Basics on MATLABsamymziouimamcourses.weebly.com/uploads/2/7/8/4/... · MATLAB has excellent...

Introduction to MATLABIntroduction to MATLABBasics on MATLAB

By D. Samy MZIOU3/15/2008

2Introduction to MatlabIntroduction to Matlab

Aims

1. To present the software

2. To introduce elementary operations

and functions.and functions.

3. To manipulate 2D and 3D graphics.

4. To introduce the notion of “files” and

“programming”.

3/15/2008 D. Samy MZIOU

p g g


1. First Steps in MATLAB

1 1 Wh t i MATLAB1.1 What is MATLAB

MATLAB (MATrix LABoratory) is a very powerful and interactive ft k ti i d f i tifi t ti d isoftware package optimized for scientific computation and, in

particular, matrix manipulation.

With MATLAB we canWith MATLAB we can

do mathematics and computation,analyze dataanalyze data, develop algorithms, do simulation and modeling,

d hi l di l d hi l i t fproduce graphical displays and graphical user interfaces.


MATLAB is an interpreted language (code is compiled each time it is run.

MATLAB is easy to use (Mathematical operations) and has a MATLAB is easy to use (Mathematical operations) and has a complete documentation online.

MATLAB is Excellent for manipulating large amounts of tabular data (arrays matrices) in a consistent waydata (arrays, matrices) in a consistent way.

MATLAB has excellent visualization tools (plotting data and functions)

MATLAB has Lots of built in functions for applied mathematics MATLAB has Lots of built-in functions for applied mathematics such data analysis,interpolation, linear algebra, Fourier analysis,…

MATLAB has many toolboxes (statistical, financial, symbolic,…)MATLAB is a good programming language. MATLAB allows to do numerical simulation based on numerical

analysis algorithmsMATLAB allows interfacing with programs in other language (C,

Fortran, …)


1.2 Short History ( http://en.wikipedia.org/wiki/MATLAB )

MATLAB was invented in the late 1970s by Cleve Moler, thenh i f h i d h U i i fchairman of the computer science department at the University of

New Mexico. He designed it to give his students access toLINPACK and EISPACK without having to learn Fortran. It soonspread to other universities and found a strong audience withinspread to other universities and found a strong audience withinthe applied mathematics community. Jack Little, an engineer, wasexposed to it during a visit Moler made to Stanford University in1983 Recognizing its commercial potential he joined with Moler1983. Recognizing its commercial potential, he joined with Molerand Steve Bangert. They rewrote MATLAB in C and founded TheMathWorks in 1984 to continue its development. These rewrittenlibraries were known as JACKPAC.MATLAB was first adopted by control design engineers, Little'sspecialty, but quickly spread to many other domains. It is nowalso used in education, in particular the teaching of linear algebraand numerical analysis, and is popular amongst scientists involvedwith image processing.


1.3 What is MATLAB useful references

Full documentation available online in HTML and PDF Full documentation available online in HTML and PDF format.

h // h k / /h l d k/h l /h l d k h lhttp://www.mathworks.com/access/helpdesk/help/helpdesk.html

Many documents on the web (http://www.google.com.sa)

ReadRead“Getting Started” section of the MATLAB manual

Notice: there are many freeware/sharewares similar to MATLAB. Forinstance SCILAB (http://www-rocq.inria.fr/scilab )


1.4 How to run MATLAB

To run MATLAB on a PC double-click on the MATLAB icon onthe desktop

To run MATLAB on a Unix system, Type MATLAB at theprompt.

When MATLAB starts, a window appears (MATLAB Desktop) containing three smaller windows of different size: the Command Window, the Current Directory Window and the Command History Wi dWindow.

