Outline

• What is MATLAB• MATLAB desktop• Variables, Vectors and Matrices• Matrix operations• Array operations• Built-in functions: Scalar, Vector, Matrix• Data visualization− 2D Plots• Flow control: ‘if’, ‘for’• User-defined functions

1

• High level language for technical computing

• Stands for Matrix Laboratory

• Easy to do linear algebra, calculus,

signals and systems and the most

complex calculations a human brain

can think of.

What is MATLAB

MATLAB

High level languages, C, C++, Basic,

Fortran, Pascal, etc.

Assembly Language

2

MATLAB desktop

3

MATLAB desktop (cont.)1. Menu and toolbar

2. Command window

4

MATLAB desktop (cont.)3. Command history 4. Workspace

5

MATLAB desktop (cont.)5. Variable editor

6

MATLAB desktop (cont.)6. Editor

7

MATLAB basics

What is difference?Variable Vector/Array Matrix

1×1Single value

1×N or M×1Row or column vector

M×N

𝑎=5or

𝑧=[1 47 3 ]

8

Variables• No need for types. i.e.

• All variables are created with double precision unless specified.

• After these statements, the variables are 1×1 matrices with double precision.

• Enter ‘who’ command in command window to view all active variables

• Enter ‘whos’ command to view all active variables with their size, allocated memory size and type of variable.

int a;double b;float c;

Example:>> a = 5;>> b = 2;

9

Vectors• Vector in space

• Can be written as

• Use ‘space’ (‘ ’) or ‘comma’ (‘,’) to separate row elements.• Use ‘semicolon’ (‘;’) to separate rows.• Define a row vector ‘r’ and column vector ‘c’.

• If we no longer need a particular variable/vector/ /matrix/object we can “erase” it from memory using the command ‘clear variable_name’.

• Erase vector ‘r’.

orRow vector Column vector

>> r = [1 2 3 4 5]; or r = [1,2,3,4,5];>> c = [6;7;8;9;10];

10

Matrices

• Almost all entities in MATLAB are matrices.

• Order of Matrix − m × nm = number of rowsn = number of rows

• Vectors are special case of Matrices− m = 1 row vector− n = 1column vector

• Define

• A vector is always a matrix but a matrix is not necessarily a vector

• Use ‘size (variable/vector/matrix name)’ to find its size.

>> A = [1 2; 3 4]

>> B = [16 3 5; 7 5 10]

11

Creating Vectors

• Creating vector with equally spaced intervals

>> x = 0:0.5:2x = 0 0.5000 1.0000 1.5000 2.0000

• Creating vector with n equally spaced intervals

>> x = linspace(0,2,5)x = 0 0.5000 1.0000 1.5000 2.0000

12

Creating Matrices from functions

• zeros(m, n): matrix with all zeros

• ones(m, n): matrix with all ones.

• eye(m, n): the identity matrix

• rand(m, n): uniformly distributed random

• randn(m, n): normally distributed random

• magic(m): square matrix whose elements have the

same sum, along the row, column and diagonal.

13

Matrix operations

• ^: exponentiation

• *: multiplication

• /: division

• \: left division. The operation A\B is effectively the

same as INV(A)*B, although left division is

calculated differently and is much quicker.

• +: addition

• -: subtraction 14

Array operations

• Evaluated element by element

• .’ : array transpose

• .^ : array power

• .* : array multiplication

• ./ : array division

• Very different from Matrix operations

15

Example

Perform the following task.

• Define matrices ‘A’ and ‘B’>> A=[1 2;3 4];>> B=[5 6;7 8];

Find product of ‘A’ and ‘B’ using Matrix and Array operator.

Which one is correct??

