Matlab Basics

Richard Wait

September 3, 2007

Contents

• What is MATLAB?

• Workspace

• MATLAB environment

• Variables in MATLAB

• Functions in MATLAB

• Examples

– Graphics

– Computation

– Pictures

– GUI

Introduction

What is MATLAB?

• Developed by MathWorks Inchttp://www.mathworks.com

• First version ready by end 1970’s

• Matrix Laboratory for

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– Numerical Computation

– Graphics

– Programming

• A simple environment for quick test of ideas and study of results

• Now, an advanced interactive software environment for computationand visualisation, runs under UNIX/Linux, windows or Macintosh

• Many predefined functions with possibility of user defined functions

• An object oriented programming language that can be linked to C++,Java and Fortran

• Over 25 specialised toolboxes

– Signal Processing

– Statistics

– Symbolic Mathematics

– Financial Mathematics

MATLAB Environment

• MATLAB Desktop has several tools, e.g. Command Window

The MATLAB Desktop

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• MATLAB steered from the command window

• Commands follow the >>-prompt and finished with <ret>

• Example:>> 42 + 19

>> ans =

61

• Note that a semicolon ; supresses the output

• Example:>> a = 75

a =

75

>> b = 34;

>> a + b

ans =

109

MATLAB Environment: Help

• Via the help menu or the command >> helpbrowser

• Via the command >> help as in

3

>> help exit

EXIT exit from MATLAB

Variables in MATLAB

A variable in MATLAB:

• always has a name

• contains a data of a particular type (real, text)

• can be a matrix without the need for any special declaration

• is displayed in the workspace window

• cam be listed using who or whos

• can be predefined e.g. pi, ans

• can be displyed in different formats

>> format short

>> pi

3.1416

>> format long

>> pi

3.14159265358979

The value is unchanged only the output changes

Matrices: Concepts

• Matrices are the basic type type

>> vrow = [1, 2, 4, 5]

vrow =

4

1 2 4 5

>> size(vrow)

ans =

1 4

>> vcol = [1; 2; 4; 5]

vcol =

1

2

4

5

>> size(vcol)

ans =

4 1

>> length(vcol)

ans =

4

• Defining a matrix

>> A = [1 2; 4 5]

A =

1 2

4 5

>> A = [1 3

7 8]

A =

1 3

7 8

>> A’

ans =

1 7

3 8

• two uses for ; and ’ means transpose

• Addition >> C=A+B

• Multiplication >> C=A*B

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• Division >> C=A/B or >> C=A\B

– >> C=A\B solves AC = B

– >> C=A/B solves CB = A

• Dimensions must be compatible, otherwise error message

• Starting from A =

(

1 37 8

)

construct A =

1 37 82 1

• Either >> A=[A ; 2 1];

• Or

>> k = [2 1];

>> A = [A; k];

• A(i,j) is the element in row i column j

• A(:,j) is the whole of column j

• A(i,:) is the whole of row i

• A(i:j,k:l) is the submatrix, rows i − j and columns k − l

• A matrix with all elements unity >> B=ones(3,5);

– >> B=ones(3); defines a 3 × 3

– >> B=ones(3,1); defines a column vector of length 3

• A matrix with all elements zero (the null matrix) >> C=zeros(2,4);

– >> C=zeros(3); defines a 3 × 3

– >> C=zeros(3,1); defines a column vector of length 3

• The unit (identity) matrix

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>> A = eye(2)

A =

1 0

0 1

•>> B = [1 7; 5 3];

>> B∧2ans =

36 28

20 44

>> B.∧2ans =

1 49

25 9

Functions and Operations

• min(x) gives the minimum value in x, columnwise if x is a matrix

• max(x) maximum value in the same sense

• sum(x) sum of elements in x

• mean(x)

• std(x) standard deviation

• real(x) real parts

• imag(x) imaginary parts

• Using the colon notation

>> v1 = 0:5

v1 =

0 1 2 3 4 5

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>> V2 = 0.0:0.05:2.;

>> length(v2)

ans =

41

• Using the linspace

>> v3 = linspace(0.0, 2.0, 41);

>> max( v2 - v3 )

ans =

2.2204e-016

• Note rounding error as MATLAB does not store real numbers exactly

Saving and Loading code

• A command file (script file) is a set of commands that would otherwisehave to be input interactively in the command window

• All the commands in the file can be executed and the results appearsin the command window