In the command window you should see a message:

T t t t d l t MATLAB H l D f th H l To get started, select MATLAB Help or Demos from the Help menu.>>


current directory

>> Playbackdemo (‘desktop’)>> l b kd ('hi t i d ‘)

l b kd ('h l i d ')

>> playbackdemo('historywindow‘)

>> playbackdemo('currdirectory')>> playbackdemo('helpwindow')

MATLAB DESKTOPcommand windows

command history


WindowsWindows PurposePurpose

Main windows enter variables and Command Windows Main windows, enter variables and commands, runs programs,…

Command History Window Logs commands entered in the Command WindowCommand Window

Current Directory Window Shows the files in the current repertory

Figure Window Contains output from the graphiccommandscommands

Editor Window Creates and debugs script and functions files

Help window Provides help informationHelp window Provides help information

Profiler Window improve the performance of your M-files is using profiling tools

Provides information about the variables Workspace Window Provides information about the variables that are used


In the command window:

To type commands the cursor must be placed after the commandTo type commands the cursor must be placed after the commandprompt (>>).

Once the command typed, you have to press the “enter” key forexecuting the commandexecuting the command.

You can type many commands on the same line separatedbetween them by a comma (,) .

1.4 How to quit MATLAB

To end a MATLAB session type

quit or exit at the MATLAB prompt.

Click on the symbol X on the upper right of the MATLAB windowClick on the symbol X on the upper right of the MATLAB window.


1.5 Help me MATLAB!

To get started, type one of these commands:

help: Opens a MATLAB help at the prompt.helpwin: Opens a MATLAB help GUIhelpdesk: Opens a MATLAB hypertext help browserd ( ) S h MATLAB d idemo(s): Starts the MATLAB demonstration

You can click on the icon on the MATLAB window?

You can learn how to use any MATLAB command by typing helpfollowed by the name of the command, for example >>help sin.

You can also use the lookfor command, which searches the helpentries for all MATLAB commands for a particular word.you could type >> lookfor inverse. MATLAB responds with the names ofthe commands that have the searched word in the first line of the helpthe commands that have the searched word in the first line of the helpentry. You can search the entire help entry for all MATLAB commands bytyping >> lookfor –all inverse.


REMARK on the “HELP” command

For example, help solve will display documentation for solve. p , p p y

Unless you have a large monitor, the output of help solve will

not fit in your MATLAB command window, and the beginning of

the documentation will scroll quickly past the top of the

screen. You can force MATLAB to display information one

screenful at a time by typing more on.

You press the space bar to display the next screenful, or ENTER

to display the next line; type help more for details. Typing

more on affects all subsequent commands, until you type

more off.


2.1 First Steps :

To allow MATLAB to carry out 1 + 1 type the following at the prompt:To allow MATLAB to carry out 1 + 1, type the following at the prompt:>> 1+1

MATLAB responds withans =ans2

The result is logged in variable called “ans”. In fact “ans” is now a variable that you can use again For example you can type “ ans*ans”variable that you can use again. For example you can type ans ansto check that 2 × 2 = 4:>> ans*ansans =4

Here MATLAB has updated the value of “ans” to be “4”.

h i bl “ ” i h d f l i blThe variable “ans” is the MATLAB default variable. It changes each time that you execute a command.


Remark :Remark :

The spacing of operators in formulae does not matter. The following formulas both give the same answer:g

>> 1+3 * 2-1 / 2*4

>> 1 + 3 * 2 - 1 / 2 * 4

The order of operations is made clearer to readers of your MATLAB code if you type carefully:

>> 1 + 3*2 - (1/2)*4


2.2 Matrices

The basic object that MATLAB deals with is a matrix A matrix is an The basic object that MATLAB deals with is a matrix. A matrix is an array of numbers. For example the following are matrices:

1 2 3 9i⎛ ⎞⎛ ⎞

⎜ ⎟⎜ ⎟( )

11 2 0 0 0 1 6 1 2 4 4 2

1( 2 ) 3 1

ei

s q r t p i

⎜ ⎟⎜ ⎟ −⎜ ⎟⎜ ⎟−⎜ ⎟−⎜ ⎟⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠

The size of a matrix is the number of rows by the number of columns.The first matrix is a 3×3 matrix. The (2,3)-element is one million “1e6”th t t d f 1 106 d th (3 2) l t i i 3 14159

3 1⎝ ⎠ ⎝ ⎠

that stands for 1 × 106 , and the (3,2)-element is pi = π = 3.14159 ...

