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UNITED INTERNATIONALUNIVERSITY (UIU)

Dept. Of Electrical & Electronic Engineering (EEE)

Course: EEE 110, Title: Simulation Laboratory

L a b Sh eet 1

Introduction to MATLABWhat is MATLAB:

MATLAB stands for MATrix LABoratory .MATLAB is a software package for computation in

engineering, science, and applied mathematics. It offers a powerful programming language, excellent

graphics, and a wide range of expert knowledge. MATLAB is published by and a trademark of The

MathWorks, Inc.

Standard Windows :When the MATLAB program starts, the following window opens which contains four smaller

windows .These windows are default and can be switched on or off if necessary.

Command

window

Command

History windowCurrent Directory &

Workspace window

Figure 1.1 : The default view of MATLAB desktop

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Four most used MATLAB Windows

Command

Window

This is where you type and execute commands

Workspace

Window

This shows current variables and allows to edit variables by opening array editor (double

click), to load variables from files and to clear variables.

Current

Directory

window

This shows current directory and MATLAB files in current folder, provides with a handy

way to change folders and to load files.

History window This shows previously executed commands. Commands can be re-executed by double-

clicking.

Working on the command window :(A)Using MATLAB as a calculatorYou can use command window part for various calculations as if you would use a calculator: Typeexpressions containing numbers, parenthesis and mathematical operations and press Enter to get the result.

Example :

>> 2^sqrt(9)

ans =

8

>> a = 1. 2;>> b=2. 3;>> c=4. 5;>> d=4;>> a 3+sqr t ( b*d) - 4*cans =- 13. 2388

Note the semicolon after each variable assignment. If you omit the semicolon, then MATLAB echoes back on

the screen the variable value.

(B)Assigning Values to VariablesTo create a variable just use it on the left hand side of an equal sign. The following examples show how to

assign values to variables, x and y.

>> x= 5x =

5>> y =log(2)

y =

0.6931

>> z = 10;

Note that :

(1) You can use who command to list the currently active variables. For the preceding session this results in

>> who

Your variables are:

ans x y z

(2) Use clear command to delete variables from computer memory

>> clear x

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>> x

??? Undefined function or variable 'x'.

(3) Suppress intermediate output with Semicolon.

MATLAB will print the result of every assignment operation unless the expression on the right hand side is

terminated with a semicolon.

(C)List of useful commands for managing variables :

Command Outcome

clear Removes all variables from memory.

clear x y z Removes only variables x,y,z from the memory .

who Displays a list the variables currently in the memory.

whos Displays a list the variables currently in the memory and their size together with

information about their bytes and class.

(D)Two important command to ensure fairness and readability

Command Outcome

clc Clears contents on the command window ensuring blank working environment

% If used before any line or statement, program ignores the line or statement.

So used to insert any comment in the program.

(E)Predefined variables :

A number of frequently used variables are already defined when MATLAB is started. Some

of the predefined variables are :

Predefined

Variables

Meaning

ans A variable that has the value of the last expression that has not assigned to a specific

variable. If the user does not assign the value of an expression to a variable, MATLAB

automatically stores the result in ans .

pi Value of the number .

eps The smallest difference between two numbers. Its value is 2.2204e-016 .

inf Used for infinity.

i or j Defined as 1

NaN Stands for Not-a-Number.Used when MATLAB cannot determine a valid numeric

value.For example 0/0.

(F)Complex numbers :MATLAB also supports complex numbers. The imaginary number is denoted with the symbol i or j, assuming

that you did not use these symbols anywhere in your program (that is very important!). Try the following:>> z =3 + 4i % note that you do not need the * after 4

>> conj(z) % computes the conjugate of z

>> angle(z) % computes the phase of z>> real(z) % computes the real part of z

>> imag(z) % computes the imaginary part of z

>> abs(z) % computes the magnitude of z

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(G)Elementary Math functions used in MATLAB:

Function Description Example

sqrt(x) Square root >> sqrt(16)

ans =

4

exp(x) Exponential (ex) >> exp(3)

ans =

20.0855

abs(x) Absolute value >> abs(-4)

ans =

4

>> abs(3+4j)

ans =

5

log(x) Natural logarithm (Base e ) >> log(1000)

ans =

6.9078

log10(x) Base 10 logarithm . >> log10(1000)

ans =

3

factorial(x) The factorial function x!

(x must be a positive integer.)

>> factorial(5)

ans =

120

sin(x) Sine of angle x (x in radians) >> sin(pi/6)ans =

0.5000

cos(x) cosine of angle x (x in radians) >> cos(pi/4)

ans =

0.7071

tan(x) Tangent of angle x (x in radians) >> tan(pi/3)

ans =

1.7321

tand(x) Cotangent of angle x (x in degree) >> tand(60)

ans =

1.7321

asin(x) Inverse sine of x >> asin(sqrt(3)/2)

ans =

1.0472

(Note that result is in radians)

round(x) Round to the nearest integer >> round(17/5)

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ans =

3

ceil(x) Round towards infinity. >> ceil(11/5)

ans =

3

floor(x) Round towards minus infinity. >> floor(9/4)

ans =

2

rem(x,y) Returns the remainder after x is divided

by y.

