Ele532 Matlabtutorial Full

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ELE 532 – Signals and Systems

MATLAB Tutorial

Friday, September 14th, 2007

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ELE 532 – Signals and SystemsFall 2007

MATLAB Tutorial

Raymond PhanDistributed Multimedia Computing Research (DMCR) Lab

Ryerson University – EPH 237

[email protected]

http://www.ee.ryerson.ca/~rphan/ele532/MATLABTutorial.ppt





ELE 532 –

Signals and SystemsMATLAB Tutorial


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Outline of Tutorial – (1)

• Introduction

• Getting Started

• Variables and Starting Basics• Vectors and Matrices

• Basic Operations

• Script Files• Function Script Files



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• Flow Control

• Basic Graphics Commands

• Other Useful Commands• Final Words



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Introduction – (1)

• So… what the hell is MATLAB and what‟s it allabout? – MATLAB: MATrix LABoratory

• Created in 1970 by a dude named Cleve Moler• Was (and still is) used extensively at Stanford

University and the University of New Mexico – Why? To make calculating the following things a lot

easier!• Matrix Theory

• Linear Algebra

• Numerical Analysis



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Introduction – (2)

• MATLAB is selected as a numerical analysis toolover languages like C and Java because: – Very EASY programming language

– Powerful graphics capabilities

– Very sleek and interactive interface – Great for general scientific and engineeringcomputation

• Later in your courses, you‟re going to start to usethis heavily, especially in: – ELE 639: Control Systems

– ELE 792: Digital Signal Processing

– … any signal processing and controls course in 4th year



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• Introduction

• Getting Started






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Getting Started – (1)

• Where can I find and use MATLAB?

• Method #1: On the EE undergraduate

network labs:

– ENG 406, 407, 408 and 409

• Log onto an EE undergraduate terminal

• A) Go to Applications – Accessories – Terminal

and type in „matlab‟ (without the quotes) • B) Go to Applications – Math – MATLAB 2007a



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Getting Started – (2)

• Method #2: If you don‟t feel like using thecomputers at school, you can install your owncopy of MATLAB on your PC or laptop – There are many ways to obtain your own copy:

• Buy a student version at the Ryerson Bookstore

• Obtain a trial version online via: http://www.mathworks.com • “Borrow” from a friend

– Version of MATLAB needed for these labs: MATLAB7.0 and up

– NOTE!: You MUST have the Java Runtime

Environment (JRE) installed on your system• At LEAST 5.0 and up

– MATLAB uses the JRE as a backbone to run thewhole application

http://www.mathworks.com/

http://www.mathworks.com/



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Getting Started – (3)• What happens next!?

– MATLAB Interface: >> means it‟s ready for input from you



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• Introduction

• Getting Started






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Variables and Basic Commands –

(1)

• One GREAT thing about MATLAB:

– MATLAB is a programming language that isdynamically typed… what does this mean?

– You can declare variables and initialize themwithout specifying what type they are

• MATLAB automatically figures this out for you, oryou can choose to manually override the type

– Example:• C or Java way: int nikhil = 1, doublejenny = 2

• MATLAB way: nikhil = 1, jenny = 2



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(2)• When you want to assign something to a

variable, use the = sign

• When you assign something to a variable,MATLAB initializes & automatically declares it

• Guidelines for variable names: – All must be single words, no spaces

– Must begin with a letter, numbers or the underscorecharacter ( _ )

– Variable names are case sensitive• i.e nikhil is NOT the same as Nikhil

• i.e muffin is NOT the same as mUFfin

– Names can be up to 19 characters in length



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(3)

• Some valid variable names:– voltage

– valueOfR1

– Ron_and_Mauro– _Alan2007_

• Some invalid variable names (why are theseinvalid?):

– 123– value of R1

– 3v

– X#*()$#$!!!