The second matrix is a row-vector, the third matrix is a column-vector containing the number i, which is a pre-defined MATLAB variable equal g , p qto the square root of −1. The last matrix is a 1 × 1 matrix, also called a scalar.


2.3 Variables and assignmentsVariable_name = numerical value or computable expressionVariables in MATLAB are named objects and are assigned using

the equals sign “=“. They can contain

d l l ttupper and lowercase lettersany number of ‘_’ charactersnumerals.

They must start with a letter They must start with a letter.

Matlab is case sensitive: A and a are different variables.

Don’t use a MATLAB built-in functions as a variable

>> a = 1

The following are valid MATLAB variable assignments:

>> speed = 1500>> BeamFormerOutput_Type1 = v*Q*v’>> name = ’John Smith’


>> 42for1 = ’yes’>> first one = 2>> clear=4*3,pi=72, ans=pi*5

These are invalid assignments:

To assign a variable without getting an echo from MATLAB we use the co semi-colon character “;” . Compare the followings:

To assign a variable without getting an echo from MATLAB we use the co semi-colon character “;” . Compare the followings:p gp g

>> a = 2; >>

>> a = 2 a=

2

Try typing the following:Try typing the following:>> a = 2;b = 3;>> c = a+b; >> who Lists the variables currently in the memory>> h S h ith i f ti b t th i b t d l>> whos Same as who with information about their bytes and class>> clear Removes all variables from the memory>> home Clean the command window display >> clc


2.4 How to generate a series of numbers

To generate a series of numbers we write all the numbers in square

brackets and we separate them either using commas or blanks.

>> [1 2 3 4 5] >> [1,2,3,4,5]

ans =

1 2 3 4 5

ans =

1 2 3 4 5

It is your turn! Try some examples yourselves


2.5 How to generate a series of numbers (The Colon Operator “:”)

To generate a vector of equally-spaced elements MATLAB provides the colon operator “:”.

>> 1 2 10>> 1:5

ans =

>> u=1:2:10

u =

1 2 3 4 5 1 3 5 7 9

The syntax “x:y” means roughly “generate the ordered set of numbers from x to y with increment 1 (default value) between them.”

Th t “ d ” hl “ t th d d t The syntax “x:d:y” means roughly “generate the ordered set of numbers from x to y with increment d between them.”


2.6 The command “Linspace”

To generate a vector of evenly spaced points between two end points, you can use the command linspace(startpoint,endpoint,npoints )

>> x = linspace(0,1,10)x =Columns 1 through 70 0 1111 0 2222 0 3333 0 4444 0 5556 0 66670 0.1111 0.2222 0.3333 0.4444 0.5556 0.6667Columns 8 through 100.7778 0.8889 1.0000

The previous command generates 10 evenly spaced points from 0 to 1.

Typing linspace(startpoint,endpoint) will generate a vector of 100 yp g p ( p , p ) g

points.


3 Typing into MATLAB

3.1 Command Line Editingg

If you make a mistake when entering a MATLAB command, you do not have to type the whole line again. The arrow keys can be used to save much typing:

↑ ctrl-p Recall previous line↓ ctrl-n Recall next line

much typing:

← ctrl-b Move back one character→ ctrl-f Move forward one characterctrl-→ ctrl-r Move right one wordctrl-← ctrl-l Move left one wordhome ctrl-a Move to beginning of lineend ctrl-e Move to end of lineesc ctrl-u Clear linedel ctrl-d Delete character at cursorbackspace ctrl-h Delete character before cursor

ctrl-k Delete (kill) to end of line


3.2 Long Lines

If you want to type a MATLAB command that is too long to fit on one line, you can continue on to the next by ending with a space followed by three full stops “…” For example, to type an expression with long variable names:variable names:

>> Final_Ans = Matrix(row_indices,column_indices) + ...Another_vector*SomethingElse;

Or to define a long text string:

>> Mission = [’DST’’s objective is to give advice that’ ...’is professional, impartial and informed on the’ ...’application of science and technology that is best’ ...’suited to French’’s defence and security needs.’];


3.3 Copying and Pasting

Your windowing system’s copy and paste facility can be used to enter text into the MATLAB command line. For example all of MATLAB’S built-in commands have some helpful text that can by accessed by typing helpp y y yp g pfollowed by the name of the command. Try typing help contour into MATLAB and you will see a description of how to create a contour plot.