>> rem(13,5)

ans =

3

sign(x) Signum function.

Returns 1 if x>0

Returns -1 if x> sign(-5)

ans =

-1

(H)Creating Vectors and MatricesThe array or matrix is a fundamental form that uses to store and manipulate data.

Unlike C programming language , array index starts from 1 in MATLAB instead of 0 in C programming.

To create a matrix In MATLAB, use the brackets. Numbers (or variables) inside the brackets can be separatedby commas, spaces, or semicolons, where commas and spaces are row separators; semicolons are column

separators. For example,

>> a=[2,5,7]a =

2 5 7

>> b=[3,4,a]

b =3 4 2 5 7

>> c=[2 3;4 5]

c =2 34 5

(I)Colon OperatorMATLAB colon operator is a compact way to create vectors. For example,

>> A=1:0.1:1.5

A =

1.0000 1.1000 1.2000 1.3000 1.4000 1.5000

Where 0.1 is the increment, if omitted, it is assumed to be one.

>> B = 1:5

B =

1 2 3 4 5

(J)Create some basic matrices using MATLAB built-in functions: ones, zeros, eye

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Commands Description Example

zeros(m,n) A matrix of dimension mn having all elements 0 >> zeros(3,4)

ans =0 0 0 0

0 0 0 0

0 0 0 0

ones(m,n) A matrix of dimension mn having all elements 1 >> ones(3,4)ans =

1 1 1 11 1 1 1

1 1 1 1

eye(n) An identity matrix of dimension nn >> eye(4)ans =

1 0 0 0

0 1 0 00 0 1 0

0 0 0 1

(K)Determine size of a matrix

Command Description Example

size(x) Determines size of the matrix >> x=[1 2 3;4 5 6;7 8 9]x =

1 2 3

4 5 6

7 8 9>> size(x)

ans =

3 3

(L)Addressing Vectors or Matrices:

Command Meaning Example when

A =1 3 5 7 9 112 4 6 8 10 12

3 6 9 12 15 184 8 12 16 20 24

5 10 15 20 25 30

A(:,n) Refers to the elements in the rows of column n of the matrix

A

>> B=A(:,3)

B =569

1215

A(n,:) Refers to the elements in all the columns of row n of

the matrix A.

>> C=A(2,:)C =

2 4 6 8 10 12

A(:,m:n) Refers to the elements in all the rows between columns m

and n of the matrix A

>> E=A(:,2:4)E =

3 5 7

4 6 86 9 128 12 16

10 15 20

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A(m:n,:) Refers to the elements in all the columns between rows

m and n of the matrix A.

>> D=A(2:4,:)

D =

2 4 6 8 10 123 6 9 12 15 18

4 8 12 16 20 24

A(m:n,p:q) Refers to the elements in rows m trough n and columns

p through q of the matrix A.

>> F=A(1:3,2:4)

F =3 5 7

4 6 8

6 9 12

(M) Generation of random numbers :Command Description Example

rand Generates a single random number between 0 and 1 >> rand

ans =

0.2311

rand(1,n) Generates an n elements row vector of random

numbers between 0 and 1

>> a=rand (1,4)

a =0.6068 0.4860 0.8913 0.7621

rand(n) Generates an nn matrix of random numbersbetween 0 and 1

>> b= rand(3)

b =

0.4568 0.4447 0.92180.0158 0.6154 0.7382

0.8214 0.7919 0.1763

rand(m,n) Generates an mn matrix of random numbersbetween 0 and 1

>> c= rand(2,4)

c =

0.4568 0.4447 0.9218 0.3529

0.0158 0.6154 0.7382 0.9533

randperm(n) Generates a row vector with n elements that are

random permutation of integers 1 through n .

randperm(8)

ans =

8 2 7 4 3 6 5 1

Mathematical operations on Arrays(A)Addition and Subtraction of Arrays :

Mathematical Review:

If

232221

131211

AAA

AAAA and

232221

131211

BBB

BBBB

Then ,

BABABA

BABABABA

232322222121

131312121111

And,

BABABA

BABABABA

232322222121

131312121111

MATLAB Example :

>> A=[1 2 3;4 5 6];>> B=[8 9 10;11 12 13];

>> A+B

ans =9 11 13

15 17 19

>> A-B

ans =

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-7 -7 -7

-7 -7 -7

(B) Array Multiplications :

Mathematical Review :

If

434241

333231

232221

131211

AAA

AAA

AAA

AAA

A

and

3231

2221

1211

BB

BB

BB

B

Be sure that, number of columns of Matrix A is equal to number of rows of Matrix B .Otherwise multiplication

is not defined.

