Lec1 Matlab Intro

7/29/2019 Lec1 Matlab Intro

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Iqra University, Islamabad Campus

COMM. SYS LAB

SPRING 2013


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INTRODUCTION TO MATLABLAB 1


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What is Matlab ?


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What is Matlab ?

*MATLAB is a programming environment for

algorithm development, data analysis,

visualization, and numerical computation. Using

MATLAB, you can solve technical computingproblems faster than with traditional

programming languages, such as C, C++, and

Fortran.

*http://www.mathworks.com/
http://www.mathworks.com/http://www.mathworks.com/http://www.mathworks.com/


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What is Matlab? cont.

A software environment for interactive numerical computations

Matlab (stands for MATrix LABoratory)

Applications:

Communications Systems

Computational Biology

Computational Finance

Control Systems

Digital Signal Processing

Embedded Systems

FPGA Design

Image and Video Processing Mechatronics

Technical Computing

Test and Measurement
http://www.mathworks.com/communications-systems/?s_cid=ML2012_tab_appshttp://www.mathworks.com/computational-biology/?s_cid=ML2012_tab_appshttp://www.mathworks.com/computational-finance/?s_cid=ML2012_tab_appshttp://www.mathworks.com/control-systems/?s_cid=ML2012_tab_appshttp://www.mathworks.com/dsp/?s_cid=ML2012_tab_appshttp://www.mathworks.com/embedded-systems/?s_cid=ML2012_tab_appshttp://www.mathworks.com/fpga-design/?s_cid=ML2012_tab_appshttp://www.mathworks.com/image-video-processing/?s_cid=ML2012_tab_appshttp://www.mathworks.com/mechatronics/?s_cid=ML2012_tab_appshttp://www.mathworks.com/technical-computing/?s_cid=ML2012_tab_appshttp://www.mathworks.com/test-measurement/?s_cid=ML2012_tab_appshttp://www.mathworks.com/test-measurement/?s_cid=ML2012_tab_appshttp://www.mathworks.com/technical-computing/?s_cid=ML2012_tab_appshttp://www.mathworks.com/mechatronics/?s_cid=ML2012_tab_appshttp://www.mathworks.com/image-video-processing/?s_cid=ML2012_tab_appshttp://www.mathworks.com/fpga-design/?s_cid=ML2012_tab_appshttp://www.mathworks.com/embedded-systems/?s_cid=ML2012_tab_appshttp://www.mathworks.com/dsp/?s_cid=ML2012_tab_appshttp://www.mathworks.com/control-systems/?s_cid=ML2012_tab_appshttp://www.mathworks.com/computational-finance/?s_cid=ML2012_tab_appshttp://www.mathworks.com/computational-biology/?s_cid=ML2012_tab_appshttp://www.mathworks.com/communications-systems/?s_cid=ML2012_tab_apps


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Strengths of MATLAB

MATLAB is relatively easy to learn

Help is too extensive

Greatbuilt-in functions support

Numerous toolboxes, blocksets and Simulink formodeling real world engineering problems

MATLAB code is optimized to be relatively quickwhen performing matrix operations

MATLAB may behave like a calculator or as a

programming language MATLAB is interpreted, errors are easier to fix

State of the artGraphical User Interface


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Matlab Interface


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Command Window

Use the Command Window to enter

variables and run functions and M-files.


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Command History

Statements you enter in the Command Window are logged

in the Command History.

In the Command History, you can view previously runstatements, and copy and execute selected statements.


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Workspace Browser

The MATLAB workspace consists of the

set of variables (named arrays) built up

during a MATLAB session and stored in

memory.


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Array Editor


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Matlab: Variable Names

Variable names ARE case sensitive

Variable names can contain up to 63 characters

Variable names must start with a letter followed

by letters, digits, and underscores.

Blanks are NOT allowed in a variable name,

however _ is allowed.


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MATLAB special variables

ans Default variable name for results

pi Value of inf Infinity

NaN Not a number e.g. 0/0 i and j i = j = imaginary number

eps Smallest incremental number

realmin The smallest usable positive realnumber

realmax The largest usable positive realnumber


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Examples:

>> a=2

a =

2

>> 2*pi

ans =

6.2832


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Types of Variables

Type Examples Integer 1362,-5656 Real 12.33,-56.3 Complex X=12.23.2i -- (i = sqrt(-1))

Complex numbers in MATLAB are represented inrectangular form.