At the end of the help message is an example You can use the mouse to At the end of the help message is an example. You can use the mouse to select the example text and paste it into the command line. Try it now and you should see a contour plot appear in the figure window.


3.4 Basic Datatypes

double: Floating point number, the most common datatype in MATLABh d

>> a = 1; whos ('a');

Name Si e B tes Class

➔ Other numeric datatypes: float, int32, uint8, ... rather uncommon

Name Size Bytes Classa 1x1 8 double array

Grand total is 1 element using 8 bytes

>> a = complex(1,-2) >> a = 1-2*i

Complex numbers:

Warning: “i” can bea =1.0000 - 2.0000i

a =1.0000 - 2.0000i

Warning: i can beredefined

(overwritten)!

StringsStrings >> a = ['test123']a =test123


3.5 Advanced Datatypes

Cell Arrays: Generalised matrixy➔ Elements can have differing datatypes➔ Elements can have different sizes

>> a = {[1,2,3], 'test123'}a =

[1x3 double] 'test123'

Structures➔ Combine various data in a 'field/value' type structure➔ Fields and associated datatypes do not have to be declared( d h t ti )(and can change at run-time)

>> a.b = 2; a.c = [2,3,4];>> aa =a

b: 2c: [2 3 4]


3.6 Matrices

3 6 1 Typing Matrices3.6.1 Typing Matrices

To type a matrix into MATLAB you must begin with a left square bracket [

l hseparate elements in a row with commas or spacesuse a semicolon “;” to separate rows or the “enter” keyend the matrix with the right square bracket ].

>> [1 2 3>> a = [1 2 3;4 5 6;7 8 9]

a =

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

a =

>> a = [1 2 34 5 67 8 9]

1 2 34 5 67 8 9

1 2 34 5 67 8 9

a =

1 2 34 5 67 8 9 4 5 67 8 9


3.6.2 Arithmetic operators

A. For scalars

Operator Description Example

+ Addition 5+3

- Subtraction 4-2

.* Multiplication 3.*4

./ Right division 4./2g

.\ Left division 2.\4

.^ Power 2.^5

Order of precedence:1. Parenthesis 2. Exponentiation3. Multiplication and Division4. Addition and Subtraction


B. For matricesOperator Description Example

+ Addition A+B

- Subtraction A-B

* Multiplication A*B

/ Right division A/B/ Right division A/B

\ Left division B\A

^ Power A^2

.’ Transpose A.’

: Column operator A(:,1:3)

O d f dOrder of precedence:1. Parenthesis 2. Exponentiation3. Multiplication and Division3. Multiplication and Division4. Addition and Subtraction5. Column operator


C. Operator PrecedenceYou can build expressions that use any combination of arithmetic, relational,

and logical operators. Precedence levels determine the order in whichMATLAB l t i Withi h d l l tMATLAB evaluates an expression. Within each precedence level, operatorshave equal precedence and are evaluated from left to right. Theprecedence rules for MATLAB operators are shown in this list, orderedfrom highest precedence level to lowest precedence level:

1. Parentheses ()2. Transpose (.'), power (.^), complex conjugate transpose ('), matrix

power (^) 3. Unary plus (+), unary minus (-), logical negation (~)4. Multiplication (.*), right division (./), left division(.\), matrix

multiplication (*), matrix right division (/), matrix left division (\)

5. Addition (+), subtraction (-)6. Colon operator (:)7. Less than (<), less than or equal to (<=), greater than (>), greater

than or equal to (>=), equal to (==), not equal to (~=)8. Element-wise AND (&)8. Element wise AND (&)9. Element-wise OR (|)


3 6 2 B ilt i MATLAB V i bl3.6.2 Built-in MATLAB Variables

Name Meaning

ans value of an expression when that expression is not assigned toa variable

eps floating point precision (2.2204e-016)

pi π, (3.141492 . . .)