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(4)

• Left panel: Current Directory / Workspace

– A) Shows you directory structure to access working

directory (more on this later)

– B) Shows you all of the variables that have beencreated and can be accessed

• Right: Command Prompt

– Enter commands and variable declarations here

– Commands without a semicolon ( ; ) echo yourcommand to screen

– Commands with a semicolon suppress that output



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(5)• Can enter commands either:

– One at a time: The end of each command, pressENTER (carriage return)

– Multiple commands in one line:• Suppress echoing: Use semicolons to separate each

command on the line• Enable echoing: Use commas ( , ) to separate each

command on the line

• Typing in a variable by itself and pressingENTER will redisplay the variable

• Entering a value, pressing ENTER, and not assigning it to anything, the value will beautomatically assigned to a variable called ans (answer)



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(6)



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(7)

• who command: Shows you all of thevariables created by you

– You can also check the workspace as well

• clear command: Clears all of the variablesshown in the workspace, and you startfrom scratch

• clc command: Flushes the commandprompt

– Variables will still be in the workspace, but itclears the command prompt screen



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(8)



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(9)

• Can also declare complex numbers too:

– Can add, subtract, multiply and divide

• You can use i or j to declare complex

numbers• Of course… you can also add, subtract,

multiply and divide normal numbers too!

– Too lazy to make a slide for it – However, we‟ll get into addition, subtraction,

multiplication and division in another way later



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(10)



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(11)

• Command History window: Used to keep trackof the commands you ran recently

• You can alsodouble click on

any of the commandsto re-run them again

• You can also pressthe up & down keys

to cycle throughthe commands aswell in the commandprompt



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• Introduction

• Getting Started






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Vectors and Matrices – (1)

• Unless otherwise defined, MATLAB treatsALL variables as 2D matrices… how isthis possible?

– Arrays and Vectors: N x 1 or 1 x N matrix

– Single value: 1 x 1 matrix

• Why does MATLAB decide to handle it thisway?

– You‟ll see later that handling variables asmatrices makes things A LOT faster andeasier to work with



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Vectors and Matrices – (2)• How do you declare a vector / array in

MATLAB? – C or Java way: int a[4] = {1, 2, 3, 4};

– MATLAB way: • a = [1 2 3 4] – row vector

– Spaces mean to move to the next column

• a = [1 2 3 4].’ – (.‟ operator means to transpose avector) - column vector

• a = [1;2;3;4] - column vector – Semicolon means to move to the next row

• You do not have to specify how big the vector isfirst before you make it – Beauty of dynamically typed languages!

– MATLAB automatically figures out how big it is andyou go from there



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Vectors and Matrices – (3)• How do I access elements in a vector /

array? – C or Java way:

•int jenny = a[0];

– MATLAB way:•jenny = a(1);

• NOTE!:

– No square brackets when accessing anelement! Use round brackets!

– Elements do not start at index 0, they start atindex 1!



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Vector and Matrices – (4)



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• How do I create a matrix in MATLAB? – C or Java way: int a[4][4] = {{1, 2,3, 4}, {5, 6, 7, 8}, {9, 10, 11,

12}, {13, 14, 15, 16}}; – MATLAB way:

• #1: a = [1 2 3 4; 5 6 7 8; 9 10 11 12;13 14 15 16];

• #2: a = [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 16];




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• How do I access elements in a matrix? – C or Java way:

• int alan = a[2][3];

– MATLAB way:• alan = a(3,4);

• What‟s the difference here? – No separate brackets for each dimension

– Comma is used to separate the dimensions

– All indices to access arrays are offset by 1!

– Remember: 1st parameter is the row, 2nd parameter isthe column




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• Here‟s something to mess you up… how do I

access a range of values in a matrix?

• Suppose I had a matrix already created called

ray – How do I get all of the elements in the 1st row?

– C or Java way:• int i;

for(i = 0; i < 4; i++)ray[i] = a[0][i];

• This is a pain in the butt!... There‟s gotta be an easier way to

do this!




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Vectors and Matrices – (8)• MATLAB way:

– ray = a(1, 1:4);– ray = a(1, :);

• What‟s the difference here?! – NO for loop!

– The colon ( : ) operator is used to access a range ofvalues• There is a more general use for this, but we‟ll get into this later

– 1 : 4 means a range from 1 through 4 for a dimension

– : by itself means give me all possible values in a

dimension – Doing 1 : 4 in the 2nd parameter means give me

columns 1 through 4

– Doing : in the 2nd parameter means give me all of thecolumns!