To separate real & imaginary partH = real(X) K= imag(X)

Conversion between polar & rectangular C1= 1-2i

Magnitude: mag_c1 = abs(C1)

Angle: angle_c1 = angle(C1) Note that angle is in radians


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Other MATLAB symbols

, separate statements and data

% start comment which ends at end of line

ShortcutCtrl+R, Ctrl+T

; (1) suppress output

(2) used as a row separator in a matrix

: specify range


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Arithmetic Operators

Operator Description

+ Addition

- Subtraction

.* Multiplication (element wise)

./ Right division (element wise)

.\ Left division (element wise)

+ Unary plus

- Unary minus

: Colon operator

.^ Power (element wise)' Transpose

* Matrix multiplication

/ Matrix right division

\ Matrix left division

^ Matrix power


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Relational & Logical Operators

Operator Description

& Returns 1 for every element location that is true(nonzero) in both arrays, and 0 for all other elements.

| Returns 1 for every element location that is true

(nonzero) in either one or the other, or both, arrays and0 for all other elements.

~ Complements each element of input array, A.

= Greater than or equal to

== Equal to

~= Not equal to


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Matrices

MATLAB treats all variables as matrices. For our

purposes a matrix can be thought of as an array, in

fact, that is how it is stored.

Vectors are special forms of matrices and contain only

one row OR one column.

Scalars are matrices with only one row AND onecolumn


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MATLAB Matrices

A matrix can be created in MATLAB asfollows (note the commas AND semicolons):

matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]

matrix =

1 2 3

4 5 6

7 8 9


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Row Vector:

A matrix with only one row is called a row vector.A row vector can be created in MATLAB asfollows (note the commas):

rowvec = [12 , 14 , 63]

rowvec =

12 14 63

Row vector can also defined in a following way:

rowvec = 2 : 2 : 10;

rowvec =

2 4 6 8 10


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Column Vector:

A matrix with only one column is called a columnvector. A column vector can be created inMATLAB as follows (note the semicolons):

colvec = [13 ; 45 ; -2]

colvec =

13

45

-2


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Extracting a Sub-Matrix

A portion of a matrix can be extracted andstored in a smaller matrix by specifying thenames of both matrices and the rows and

columns to extract. The syntax is:

sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;

where r1 and r2 specify the beginning andending rows and c1 and c2 specify thebeginning and ending columns to beextracted to make the new matrix.


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Extracting a Sub-Matrix

A row vector can be extracted from amatrix. As an example we create amatrix below:

matrix=[1,2,3;4,5,6;7,8,9]

matrix =

1 2 3

4 5 6

7 8 9

Here we extract row 2 of the matrixand make a row vector. Note that the2:2 specifies the second row and the1:3 specifies which columns of the row.

rowvec=matrix(2 : 2 , 1 : 3)

rowvec =

4 5 6


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Concatenation

New matrices may be formed out of old ones

Suppose we have:

>> a = [1 2 5; 3 4 6; 6 8 9];

b = a(1:2 , 1:2); b = ??

c = a(1 , :); c = ?? d = a(2:3 , :); d = ??

e = a[d ;d]; e = ??


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Concatenation

Input Output

[a, a, a] ans = 1 2 1 2 1 23 4 3 4 3 4

[a; a; a] ans = 1 23 41 23 41 23 4

[a, zeros(2); zeros(2), a'] ans = 1 2 0 03 4 0 00 0 1 30 0 2 4


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Useful MATLAB Commands

clear Clear all variables from work space

clear x y Clear variables x and y from work space

clc Clear the command window

who List known variables whos List known variables plus their size

lookfor look up whole matlab directory foravailable functions

doc open the html based help window

tic toc measure the simulation time ofprogram


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Scalar Matrix Addition & Subtraction

a=3;

b=[1, 2, 3;4, 5, 6]

b =

1 2 3 4 5 6

c= b+a % Add a to each element of b

c =

4 5 6

7 8 9


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Scalar - Matrix Multiplication

a=3;

b=[1, 2, 3; 4, 5, 6]

b =

1 2 3

4 5 6

c = a * b % Multiply each element of b by a

c = 3 6 9

12 15 18


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Other matrices ops:Determinant & Inverse

Let a=[1 4 3;4 2 6 ;7 8 9]

det(a)

48

inv(a)

ans =

-0.6250 -0.2500 0.3750 0.1250 -0.2500 0.1250

0.3750 0.4167 -0.2917


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Other matrices Operations cont.

a (Find the transpose of matrix)

ans =

1 4 7

4 2 83 6 9

min(a) :Return a row vector containing theminimum element from each column.

