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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)

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What is matlab
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
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
Accessing Matlab

  • Start Menu.. Programs.. Matlab

  • To exit..

    • >>quit


Entering matrices
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
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


Entering matrices contd1
Entering matrices (contd.)

  • 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.


Matrix operations
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
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
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
Matrix Building Functions

  • Convenient Matrix Building Functions are

    • Eye

    • Zeros

    • Ones

    • Diag

    • Triu

    • Tril

    • Rand

    • Hilb

    • Magic

    • Toeplitz


For while if and relations
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
Relations

  • < less than

  • > greater than

  • <= less than or equal

  • >= greater than or equal

  • == equal

  • ~= not equal

  • & and

  • | or

  • ~ not


Scalar vector functions
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
Matrix Functions

  • Eig chol svd inv lu qr

  • Hess schur rref expm sqrtm poly

  • Det size norm cond rank


Command line editing recall
Command Line Editing & Recall

  • Use left & right arrows

  • Backspace & delete keys

  • Home, end, Delete

  • Up/Down arrow keys


Submatrices colon notation
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
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
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
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 input hardcopy
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
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
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)


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