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Vectors and Matrices – (10)• Some more examples:

– sally = a(2,3);

– sally = a(1:3,3:4);

– sally = a(:, 1:3);

– sally = a(2:4,:);

• 1st line: Access 2nd row, 3rd column element, and assign

it to sally • 2nd line: Get a matrix with elements between rows 1 – 3,

and columns 3 – 4 and assign this to sally

• 3rd line: Get a matrix with elements between columns 1 – 3 and give me every possible row, and assign this tosally

• 4th line: Get a matrix with elements between rows 2 – 4and give me every possible column, and assign this tosally




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• Here‟s a curve ball!

– Joe = a(:,:);

– Joe = a;

• What does this mean? Copy the entire matrix, a, and assign it to Joe

• You can also do the 2nd line too. It‟s

exactly the same meaning




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• Example Time!

• 1) How do we define M in MATLAB

syntax?• 2) How do we execute a), b), c) and d)?




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• Example #2!




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• In other words, with matrices A, B and C,

make me a matrix that looks like this!

• What do we need to do? – How do we define matrices A, B and C?

– How do we create M?




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• MATLAB has a really cool way of making

vectors / arrays where consecutive

elements are uniformly spaced

• Example:

– Ray = 0 : 0.1 : 1.0;

• This generates a vector / array with 11

elements, such that

– Ray = [0 0.1 0.2 0.3 … 1.0];




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• General Form:– new_array = first_value : increment :last_value

– Make note of the colons ( : )!

• first_value: The first value in the new vector/ array

• last_value: The last value in the new vector /array

• increment: The step size

– If you don‟t include this value, it is automaticallyassumed to be 1






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• 3rd line: Creates an 10 element vector– ron = [1 2 3 … 9 10];

• 4th line: Creates a 8 element vector

– mauro = [2.0 1.8 … 0.6 0.4];

• Pretty easy don‟t you think!?

• Remember how I told you about that colon

operator?... Well, here you go!• To do this in C and Java, it requires a bit

more work.




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• Some useful matrix and vector / array

commands

– eye(n): Creates an n x n identity matrix




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commands

– ones(n,m): Creates an n x m matrix full of ones

– ones(1,n) or ones(n,1): Creates an array /

vector that has n elements, full of ones




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commands

– zeros(n,m): Creates an n x m matrix full of zeros

– zeros(1,n) or zeros(n,1): Creates an array /

vector that has n elements, full of zeros




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• Last important note: – MATLAB evaluates expressions to the right of the

equals sign first

– After, it assigns this result to the variable to the left of

the equals sign – Here‟s an example:

sum = 2;sum = sum + 3;

– What happens here? sum gets assigned the value of2 first, then it gets added with 3, and stored back intosum

• … and that‟s it for this section… whew!




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• Introduction

• Getting Started

• Variables and Starting Basics

• Vectors and Matrices






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Basic Operations – (1)

• Let‟s assume the following: – A and B: Are matrices or vectors / arrays of

compatible dimensions

• Assume they can be added, subtracted, multipliedand divided properly

– n is a scalar (single value number)

• Here‟s a table that provides a good

summary of all of the basic operations youcan perform on matrices and vectors /arrays





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• Here, the elements in the matrices or vectors /arrays can be real or complex

• Addition and Subtraction will just add and

subtract two matrices normally• For vectors, each corresponding component

gets added or subtracted





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• Multiplication (this kind) only works for matrices

– * is for matrix multiplication

• Division is a little bit more complicated – We have left division and right division• Left Division == A-1B

• Right Division == AB-1





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• Transposition: Transposes a matrix or vector

– „ operator

• Real valued entries: Normal Transpose

• Complex valued entries: Tranposes and performs complexconjugate

– .‟ operator

• Real and Complex valued entries: Normal Transpose





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• Exponentiation multiplies a matrix with itself n

times

• For calculations with *, /, \, and ^, there is

something called element-by-elementoperations for vectors / arrays and matrices

– You put a dot operator ( . ) before the operation

• Example: .* or ./ or .\ or .^

– The 1st element of A is *, /, \ or ^ with the 1st elementof B, and that result gets stored

– … don‟t get it? Here‟s an example





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Basic Operations – (9)• Special Case:

– If you wanted to multiply or divide every number in a matrix orvector / array by a constant, you can just simply do the following:

Example:t = 0 : 2 : 20; t = [0 2 4 … 18 20];

g = 2*t; g = [0 4 8 … 36 40]; or g = 2.*t;

h = t/4; h = [0 0.5 1 … 4.5 5]; or h = t./4;

• All you have to do is multiply or divide by the desired

number – No need to create another matrix or vector / array and do point-by-

point multiplication or division!