ans =1 2 3

min(min(a)): Return the smallest element inmatrix


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max(a): Return a row vector containing themaximum element from each column.

ans =7 8 9

max(max(a)): Return the max element from

matrix:ans = 9

a.^2 :Bitwise calculate the square of eachelement of matrix:

ans =

1 16 9

16 4 36

49 64 81


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sum (a): treats the columns of a as vectors,returning a row vector of the sums of each

column. ans =

12 14 18

sum(sum(a)): Calculate the sum of all the

elements in the matrix.ans =

44


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Example

Let a=[1 2 3] ; b=[4 5 6];

a.*b :Bitwise multiply the each element of vector

a and b:

ans =

4 10 18


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Matrix Division

MATLAB has several options for matrix division.You can right divide and left divide.

Right Division: use the slash character A / B

This is equivalent to the MATLAB expression

A*inv (B)

Left Division: use the backslash character

A \ B

This is equivalent to the MATLAB expression

inv (A)*B


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Common Matrices and Vectors

Matrix of Zeros - zeros

Matrix of Ones - ones

Identity Matrix eye

Magic Matrix - magic


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zeros Matrix

Syntax : zeros array

Format : zeros(N), zeros(M,N)

Description:

This function is used to produce an array ofzeros, defined by the arguments.

(N) is an N-by-N matrix of array.(M,N) is an M-by-N matrix of array.

Example;>> zeros(2) >> zeros(1,2)ans = ans =

0 0 0 00 0


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Ones Matrix

Syntax : ones array Format : ones(N), ones(M,N) Description:

This function is used to produce anarray of ones, defined by the arguments. (N) is an N-by-N matrix of array. (M,N) is an M-by-N matrix of array. Example; >> ones(2) >> ones(1,2) ans = ans = 1 1 1 1 1 1


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Eye Matrix

Syntax : identity matrix

Format : eye (N), eye (M,N)

Description: Create an NxN or MxN identity matrix (i.e., 1s on the

diagonal elements with all others equal to zero). (Usually the identitymatrix is represented by the letter I. Type

Example;

>> I=eye(3)I =

1 0 0

0 1 0

0 0 1


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The Help System

Search for appropriate function

>> lookfor keyword Rapid help with syntax and function definition >> help function An advanced hyperlinked help system is

launched by >> helpdesk Complete manuals as PDF files


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INTRODUCTION TO MATLAB - cont


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Outline

Programming environment and search path

M-files

Flow Control

Plotting in Matlab

Matlab help System


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Matlab environment

Matlab construction

Core functionality as compiled C-code, m-files

Additional functionality in toolboxes (m-files)

Today: Matlab programming (construct own m-files)

Core m-filesC-kernel

Sig. Proc Contr. Syst.

User defined


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The programming environment

The working directory is controlled by >> dir >> cd catalogue >> pwd The path variable defines where matlab

searches for m-files >> path >> addpath


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The programming environment

Matlab cant tell if identifier is variable or function

>> z=theta; Matlab searches for identifier in the following order

1. variable in current workspace

2. built-in variable

3. built-in m-file

4. m-file in current directory

5. m-file on search path

Note: m-files can be located in current directory, orin path


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M-files

MATLAB can execute a sequence of MATLAB statements

stored on disk. Such files are called "M-files"

they must have the file type of ".m"

There are two types of M-files: Script files

Function files.


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M-files

To make the m-file click on File next select New and click on M-File from

the pull-down menu as shown in fig


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M-files

Here you will type your code, can make changes, etc.

Save the file with .m extension


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Types of M-files

Script Files

Function Files

M-files


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Script files

Script-files contain a sequence of Matlab

commands%FACTSCRIPT Compute n-factorial, n!=1*2*...*n

y = prod(1:n);

factscript.m

Executed by typing its name

>> factscript

Operates on variables in global workspace

Variable n must exist in workspace

Variable y is created (or over-written)

Use comment lines (starting with %) to document file!


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Functions

Functions describe subprogramsTake inputs, generate outputs

Have local variables (invisible in global workspace)

function [output_arguments]= function_name(input_arguments) % Comment lines

function [z]=factfun(n)% FACTFUN Compute factorial% Z=FACTFUN(N)z = prod(1:n);

factfun.m>> y=factfun(10);

Functions


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Functions

NOTE:

The function_name must also be the same as the file name (without the ``.m'') in which the

function

is stored


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function y = mean (x)% MEAN Average or mean value.