• All files must be named with the suffix m such as myfile.m

• To execute write the name in the command window (without suffix .m)thus

>> myfile

Programming in MATLAB

M-Files

• MATLAB instructions can be stored

• M-files

– Script files

– Functions can be defined in MATLAB

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Operations

• relational operators

– < less than

– <= less than or equal to

– == equal to

– ∼= not equal to

• MATLAB logical operations

– A&B A and B

– A|B A or B

– ∼A not A

• Examples

– (x==1) & (y<2)

– abs(x-pi) > 1e-14

Conditional Statement

• If - End

x = input(’Give a number x:’);

if x>0

disp(’x greater than zero!’)

end

If - Else

• if - else

if <logical expression>

statements

else

statements

end

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• elseif

if <logical expression>

statements

elseif <logical expression>

statements

else

statements

end

Iteration

• for - end

x = input(’Give a number x:’);

for i = 1:10

x = (x+1/x)/2;

end

For - End

• Standard form

for variable = <expression>

statements

end

• one-line

for var = <exp>, ..., end

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Example

•r = []; s = [];

for x=-2.0:0.25:-0.75

y = 1+1/x;

r = [r x];

s = [s y];

end

[r; s]’

Iteration

• while - end

x = [];

a = 1;

while a > 0

x = [x a];

a = input (’Enter value; ’);

end

while - end

• Standard form

while <logical expression>

statements

end

• one-line

while <logical exp>, ..., end

Functions

• Standard functions sin(x), etc.

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• User defined functions

function[x, y] = myfunc(x0,x1,n)

% My first function

x = linspace(x0, x1, n);

y = cos(x) + sin(x);

plot(x,y)

• Save as myfunc.m

Using Functions

• Execute as

xstart = 0; xend = pi; n = 100;

[x, y] = myfunc(xstart, xend, n);

Optional arguments

• Using varagin

function[x, y] = myfunc(x0,x1,...

n, varargin)

x = linspace(x0, x1, n);

y = cos(x) + sin(x);

plot(x,y,varargin{:})

• Execute as

[x, y] = myfunc(xstart, xend, n);

• Or execute as

[x, y] = myfunc(xstart, xend, ...

n, ’color’,[.5 .7 .3], ...

’linestyle’,’:’);

Global Parameters

function[y] = myfunc(x)

global w

z = cos(x) + w;

y = z + sin(x);

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• Input parameters - x

• Output parameters - y

• Local variables - z

• Global variables - w

• Execute as

global w;

x = 1; w = 2;

y = myfunc(x);

Plotting a function

x=linspace(0,1);

y=x.*sin(x);

plot(x,y)

Multiple plots

x=linspace(0,2*pi,10);

y=cos(x).*sin(x);

plot(x,y)

hold on

y=sin(x); plot(x,y)

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Simple plots

ezplot(’sin(x)’,[0,10])

0 1 2 3 4 5 6 7 8 9 10

−1

−0.5

0

0.5

1

x

sin(x)

Data Plots

x=[10,15,5,3,7,20];

stem(x)

title(’Parking’)

xlabel(’CarType’)

ylabel(’No of Cars’)

print -deps matplot3

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1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

2

4

6

8

10

12

14

16

18

20Parking

CarType

No

of C

ars

Data Plots

pie(x,{’blue’,’red’,’black’,...

’yellow’,’white’,’other’})

title(’Parking’)

print -deps matplot4

blue

red

black yellow

white

other

Parking

ld=rand(1,100)/2+1.6;

hist(ld)

title(’heights’)

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1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.10

5

10

15heights

Scatter Plots

ld=rand(1,10)/2+1.6;

y=1:10;

plot(y,ld,’ro’)

1 2 3 4 5 6 7 8 9 101.65

1.7

1.75

1.8

1.85

1.9

1.95

2

2.05

2.1

Plots in 3D

t=0:0.01:10; x=sin(t);

y=cos(t); z=exp(t/10);

plot3(x,y,z)

xlabel(’x’), ylabel(’y’),

zlabel(’z’)

grid

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−1

−0.5

0

0.5

1

−1

−0.5

0

0.5

11

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

xy

z

Simple Surface Plots

ezsurf(’x*exp(-x^2-y^2)’)

−3−2

−10

12

3

−3

−2

−1

0

1

2

3−0.5

0

0.5

x

x exp(−x2−y2)

y

Graphics Output

• The Graph appears as a separate window

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Saving graphics

print stuff1

• print creates a file stuff1.ps

• black and white postscript is the default

print -d epsc stuff2

• print creates a file stuff2.eps

• other alternatives include encapsulated postscript eps with colour epsc

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0 5 10 15 20 25 30 35 40 45

15

20

25

30

35

40

45

50

exam marks

hom

ewor

k m

arks

Least squares lines to fit observed data

X=10.6069+0.41823*YY=16.9983+0.51059*X

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