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• Special Case #2: – If you wanted to add or subtract every number in a matrix orvector / array by a constant, you can just simply do the following:

Example:t = 0 : 20; t = [0 2 4 … 18 20];

g = t + 2; g = [2 4 6 … 20 22];

h = t - 4; h = [-2 0 2 … 16 18];

• All you have to do is add or subtract by the desired

number – No need to create another matrix or vector / array and add or

subtract that way!





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• Here are some useful commands for matricesand vectors / arrays:

• Assume that V is a vector of arbitrary length andM is a matrix of arbitrary size

• len = length(V); – Gives the number of elements the vector V has, and

stores it into len

• [rows cols] = size(M);

– Gives the number of rows and columns and storesthem into rows and cols respectively

– Don‟t worry about the square braces for now, we‟lldeal with them later.





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• sum(V): Returns the sum of all elements

contained in vector V

• sum(M): Returns a row vector, where

each element is the sum of the columns ofmatrix M

• … confused? Don‟t worry, check out this

example





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• prod(V): Returns the product of allelements contained in vector V

– We multiply every single element in the vector

with each other• prod(M): Returns a row vector, where

each element is the product of thecolumns of matrix M

• … confused? Don‟t worry, check out thisexample





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• Quick quiz:

– Suppose I perform this operation:

•V = n : -1 : 1;

– n can be any number > 0•sum = prod(V);

– What is the above operation equivalently

called in mathematics?

– …you‟ve seen this before. Think MTH 314





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• It’s a factorial!

• Anyway, let‟s keep going

• max(V) / min(V): Returns the maximum /

minimum of all elements contained in vector V• max(M) / min(M): Returns a row vector,

where each element is the maximum / minimumof the columns of matrix M

• … confused again? No worries, here‟s another

example





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• Introduction

• Getting Started









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Script Files – (1)

• So far, you‟ve seen that MATLAB can accept

and execute commands interactively through the

command prompt

– … what happens if you‟ve got A LOT of commands toexecute?

• Think C or Java: You put all commands or

syntax into a file and execute that file.

• You can do this with MATLAB, and you don‟thave to input all of the commands individually.





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• This kind of file is called a script file or M-file (Mfor MATLAB!) – You place all commands you want to execute in a file

with extension .m at the end, and you run the script

file – MATLAB will run all of these commands in sequence

for you

• To execute a script file, make sure you set the

working directory to be where the script file islocated (remember I said we‟d get back to thisearlier?)





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• MATLAB has a M-file editor that you can

use where you can create your scripts

– You can also use any other word processing

editor. Just make sure the extension of thefile is .m

– It‟s got:

• Some nice colour coding features

• Debugging Tools

• Interoperability with the MATLAB command prompt





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• Once a script file has been created, type in thename of the file (without the .m) in the command

prompt to execute the script

– Make sure you set the proper working directory!

• When you execute a script file, all of the

variables created in the script file get stored in

the workspace for future use

• Let‟s do an example: – Let‟s make the factorial example into a script file





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• The great thing about script files is thatcommands can be re-executed without

having to enter them all again!

– All you have to do is modify parts of the scriptfile to give you the result you want

• The script file is now set to compute 4!

What if I wanted to do 9!, or 12!, or 5! ? – Just change the n parameter accordingly





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• Introduction

• Getting Started





S ( )





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Function Script Files – (1)

• So, you‟ve seen how script files work – So what are function script files?

• Think Java: These are methods – You send input variables into a function

• Difference: You don’t have to define what the variable types are.

Remember: Dynamically Typed! – The function performs MATLAB commands with these input

variables

– The function returns output variables• Difference: You can return more than one variable!