% For vectors, MEAN(x) returns the mean value.% For matrices, MEAN(x) is a row vector% containing the mean value of each column.[m,n] = size(x);if m == 1

m = n;end

y = sum(x)/m;

Output Arguments Input ArgumentsFunction Name

Comments

Function Code

Example


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Flow Control


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Flow control - selection

The if-elseif-else construction

if elseif elseend

if height>170disp(tall)

elseif height


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Logical expressions

Relational operators (compare arrays of same sizes)

== (equal to) ~= (not equal)< (less than) (greater than) >= (greater than or equal to)

Logical operators (combinations of relational operators) & (and)

| (or)~ (not)

Logical functions

xorisemptyanyall

if (x>=0) & (x


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Flow control - selection

The switch construction

Switch

case ,

otherwise< condition >,

< statement>

end

method = 'Bilinear';

switch (method)

case {'linear','bilinear'}

disp('Method is linear')

case 'cubic'

disp('Method is cubic')

case 'nearest'

disp('Method is nearest')

otherwise

disp('Unknown method.')end


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Flow control - repetition

Repeats a code segment a fixed number of

timesfor index=endThe are executed repeatedly.At each iteration, the variable index is assigneda new value from .

for k=1:12kfac=prod(1:k);disp([num2str(k), ,num2str(kfac)])

end


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Example selection and repetition

function y=fact(n)% FACT Display factorials of integers 1..n

if n < 1error(No input argument assigned)

elseif n < 0error(Input must be non-negative)

elseif abs(n-round(n)) > epserror(Input must be an integer)

endfor k=1:n

kfac=prod(1:k);disp([num2str(k), ,num2str(kfac)])

y(k)=kfac;

end;

fact.m


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Flow control conditional repetition

while-loops

are executed repeatedly as long as the evaluates to true

while end

k=1;

while prod(1:k)~=Inf,k=k+1;

enddisp([Largest factorial in Matlab:,num2str(k)]);

d k


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Programming tips and tricks

Programming style has huge influence on

program speed!

tic;X=-250:0.1:250;for ii=1:length(x)

if x(ii)>=0,s(ii)=sqrt(x(ii));

elses(ii)=0;

end;end;

toc

tic

x=-250:0.1:250;s=sqrt(x);s(x


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Break Command

Terminate execution of WHILE or FOR

loop.

In nested loops, BREAK exits from the

innermost loop only.

BREAK is not defined outside of a FOR

or WHILE loop.n = 1;

while prod(1:n) < 700

n = n + 1;

if n==5

break;

end

end


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Plotting in Matlab


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TWO-DIMENSIONALplot() COMMAND

where x is a vector (one dimensional array), and y is a vector.Both vectors

musthave the same number of elements.

The plot command creates a single curve with the x values on

the abscissa (horizontal axis) and the y values on the ordinate(vertical axis).

The curve is made from segments of lines that connect the

points that are defined by the x and y coordinates of theelements in the two vectors.

The basic 2-D plot command is:

plot(x,y)


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PLOT OF GIVEN DATA

Given data:

>> x=[1 2 3 5 7 7.5 8 10];>> y=[2 6.5 7 7 5.5 4 6 8];>> plot(x,y)

A plot can be created by the commands shown below. This can be done

in the Command Window, or by writing and then running a script file.

Once the plot command is executed, the Figure Window opens with the

following plot.

x

y

1 2 3 5 7 7.5 8

6.5 7 7 5.5 4 6 8

10

2


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PLOT OF GIVEN DATA


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LINE SPECIFIERS IN THEplot() COMMAND

Line specifiers can be added in theplot command to:

Specify the style of the line.

Specify the color of the line.

Specify the type of the markers (if markers are desired).

plot(x,y,line specifiers)


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Line Specifier Line Specifier Marker SpecifierStyle Color Type

Solid - red r plus sign +

dotted : green g circle o

dashed -- blue b asterisk *

dash-dot -. Cyan c point .

magenta m square s

yellow y diamond d

black k

plot(x,y,line specifiers)


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The specifiers are typed inside theplot() command as strings.

Within the string the specifiers can be typed in any order.

The specifiers are optional. This means that none, one, two, or all the

three can be included in a command.

EXAMPLES:

plot(x,y) A solid blue line connects the points with no markers.

plot(x,y,r) A solid red line connects the points with no markers.

plot(x,y,--y) A yellow dashed line connects the points.

plot(x,y,*) The points are marked with * (no line between the

points.)

plot(x,y,g:d) A green dotted line connects the points which are

marked with diamond markers.