Hint: Solve on paper before using MATLAB16

Matrix IndexingGiven the matrix:

Then:

A(1,2) = 0.6068

A(3) = 0.6068

A(:,1) = [0.9501

0.2311 ]

A(1,2:3)=[0.6068 0.4231]

𝐴=[0 .9501 0.6068 0.42310.2311 0.4860 0.2774 ]

17

Adding Elements to a Vector or a Matrix

>> C=[1 2; 3 4]C= 1 2 3 4 >> C(3,:)=[5 6];C= 1 2 3 4 5 6

>> D=linspace(4,12,3);>> E=[C D’] E= 1 2 4 3 4 8 5 6 12

>> A=1:3A= 1 2 3>> A(4:6)=5:2:9A= 1 2 3 5 7 9

>> B=1:2B= 1 2>> B(5)=7;B= 1 2 0 0 7

18

Built-in Functions: Scalar Functions

• sin: trigonometric sine• cos: trigonometric cosine• tan: trigonometric tangent• asin: trigonometric inverse sine (arcsine)• acos: trigonometric inverse cosine (arccosine)• atan: trigonometric inverse tangent (arctangent)• exp: exponential• log: natural logarithm• log10: base 10 logarithm• abs: absolute value• angle: phase value• sqrt: square root• rem: remainder 19

Built-in Functions: Vector Functions

• max: largest component

• min: smallest component

• length: length of a vector

• sort: sort in ascending order

• sum: sum of elements

• prod: product of elements

• mean: mean value

• std: standard deviation20

Built-in Functions: Matrix Functions

• size: size of a matrix• det: determinant of a square matrix• inv: inverse of a matrix• rank: rank of a matrix• rref: reduced row echelon form• eig: eigenvalues and eigenvectors• poly: characteristic polynomial• lu: LU factorization• qr: QR factorization• chol: cholesky decomposition• svd: singular value decomposition

21

Data visualization − 2D plots

• If ‘x’ and ‘y’ are two vectors of the same length then

‘plot(x,y)’ plots x versus y.

• Example:

Plot y=cos(x) from −π to π with increment of 0.01

» x=-pi:0.01:pi;

» y=cos(x);

» plot(x,y)

22

2D plots − Overlay plots

• To change curve style, specify marker style

plot(xdata, ydata, ‘marker_style’);

• Example>> x=-5:0.1:5;>> y=x.^2;>> p1=plot(x, y, 'r:s');

• Use hold on for overlaying graphs>> hold on;>> z=x.^3;>> p2=plot(x, z,‘b-o');

23

2D plots − Annotation

• Use title, xlabel, ylabel and legend for annotation

Example

>> title('Demo plot');

>> xlabel('X Axis');

>> ylabel('Y Axis');

>> legend([pl, p2], 'x^2', 'x^3'); 24

2D plots − Line types

• y: yellow• m: magenta• c: cyan• r: red• g: green• b: blue• w: white• k: black

• .: point• o: circle• x: x-mark• +: plus• -: solid• *: star• :: dotted• -.: dashdot• --: dashed

25

2D plots − Other commands

• figure: opens new window for plot

• close all: closes all opened figures

• subplot: creates an array of plots in the same

window

• loglog: plot using log-log scale

• semilogx: plot using log scale on the x-axis

• semilogy: plot using log scale on the y-axis

26

Flow control: ‘for’ loop

• A loop is a statement which is executed repeatedly.• If you want to repeat some commands, you can use

‘for’ loop.• Must tell MATLAB where to start and where to end.

for index = start : end program statements :end

• Examplefor i=1:4iend 27

Flow control: ‘if’ statement

• Execute statements if condition is true

if (condition_1)program statements

elseif (condition_2)program statements

elseprogram statements

end

28

• Dummy examplesif (x<5)

:end

if (a<3):

elseif (b~=5):

end

Flow control: Operators

29

• Logical operators• <: less than• >: greater than• <=: less than or equal to• >=: greater than or equal to• ==: equal to• ~=: not equal to

• Logical operators• &: and• |: or• ~: not

User-defined functions

30

• Functions are m-files which can be executed by specifying some inputs and supply some desired outputs.

function output = functionname(inputs)

function [out1,out2,…] = functionname(in1,in2…)

• Write this command at the beginning of the m-file and save the m-file with a file name same as the function name.

User-defined functions (cont.)

31

Examples

• Write a function which takes a number and returns its square.

• Write a function which takes the square of the input matrix if the input indicator is equal to 1. And takes the element by element square of the input matrix if the input indicator is equal to 2