• You don‟t have to define the variable type either!

• Unlike C or Java, you do not require return statementsto return variables – All you have to do is assign something to the variable, and that‟s

it.

F i S i Fil (2)





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Function Script Files – (2)• Why would you want function script files?

– Instead of changing some parts of a script file, youcan do these changes by providing different variablesto the input of the function

– There may be a case where when you run a script,

you don‟t want variables created in the script to besaved to the workspace

• Function scripts only communicate with theMATLAB workspace with:

– The variables that you pass to it – The variables that get sent to the output after it‟s

finished

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• What does this mean? – Any variables you create within the function

will be discarded after the function hasfinished executing

– This is what we call local scope

• How do we create a function script file?

– Pretty much the same as a normal script file

• .m as the extension to the file

– Remember, with a script file, all you had to dowas enter in the commands in sequence

F ti S i t Fil (4)





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• However, there are two differencesbetween a script file, and a function script

file

– The file name of the function has to be thesame as the function itself

– The first line of a function script file must be

the following:function [output1, output2,…] =

function_name(input1, input2, …)

F ti S i t Fil (5)





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Function Script Files – (5)• The function keyword means that this script

file is a function script file• input1, input2, … represents the input

variables going into the function

• output1, output2, … represents the output

variables going into the function• You may have noticed that there are square

braces ( [ ] ) surrounding the output variables inthe function header

– In order to return more than one variable, MATLABputs all of the variables into one vector and returnsthis vector, hence the [ ] … smart eh?

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• Use the % operator to put in comments – If you want to perform the modulus, use the mod function

– mod(x,y) == x % y in C or Java

• If you want to comment out a block of code, do thefollowing:

%{… commands that are commented out…

%}

• When you‟re coding a function script file, it‟s a good ideato put an author’s block at the beginning of the file, thattells someone how the function works, what inputs youneed, what outputs come out, and how to use it

F ti S i t Fil (7)





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Function Script Files – (7)• Some examples of function script files that you have

seen already:– eye(n)

• Input: number n, n > 0

• Output: n x n identity matrix

– prod(V), prod(M)• Input: Vector V or Matrix M

• Output: A number or a vector – sum(V), sum(M)

• Input: Vector V or Matrix M

• Output: A number or a vector

– max(V), max(M)• Input: Vector V or Matrix M


– min(V), min(M)• Input: Vector V or Matrix M


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• Here‟s another one that you saw earlier: – [rows cols] = size(M)

• Input: Matrix M

• Output: 2 numbers, the rows and columns of the matrix

– When you call this function script file in MATLAB,

make sure the square braces are there

– This is required if the function script file returns more

than 1 variable

– Failing to do this will result in the very last output

variable to be saved instead

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• So now with this, let‟s go back to ourfactorial example and make this a function

script file

• What do we need to do in order to makethis a function script file?

– Think back to the two differences that I said

earlier about script files and function scriptfiles

F ti S i t Fil (10)





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F ti S i t Fil (11)





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F ti S i t Fil (12)





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• Some important things to be reminded of:– n in the function script file is not saved to the

workspace•n has a local scope!

– Instead of changing the parameter n, as wedid in a script file, we simply changed theinput parameter of the function

– If your function returns more than onevariable, make sure you save them to avector!

O tli f T t i l (1)





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• Introduction

• Getting Started





O tline of T torial (2)





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• Flow Control


• Other Useful Commands

• Final Words

Flow Control (1)





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Flow Control – (1)

• You‟ve seen this in C or Java many times • Flow control allows your script or function script

file to have decision making abilities

• …understand what I mean? If you don‟t,

MATLAB supports the following common flowcontrol methods– for loop

– while loop

– if-else & else-if statements

– switch-case-otherwise statements

• … now you see what I mean right?

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• for loops allow a group of commands to beexecuted a predetermined amount of times

• This loop has the following structure:

for i = any_array…

commands to be executed

…

end

• any_array is any valid array

• Can be any row or column vector

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• How this for loop works is as follows: – 1st iteration, i = any_array(1), then execute

commands

– 2nd iteration, i = any_array(2), then executecommands

– … – nth iteration, i = any_array(n), then execute

commands

• This can prove to be a very powerful mechanism

– Your for loop indices never have to be in uniformsteps!