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Year

Sales (M)

1988 1989 1990 1991 1992 1993 1994

127 130 136 145 158 178 211

PLOT OF GIVEN DATA USING LINE

SPECIFIERS IN THEplot() COMMAND

>> year = [1988:1:1994];>> sales = [127, 130, 136, 145, 158, 178, 211];>> plot(year,sales,'--r*')

Line Specifiers:

dashed red line and

asterisk markers.


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PLOT OF GIVEN DATA USING LINE

SPECIFIERS IN THEplot() COMMAND

Dashed red line and

asterisk markers.


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Formatting the plots


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8 10 12 14 16 18 20 22 240

200

400

600

800

1000

1200

DISTANCE (cm)

INTENSITY(

lux)

Light Intensity as a Function of Distance

Comparison between theory and experiment.

Theory

Experiment

Plot title

y axislabel

x axis

label

Text

EXAMPLE OF A FORMATTED 2-D PLOT

Data symbol

Legend

Tick-mark

Tick-mark label


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FORMATTING PLOTS

A plot can be formatted to have a required appearance.

With formatting you can:

Add title to the plot.

Add labels to axes.

Change range of the axes.

Add legend.

Add text blocks.

Add grid.


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FORMATTING COMMANDS

title(string)Adds the string as a title at the top of the plot.

xlabel(string)

Adds the string as a label to the x-axis.

ylabel(string)

Adds the string as a label to the y-axis.

axis([xmin xmax ymin ymax])

Sets the minimum and maximum limits of the x- and y-axes.


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FORMATTING COMMANDS

legend(string1,string2,string3)

Creates a legend using the strings to label various curves (when

several curves are in one plot). The location of the legend is specified

by the mouse.

text(x,y,string)

Places the string (text) on the plot at coordinate x,y relative to the plot

axes.

Example of a formatted plot


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Example of a formatted plot

Syntax:

Example:

plot(x1, y1, 'clm1', x2, y2, 'clm2', ...)

x=[0:0.1:2*pi];

y=sin(x);

z=cos(x);

plot(x,y,x,z)

title('Sample Plot','fontsize',14);

xlabel('X values','fontsize',14);ylabel('Y values','fontsize',14);

legend('Y data','Z data')

grid on

colorline marker

Sample Plot


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Sample Plot

Title

Ylabel

Xlabel

Grid

Legend

EXAMPLE OF A FORMATTED PLOT


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EXAMPLE OF A FORMATTED PLOT

Syntax:

Example:

plot(x1, y1, 'clm1', x2, y2, 'clm2', ...)

x=[0:0.1:2*pi];

y=sin(x);

z=cos(x);

plot(x,y,x,z)

title('Sample Plot','fontsize',14);

xlabel('X values','fontsize',14);ylabel('Y values','fontsize',14);

legend('Y data','Z data')

grid on

color line marker

Displaying Multiple Plots


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Displaying Multiple Plots

Two typical ways to display multiple curves in

MATLAB (other combinations are possible)

One figure contains one plot that contains multiple

curves Requires the use of the command hold (see

MATLAB help)

One figure contains multiple plots, each plot containing

one curve Requires the use of the command subplot

Sample plot [using hold on command]


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Sample plot [using hold on command]

x=[0:0.1:2*pi];

y=sin(x);

z=cos(x);

plot(x,y,x,z)

grid on

x=[0:0.1:2*pi];

y=sin(x);

z=cos(x);

plot(x,y,b)

hold onplot(x,z,g)

hold off

grid on

Subplots


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Subplots

subplot divides the current figure into rectangular panesthat are numbered rowwise.

Syntax: subplot(rows,cols,index)

subplot(2,2,1);

subplot(2,2,2)

...

subplot(2,2,3)

...

subplot(2,2,4)

...

Example of subplot


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Example of subplot

x=[0:0.1:2*pi];y=sin(x);

z=cos(x);

subplot(1,2,1);

plot(x,y)subplot(1,2,2)

plot(x,z)

grid on

Summary


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Summary

User-defined functionality in m-files Stored in current directory, or on search path

Script-files vs. functions Functions have local variables, Scripts operate on global workspace

Writing m-files Header (function definition), comments, program body Flow control: if...elseif...if, for, while General-purpose functions: use functions as inputs

Programming style and speed

Vectorization, memory allocation, profiler Plotting in Matlab

Plot, subplot


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THE END

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