What is MATLAB ?

• MATrix LABratory– Originally, it was a front-end to FORTRAN

matrix routines developed in the 1970’s @ U. of New Mexico and Stanford

– Today it is a powerful, interactive mathematics ENVIRONMENT with many powerful capabilities (matrices, symbolic math, analysis)

• Not unlike a UNIX shell

Support Materials

• MATLAB is available @ the ECE front desk, and at the ODU bookstore– The only way to master MATLAB is to use it

(just like any programming language or skill)

• User’s Guide (comes with student edition)

• Internet FAQ’s (e.g. www.mathworks.com) MATLAB Primer (Bound copy ~$3.00)

Accessing Matlab

• Start Menu.. Programs.. Matlab

• To exit..– >>quit

Entering Matrices

• MATLAB works with essentially one kind of object – a rectangular numerical MATRIX with possibly complex entries

• 1 x 1 interpreted as scalars

• 1 x n or m x 1 interpreted as vectors

• Entered by explicit list of elements, or

• Generated by built-in statements and functions

• Created in M-files

• Loaded from external data files

Entering matrices (contd.)

• Example A = [1,2,3; 4,5,6; 7,8,9] or

• A = [– 1 2 3

– 4 5 6

– 7 8 9 ] creates a 3 x 3 matrix and assigns it to a variable A.

• , or blank separates the element in a matrix

• Avoid blank spaces while listing a number in exponential form (e.g. 2.34e-9)

• Large Matrix best done in M – file (easy to edit)

• Built in functions: rand, magic, hilb

• rand (n) creates a n x n matrix with random entries uniformly distributed between 0 and 1

• rand (m x n) will create an m x n matrix

• magic (n) will create a an integral n x n matrix which is a magic square

• hilb(n) will create the n x n Hilbert matrix

• Individual matrix and vector entries can be referenced with indices (only positive integers) within the parentheses– E.g. A(2,3) refers to entry in second row and third column.

– X(3) woild denote third coordinate of a vector x.

Entering matrices (contd.)

Matrix Operations

• Addition +

• Substraction -

• Multiplication x

• Power ^

• Transpose `

• Left Division \

• Right division /– E.g. x = A\b is the solution of A * x = b

– x = b/A is the solution of x * A = b

Array Operations

• Addition & substraction Operate entrywise

• Other can be made entrywise by preceding them with a period – for *,^,\,/– E. g. [1 2 3 4] .*[1 2 3 4] will yield [1 4 9 16]– [1 2 3 4].^2 will yield [1 4 9 16]

• Useful in MATLAB graphics

Statements, Expressions & Variables

• MATLAB is an expression language – CASE SENSITIVE• Statements are of the form

– Variable = expression, or simply– Expression

• Expressions are composed from operators, functions , and variable names.• Result is a Matrix assigned to the variable for future use.• If variable name and = sign are omitted, then a variable ans (for answer) is

created.• Statement terminated with a CR, use … to continue to next line• Same line use comma to separate statements• Last character semicolon suppresses the printing• Who – lists all the variables• Clear – clears the variables• Runaway Display can be stopped by CTRL-C

Matrix Building Functions

• Convenient Matrix Building Functions are– Eye

– Zeros

– Ones

– Diag

– Triu

– Tril

– Rand

– Hilb

– Magic

– Toeplitz

For,While, if – and relations

• MATLAB flow control statements operate like those in most computer languages

• For– x =[]; for i = 1:4, x = [x,i^2],end– x =[]; for i = 4:-1:1, x = [x,i^2],end

• While– While relation– Statements– End

• If– If relation– Statements– end

Relations

• < less than

• > greater than

• <= less than or equal

• >= greater than or equal

• == equal

• ~= not equal

• & and

• | or

• ~ not

Scalar & Vector functions

• Scalar– Sin asin exp abs round– Cos acos log sqrt floor– Tan atan rem sign ceil

• Vector– Max sum median any– Min prod mean all– Sort std

Matrix Functions

– Eig chol svd inv lu qr– Hess schur rref expm sqrtm poly– Det size norm cond rank

Command Line Editing & Recall

• Use left & right arrows

• Backspace & delete keys

• Home, end, Delete

• Up/Down arrow keys

Submatrices & Colon Notation

• To achieve fairly complex data manipulation

• Colon Notation (generate vectors and reference submatrices

• Expression 1:5 generates [1 2 3 4 5]

• Expressions 0.2:0.2:1.2 generates [0.2 0.4 0.6 0.8 1.0 1.2]

• Expression 5:-1:1 gives [5 4 3 2 1]

• X= [0.0:0.1:2.0]’;y=sin(x);[x,y] gives a table of sines

• Colon Notation – used to access submatrices of a matix– A(1:4,3), A(:,3), A(1:4,:) , A(:, [2,4])

– A(:[2,4,5]) = B(:,1:3)

– A(:[2,4]) = A(:,[2,4])*[1,2:3,4]

M files

• To execute a sequence of statements

• Script files

– Sequence of normal MATLAB statements

– Variables are global

– Used to enter data into a large matrix

– Entry errors can be easily edited

• Function files– Provide extensibility to MATLAB

– Create new functions specific to a problem

– Variables are local

– We can however declare them global if so desired.

Function files

Example

function a = randint(m,n)

a= floor (10 * rand(m,n)

Place in a file called randint.m

first line declares function name,input arguments and output arguments

without this line the file would be a script file

A statement z = randint(4,5) will pass 4,5 to m,n in the function file with the output result passed to variable z.

Function file (contd.)

• Example 2– Function [mean, stdev] = stat (x);

– [m,n] = size(x);

– If m == 1

– M = n;

– End

– Mean = sum(x)/m

– Stdev = sqrt (sum(x.^2)/m – mean.^2);

• % to write comment statements

Text Strings, error messages, inputHardcopy

• Text Strings – use single quotes

• Use disp to display text strings

• Use error to display error messages

• Use input to interactively input data

• Use diary to get a hardcopy – To turn off use diary off

Graphics

• Use plot to create linear x,y plots

– x = -4:0.1:4; y = sin(x); plot (x,y)

– x = -1.5:0.01:1.5; y = exp(-x.^2); plot (x,y)

– t = 0:.001:2*pi;x=cos(3*t);y=sin(2*t),plot(x,y)

• Use shg to see the graphics screen

• Labelling– Title xlabel ylabel gtext text axis

– Default is auto scaling

• Multiple plots – Hold

• Linetypes and pointtypes

Graphics (contd.)

• 3-D mesh plots– Use function mesh

• 3-D perspective of elements of matrix z

• Mesh (eye(10))

• xx = -2:.1:2;yy=xx;[x,y] = meshdom(xx,yy);z = exp(-x.^2 - -y.^2);mesh(z)