• Don‟t know what I mean?... Let‟s do an example

Flow Control (4)





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• First Example: for loop in uniform steps– f = 1;for i = 1:n

f = f*i;

end – Here, we‟re computing our factorial function, but with

the use of a for loop

• i is assigned 1 for the 1st iteration, 2 for the 2nd iteration, and

n for the nth iteration

• For each iteration, we take the previous value off and multiply by the current value of i

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• Second Example: for loop in non-uniform steps– val = 0;array = 1 : 20;for i = [1 4 8 9 10 2 5]

val = val + array(i);

end – Here, we‟re computing the sum of random elements in an arrayand storing them into val

• Take a close look at what I did in the for loop

• The 1st iteration, i = 1, the 2nd iteration, i = 4, the 3rd

iteration, i = 8, and so on• Pretty cool eh!? You don‟t have to have uniform steps in

your for loops!

Flow Control (6)





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• while loops let you execute a group ofcommands indefinitely until a condition is

met

• The structure for this loop is as follows:while expression

…

commands to be executed…

end

Flow Control (7)





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Flow Control – (7)• The commands between the while and

the end statements are executed untilexpression is evaluated as false, or azero (0) value

• You usually use relational or equalityoperators in the expression statementof the while loop

• A relational or equality expression isassigned a value of 1 if it‟s true, and 0 ifit‟s false

Flow Control (8)





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• Everything here is the same as C and Java,

except for the not equals to operator. MATLABhas it as ~=, and C or Java has it as !=… becareful not to mix these up!

Flow Control (9)





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Flow Control – (9)• if-else & else-if statements help you execute

blocks of commands when some condition is true• Here‟s the syntax for it… but I‟m sure you already know

thisif exp_1

… commands to be executed if exp_1 is true

… elseif exp_2…

commands to be executed if exp_2 is true…

elseif exp_3…

commands to be executed if exp_3 is true

… else…

commands to be executed if none of the above is true…

end

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• Note the following:– elseif and else operators are optional

– You can have if statements by themselves as wellwithout the above operators

• The break command: – Used often in for and while loops

– When this command is encountered, the loop stopsexecuting immediately and carries onto the next block

of code – If you‟re using this within nested loops, the inner most

loop stops executing only

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• switch-case-otherwise statements are aspecial case (no pun intended) of the if-else & else-if statements

• You choose between a finite number of choices;

each choice consists of a block of commands tobe executed

• If the choice you make is none of the choicesprovided in this statement, we execute a default(otherwise) code block

• … so this is what this kind of statement lookslike:

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switch exprcase value1,… commands to be executed if expr equals value1…

case value2,… commands to be executed if expr equals value2…

… otherwise,

… commands to be executed if the value of expr isnot equal to any of the above values…

end• You usually use switch statements when you want your program to run

differently, based on the input parameters that are given to your functionscript file

Flow Control (13)





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Flow Control – (13)• Let‟s do an example!

– Let‟s use the while and if-else statements tomake a simple program

– You all have studied logic gates in COE 328, so let‟suse some simple facts from this

– Let‟s make a program that will classify a set of input

voltages according to the following specs:• If Vout is between 0V and 0.5V, this is a logic 0 (0)

• If Vout is between 2.7V and 5V, this is a logic 1 (1)

• All other voltages are classified as invalid (-1)

– The program will read in an array of continuous input

voltages, and output an array of the same size – Each element will take 1 of 3 possible values: 0, 1

and -1

Flow Control (14)





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Flow Control – (14)• What do I need to do?

– Set up a function script file with the function

keyword, and the appropriate inputs and outputs• Let‟s call this function: classify_TTL

• Inputs: V, an array of continuous input voltages

• Outputs: logic_levels, an classification array telling youwhether you have logic 0, logic 1, or invalid voltages

– Naturally, you want to use a for or while loop for

this program because you want to check through

every element in this input array – You use an if-else statement to check to see what

the voltage inputs are, then you classify accordingly






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• Above, I declared an array of 7 input voltages

and ran the function• The 2nd element is valid as logic 0 because it‟s

between 0V and 0.5V

• The 5th and 6th element is valid as logic 1because they‟re between 2.7V and 5V

• The rest are invalid






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• Flow Control



• Final Words

Basic Graphics Commands – (1)





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Basic Graphics Commands (1)

• MATLAB provides a variety of sophisticatedtechniques for presenting and visualizing data

• Also, MATLAB makes it very easy to plot data!

