Lecture 2 - Matlab Introduction

CVEN 302

August 29, 2001

Lecture Goals

• Scalar Operations

• Vectors Operations

• Matrix Operations

• Plot & Graphics

• Matlab files

• Matlab controls

Scalar OperationsScalar Operations

• Addition - a + b

• Subtraction - a - b

• Multiplication - a * b

• Right Division - a / b

• Left Division - b \ a

• Exponential - a^b

Order of Precedence of Order of Precedence of Arithmetic OperationsArithmetic Operations

Precedence( 1 ) - Parenthesis

( 2 ) - Exponential from left to right

( 3 ) - Multiplication and division from left to right.

( 4 ) - Addition and subtraction from left to right.

Vector

A vector is defined as a combination of variables values to with components of xj , where j = 1,…n values.

3

2

1

T

321 ,...,,

x

x

x

x

xxxx

Vectors

• Matlab is designed for vector and matrix manipulation some of the basic commands are given as

]6

6

4

1

t [1;4;6] or t 4

1 [

6

4

3

1

t 6,4,3,1

t

t

Vectors

• t’ represents the transpose of the vector “t”.• Individual components can be represented by

t = [ 4,5,6,9], where t(3) = 6.• [ ] represent the start and finish of the vector

and/or matrix. ( ) represent components of the vector.

• A period “.” represent an elemental set of functions, such as multiplication, division,etc.

Vector element Operations

• Individual addition A + B A + B• Individual subtraction A – B A - B• Individual multiplication A*B A.*B• Individual division (left) A/B A./B• Individual division (right) A\B A.\B

• Individual power AB A.^B

Hierarchy of the vector operations

Precedence( 1 ) - Parenthesis

( 2 ) - Exponential from left to right

( 3 ) - Multiplication and division from left to right.

( 4 ) - Addition and subtraction from left to right.

Vector Operations

• Vector product - A is 1 x n vector

• The magnitude of the vector is a dot product of the vector.

nn x n x 1*1n x A'*A

1 x 11n x *n x 1A'*A

'A*AA

1 x 11n x *n x 1A'*A

Vector Examples

Matrix

• A matrix is a two dimensional arrays, where the matrix B is represented by a [ m x n ]

nm,m,1

n1,1,1

bb

bb

B

Matrix Operations

• For addition and subtraction, the matrix sizes must match up. If you are adding to each component of the matrix you can do a simple scalar addition.

• Examples: [A] + [B] = [C] [A] + 3 = [D]

Matrix Operation

• Multiplication of matrices will need to match up the columns to the row values of the following matrix. Scalar multiplication will work.

• Division is different. You will either divide member by member, where the matrices are the same size or you will need to find the inverse of the matrix.

Matrix Multiplication Examples

Graphical Representation

• Matlab has a function known as “plot( ), where the values are plotted on an x-y plane.

• General format of the graph is given as,plot(x,y,’symbols’)

• The symbols represent the color, point shape, and the line type.

Plot symbols commandsColors Symbols Lines

y – yellow . – point - – solid line

m – mag o – circle : – dots

c – cyan x – xmark -. – line dot

r – red + – plus - - – dashes

g – green * – star

b – blue s – square

w – white d – diamond

k – black v – triangle down^ – triangle up< – left

< – right

p – pentagram

h – hexagram

Plot Commands

t = linspace(0, 2*pi); - results in 100 data points

y1 = cos(t); - cosine of the points

y2 = sin(t); - sine of the points

y3 = y1.*y2; - cos(t)*sin(t)

plot(t,y1,’-’) ; - plots cosine verse t with a straight line.

plot(t,y3,’r:’) - plots cosine*sine verse t with red dots.

Plot Commands

Example:

plot(t,y1,’-’,t,y2,’g*’,t,y3,’r-.’) - plots all 3

axis( [0 2*pi -1.5 1.5]) - adds axes

legend(‘cos(t)’,’sin(t)’,’cos(t)*sin(t)’) - legend

Note that the [ ] represent an array and ( ) represent a function, and ‘ ‘ represent the symbols.

Matlab commands for file management

The files can be written as a script, which can be loaded into the memory. From the command line:

• “echo” - causes the file to be echoed to the screen.• “what” - shows the type of file in the current

directory.

• “type” - will present show the file contents

Matlab Files

There are three types of files:• Data files

– Matlab files have their own format for saving data

– ascii files are standard text files, which can be printed out or used in excel files.

• m-files represent the program files.

• function files are functions similar to ‘sin(x)’, cos(x), etc.

Data Files

Data files can be written in two forms:

• Matlab format

• ascii format

Matlab data format

MatLab generates a data

file, which will have

look like:

“filename”.mat

File can be loaded into

the memory with:

load “filename”

t = linspace(0, 2*pi)

x = cos(t)

save data1 t x

clear

what

data1.mat

load data1

ACSII format

An ascii file type can be

created by adding a flag

on the end of the save

command

save “filename”.dat -ascii

t = linspace(0 2*pi)

x = sin(t)

save data2.dat t x -ascii

dir

data2.dat

clear

load data2.dat -ascii

Loading Data Files

Matlab Files

load “filename”

The file will load the file into

the same format as it was

saved.

ASCII Files

load “filename.dat” -ascii

The file will be loaded as an

data array and will require

you to modify to obtained the

data vectors.

Data file example

t=linspace(0,2*pi);

y1 = sin(x);

save data1 t y1;

clear

(created data1.mat and

will show up in home

directory.)

load data1;

(data1 will have created

t and y1 vectors.)

save data2.dat t y1 -ascii

clear

(created a ascii file with

the data)

load data2 -ascii

Data file example continued

(loaded an ascii file into

memory as data2 array)

whos

data2 2X100 double array

t= data2(1,:);

y1= data2(2,:);

: assigns the row to the

vector

Homework

• Check the Homework files– create a data file– input a simple program– run the program– plot the results