >, < program > end If - else - end Construct: if < condition 1 >, < program 1> else < program2 > If - elseif - end Construct: if < condition1 >, < program 1> elseif <condition2> < program2 > end

Looping Constructs For Loops: While Loops: Nested For Loops: for i = 1 : n , < program>, end While Loops: while < condition >, < program >, Nested For Loops: for i = 1 : n , for j = 1 : n , A(i,j) = i/j ; end

Matlab M-files Matlab commands can be run from one file without having to enter each command one by one at Matlab prompt. In order to use the programs later in Matlab they are to be saved first. For this purpose programs should be written in the editor / debugger. In command window go to File menu, new and select M-file. Code your algorithm Execute it from the command window by typing file name

Matlab User Defined Function Matlab User Defined Function can have an input and output. Arguments can be passed to a function for computation For this purpose programs should be written in the editor / debugger. In command window go to File menu, new and select M-file. function add x = 3; y = 5; z = x + y Save the file and write add at the command prompt function addv (x,y) Z = x + y Save the file and write addv(5,6) at the command prompt % is used for commenting in front of a statement

Input/ Output Request User Input Ouput Data data=input(‘message’); data=input(‘message’,’s’) Ouput Data disp(‘message’) disp(variable_name)

Matlab Graphics x = 0:pi/100:2*pi; y = sin(x); plot(x,y) xlabel('x = 0:2\pi') ylabel('Sine of x') title('Plot of the Sine Function')

Multiple Graphs t = 0:pi/100:2*pi; y1=sin(t); y2=sin(t+pi/2); plot(t,y1,t,y2) grid on

Multiple Graphs x = 0 : .01 : 2 * pi; y1= sin (x); y2 =sin (2*x); plot(x,y1,‘--',x,y2,‘-‘,x,y3,‘+') grid title ('Dashed line and dotted line graph')

Multiple Plots t = 0:pi/100:2*pi; y1=sin(t); y2=sin(t+pi/2); subplot(2,2,1) plot(t,y1) subplot(2,2,2) plot(t,y2)

Three Dimensional Graphics x = -1:.1:1 ; y = -1:.1:1; for i=1:1:length(x) for j=1:1:length(y) z(i,j)=x(i)^2+y(j)^2; end mesh(z);

Graph Functions (summary) plot (x,y) linear plot plot (x,y1,x,y2) multiple plots on the same graph mesh(z) 3-D graph stem (x) discrete plot xlabel (‘X-axis label ’) add X-axis label ylabel (‘Y-axis label ’) add Y-axis label title (‘title of plot’) add graph title subplot (m,n,p) divide figure window grid add grid lines hold hold current graph in the figure zoom allow zoom in/out using mouse figure create new figure window pause wait for user response