– I have never used MS Excel ever again becauseMATLAB makes it easy!

• The watered down version:

– Provide an array of values for each set of axes

– Run a function that plots things for you – Run a few more commands that will make a grid, set

the title of the graph, the title of the axes and so on






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• 2D plotting: MATLAB makes this veryeasy!

– If x and y are arrays of elements that are the

same size, you can plot them using this datawith the following command:plot(x, y);

– This will bring up a window plotting a graph of

y vs. x

– To plot something simple, that‟s just about it!






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• Here‟s a basic example if you don‟t believe me • Let‟s say I wanted to plot the line y = x

• Let‟s choose 101 points between 0 to 10 in stepsof 0.1

• Here‟s the syntax I‟d use:

… and that‟s it! • This is what the graph looks like…






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• If you want to plot multiple plots on a singlegraph, you do the following:plot(x1,y1,x2,y2,…,xN,yN);

• N is the number of plots you want to appear on

the single graph

• xi and yi are the points to the ith graph you

want plotted on the single graph

• The number of elements between (x1,y1),(x2,y2), … (xN,yN) must all be the same!






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• Let‟s do another example: – Let‟s plot the following 5 lines:

y1 = 0.1x

y2 = 0.5x

y3 = 2xy4 = 5x

y5 = 10x

– For now, let‟s make them all go from 0 to 10 in step

sizes of 0.1 – These plots don‟t all have to have the same step size!






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• This is what I‟d put into the commandprompt in MATLAB

– You can also make a script file too if you

want!

• … and this is what the graph looks like!






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• MATLAB automatically colour codes thedifferent plots that are on the graph

• This graph looks pretty plain… there‟sgotta be more that you can add, and yes

you can• You can add a title, label the axes, put a

grid on and even a legend!

– You can add these in the graph GUI thatyou‟ve just seen, or do it through thecommand prompt





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• So let‟s say I wanted to add a title, add agrid, label the axes and put up a legend,

how would I do that?





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• grid puts a grid on the graph – The spacing for the grid is automatically figured out

by MATLAB

• title(‘…’) lets your graph have a title

• xlabel(‘…’), ylabel(‘…’) labels the x andy axes accordingly – Put the labels inside the quotations

– Don‟t forget the quotations „ „!

• legend(‘…’, ‘…’, …, ‘…’) produces alegend, labeling what each plot is on the graph





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• Remember, for the legend command,you label the plots the same order as howyou plotted them!

• By default, MATLAB takes all points andconnects them with a solid line, and it‟s gotits own way of determining which colourbelongs to what plot

• Is there a way to control this?... Yes thereis!





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p ( )

• In addition to the x and y points, youspecify an additional parameter:plot(x, y, ‘line_style’);

• line_style is a character string of 2characters

– The 1st character specifies the colour of your

plot – The 2nd character specifies how your plot will

be plotted on the graph, or the plot style





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p ( )

• Supported colours: – blue, green, r ed, cyan, magenta, yellow,

black

• Supported plot styles:





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p ( )

• Examples: x = 0:0.1:10;

y = x;

– plot(x,y,’g.’); • This will plot a green line with dots at each point

– plot(x,y,’bo’);

• This will plot a blue line with circles at each point

– plot(x,y,'rx’);

• This will plot a red line with crosses at each point





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p ( )

• Like how we saw before, you can put multiple plots on asingle graph, each with their own colour and plot styleswith the following:plot(x1, y1, ’line_style1’, x2, y2,’line_style2’,..., xN, yN, ’line_styleN’);

• N is the number of plots you want to appear on the singlegraph

• xi and yi are the points to the ith graph you want plottedon the single graph

• line_stylei is the plot style and colour of that ith

graph • The number of elements between (x1,y1), (x2,y2),… (xN,yN) must all be the same!