Then,

434241

333231

232221

131211

AAA

AAA

AAA

AAA

AB

3231

2221

1211

BB

BB

BB

=

324322421241314321421141

323322321231313321321131

322322221221312321221121

321322121211311321121111

BABABABABABA

BABABABABABA

BABABABABABA

BABABABABABA

A numerical example :

A=

825

162

341

and B=

62

31

45

Then,

AB

825

162

341

62

31

45

=

8.62.35.48.22.15.5

1.66.32.41.26.12.5

3.64.31.42.31.45.1

=

7443

3218

3415

MATLAB Example :

>> A=[1 4 3;2 6 1;5 2 8];>> B=[5 4;1 3;2 6];

>> A*B

ans =

15 3418 3243 74

(C) Inverse of a MatrixMATLAB Example :>> A=[2 1 4;4 1 8;2 -1 3];

>> inv(A)

ans =

5.5000 -3.5000 2.0000

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2.0000 -1.0000 0

-3.0000 2.0000 -1.0000

Note: The Command >>A^-1 will have the same effect.

(D)Left Division and right Division

Command Name Meaning Example

A\B Left Division A-1B >> A=[1 2 3;4 5 6;7 8 9];>> B=[10 11 12;13 14 15;16 17 18];

>> A\B % Left division

ans =

-20.0000 -17.0000 -18.000033.0000 26.0000 27.0000

-12.0000 -8.0000 -8.0000

A/B Right Division AB-1

>> A/B % right division

ans =

1.0000 3.0000 -3.00001.0000 2.0000 -2.0000

0.5000 2.0000 -1.5000

(E)Element-By-Element Operations (Very Very Important)

If two matrices are

333231

232221

131211

AAA

AAA

AAA

A and

333231

232221

131211

BBB

BBB

BBB

B

Then, observe the following operation :

Command Meaning OutcomeA.*B Multiplies

every element

of A with

correspondingelement of B

333332323131

232322222121

131312121111

BABABA

BABABA

BABABA

B*.A

A./B Divides every

element of A

bycorresponding

element of B

333332323131

232322222121

131312121111

B/A/BA/BA

B/A/BA/BA

B/A/BA/BA

B/.A

A.^n Every

element of A

is raised by apower n.

n

33

n

32

n

31

n23

n22

n21

n

13

n

12

n

11

AAA

AAA

AAA

n.^A

Note: Observe carefully difference between using dot and not using dot.

(F)Built in functions for analyzing arrays :

Function Description Examplemean(A) Returns mean value of the elements of vector A. >> A=[5 9 2 4];

>> mean(A)

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ans =

5

c = max(A) Returns maximum value of the elements of vector A >> c=max(A)

c =

9

[d n] =max(A) Returns maximum value of the elements of vector A and

also return its position.

>> A=[5 9 2 4];

>> [d n] =max(A)d =9

n =

2

c=min(A) Returns minimum value of the elements of vector A >> A=[3 4 5 7 -5 10];

>> c=min(A)

c =-5

[d n]=min(A) Returns maximum value of the elements of vector A and

also return its position.

>> A=[3 4 5 7 -5 10];

>> [d n]=min(A)

d =-5

n =

5

sum(A) Returns the sum of the vector A. >> A=[5 9 2 4];

>> sum(A)

ans =

20

sort(A) Arranges the elements of vector A in ascending order. >> A=[5 9 2 4];>> sort(A)

ans =

2 4 5 9

median(A) Returns the median value of the elements of vector A. >> A=[5 9 2 4];>> median(A)

ans =4.5000

std(A) Returns the standard deviation of the elements of vector A. >> A=[5 9 2 4];>> std(A)

ans =2.9439

det(A) Returns the determinant of matrix A.A must be square matrix.

>> A=[2 4 6;6 9 1;0 2 7];>> det(A)

ans =

26

dot(a,b) Returns the scalar or dot product of two vectors a and b. >> a=[1 2 3];

>> b=[3 4 5];

>> dot(a,b)ans =

26

cross(a,b) Returns the scalar or dot product of two vectors a and b. >> a=[1 2 3];>> b=[3 4 5];>> cross(a,b)

ans =

-2 4 -2

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Report : [Submit as lab report in the next session.]

Q1. Use MATLAB to determine how many elements are in the arraycos(0.1):0.02:log10(105) .

Use MATLAB to find the 25th

element.

Q2. The table 1.1 gives the speed of an aircraft on each leg of a certain trip and the time

spent on each leg . Compute the km traveled on each leg and the sum of km traveledby all four legs.

Legs

1 2 3 4

Speed (Km/hr) 200 250 400 300

Time(Hr) 2 5 3 4

Table 1.1

Q3. Write MATLAB Command to evaluate the following :

W10W,87.60,10R,5I,255Vfor,WRIcosVI

cosVIEfficiency c

0

c

2

Q4. Use matrix operations to solve the following system of linear equations :

0z3y10x6

4z2y8x2

8z6y2x4

[Hints : AX=B

Where, A=

3106

282

62-4

and, B=

0

4

8

Q5. Create the following matrix C :

352821147

1512963

108642

C

Use the matrix C to:

Create a six element column vector named Athat contains the elements of the 2nd

and 3rd column of C.

Lab Sheet prepared by:

B.K.M. Mizanur Rahman

Assistant Professor , Department of EEE,United International University.

Last update : Spring 2013

The easiest and best way to learn MATLAB is to use MATLAB.