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p ( )

• There is also a way to produce multiplegraphs in one window

– You can have more than 1 graph in onewindow at a time!

• You do this by using the subplot command

• The subplot command treats the window

as if it had multiple slots – Each slot takes in a graph





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p ( )

• How do we use the subplot command?– subplot(m,n,p) or subplot(mnp)

– m and n you need to know before hand

• These determine the number of rows (m) and columns (n)

for the amount of graphs you want• p determines which location in the window you want the plot

to go to

• The order is from left to right, top to bottom

– In order to properly use subplot, you must call thisfunction first

– After, you code the syntax to plot something normally





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p ( )• Here‟s a small example:

– If I wanted to make a window that has 4 plots, 2 plots in eachrow 2 rows, here‟s what I‟d do

• Do subplot(221) Specify that we want to work on the top leftcorner

• Next, code the syntax to plot normally. The plot will appear on thetop left corner

• Do subplot(222) Specify that we want to work on the top right

corner• Next, code the syntax to plot normally. The plot will appear on the

top right corner

• Do subplot(223) Specify that we want to work on the bottomleft corner

• Next, code the syntax to plot normally. The plot will appear on thebottom left corner

• Do subplot(224) Specify that we want to work on the bottomright corner

• Next, code the syntax to plot normally. The plot will appear on thebottom right corner





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p ( )

• Let‟s do another example… in case you didn‟tget what I meant earlier

• Let‟s make 4 graphs, have 2 rows and 2columns for the window.

• Each graph will have one plot. – Let‟s make each plot the following: 1. y1 = sin(x);2. y2 = cos(x);3. y3 = 3x;4. y4 = 6x;

– Let‟s make the range of the plot go from:x = -10 : 0.1 : 10;… now what?





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p ( )







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p ( )





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( )

• Some functions, like cos and sin take in, notonly single values, but vectors / arrays and

matrices

• cos and sin apply their respective

mathematical operations to every element if the

input is a vector / array, or matrix

• The output will be a vector / array, or matrix, of

the same size, with the function applied to eachelement in that memory chunk





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( )

• Flow Control• Basic Graphics Commands


• Final Words

Other Useful Commands – (1)




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( )

• MATLAB has a great help facility, boththrough its interface and online

• If you need help regarding how a certain

command works, type in the following inthe command prompt:

– help command

• command is the command you want tolook up and to see how it works





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( )

• If you don‟t know what a particular functionis called, you can use the lookfor command

• It‟s called the following way: – lookfor command

• Where command is the function you‟relooking for

• MATLAB searches all of its libraries thatare related to command





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( )

• A list of all of the MATLAB commands you have invokedin a session in the command prompt can be written intoa file with the diary command

• You call this command this way in the command promptdiary diary_file

• diary_file is the name of the file where yourcommands you invoked in that session will be stored

• If the file already exists, your commands in the currentsession will be appended to the file

• Use diary off to turn off the diary command, anddiary on to reactivate it





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• Flow Control• Basic Graphics Commands


• Final Words

Final Words – (1)




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• This tutorial provided you the basics of how touse MATLAB and enough to get you started withthese labs

• This tutorial, however, is not exhaustive

– There are still a lot of commands out there thatperform really cool stuff for you

– Consider taking some time to look at them and seehow cool MATLAB is

• Always use the help and lookfor commandswhen you‟re learning a new function

• If all else fails, ask me!

Final Words – (2)




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• I adapted this tutorial from Dr. Y. C. Chen‟s – “Introduction to MATLAB” tutorial and can

be found here:

– http://www.ee.ryerson.ca/~rphan/matlabtutorial.pdf • I also wrote a tutorial for the Ryerson IEEE

Student Branch website 3 years ago, and

can be found here: – http://www.ee.ryerson.ca/~ieee/articles/MATLAB.html

Thanks

http://www.ee.ryerson.ca/~rphan/matlabtutorial.pdf

http://www.ee.ryerson.ca/~ieee/articles/MATLAB.html

http://www.ee.ryerson.ca/~ieee/articles/MATLAB.html

http://www.ee.ryerson.ca/~rphan/matlabtutorial.pdf



Thanks

ForListening!

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Questions?

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