l l i i fl i i b (1 7977 308)realmax largest positive floating point number (1.7977e+308)

realmin smallest positive floating point number (2.2251e-308)

Inf ∞, a number larger than realmax,

NaN not a number, the result of evaluating 0/0

i, j preassigned to square root of −1


3 6 3 B ilt i MATLAB F ti3.6.3 Built-in MATLAB Functions

Name Meaning

sqrt(x) Square root

exp(x) exponential

b ( ) Ab l t l abs(x) Absolute value

log(x), log10(x) Natural and base 10 logarithm

factorial(x) Factorial function

sin(x),cos(x),tan(x),cot(x) Trigonometric functions

round(x) Round to the nearest integer

fix(x) Round towards zerofix(x) Round towards zero

ceil(x) Round towards infinity

floor(x) Round towards minus infinity

rem(x y) Remainder when x is divided by yrem(x,y) Remainder when x is divided by y

sign(x) Signum function


3 6 4 C t ti M t i

Matrices can be made up of submatrices. This process is called concatenation. The pair of square brackets “ []” is the concatenation Matrices can be made up of submatrices. This process is called concatenation. The pair of square brackets “ []” is the concatenation

3.6.4 Concatenating Matrices

operator. Try this:operator. Try this:

>> A = [1 2 3;4 5 6;7 8 9] % Generate a matrix A

>> B= [A 10*A ; -A [1 0 0;0 1 0;0 0 1]] % Create a matrix B by concatenation

B =

1 2 3 10 20 304 5 6 40 50 607 8 9 70 80 90-1 -2 -3 1 0 0-4 -5 -6 0 1 0-7 -8 -9 0 0 1


3 6 5 C t ti M t i Th f ti “ t”3.6.5 Concatenating Matrices: The function “repmat”

The “repmat” function can be used to replicate a matrix. For instance

>> A = [1 2; 3 4]>> A [1 2; 3 4]A =

1 23 4

>> B=repmat(A,2,3)B =

1 2 1 2 1 23 4 3 4 3 41 2 1 2 1 23 4 3 4 3 4


3 7 U f l M t i t3.7 Useful Matrix generators

MATLAB provides four easy ways to generate certain simple matrices.These are :1. zeros : a matrix filled with zeros2. ones : a matrix filled with ones3. rand : a matrix with uniformly distributed random elements

randn : a matrix with normally distributed random elementsrandn : a matrix with normally distributed random elements4. eye : identity matrix

To tell MATLAB how big these matrices should be you give the functionsthe number of rows and columns. For example:

>> a = zeros(2,3)

a =0 0 00 0 0


>> b = ones(2,2)/2b =0 5000 0 5000

>> u = rand(1,5)u =0 9218 0 7382 0 1763 0 4057 0 93550.5000 0.5000

0.5000 0.50000.9218 0.7382 0.1763 0.4057 0.9355

>> n = randn(5,5)n =

-0.4326 1.1909 -0.1867 0.1139 0.29441 6656 1 1892 0 7258 1 0668 1 3362

>> eye(3)ans =

1 0 0-1.6656 1.1892 0.7258 1.0668 -1.33620.1253 -0.0376 -0.5883 0.0593 0.71430.2877 0.3273 2.1832 -0.0956 1.6236

-1.1465 0.1746 -0.1364 -0.8323 -0.6918

1 0 00 1 00 0 1


3.7 Subscripting

>> u = rand(1,5)u =u 0.9218 0.7382 0.1763 0.4057 0.9355

Individual elements in a matrix are denoted by a row index and a column index To pick out the third element of the vector u type:column index. To pick out the third element of the vector u type:

>> u(3)ans =

0 17630.1763

You can use the vector [1 2 3] as an index to u. To pick the first three elements of u type :

>> u([1 2 3])ans =

0.9218 0.7382 0.1763

Remembering what the colon operator does, you can abbreviate this to


>> u(1:3)>> u(1:3)ans =0.9218 0.7382 0.1763

You can also use a variable as a subscript:

>> i = 1:3;>> u(i)

ans =0.9218 0.7382 0.1763

Two dimensional matrices are indexed the same way, only you y, y yhave to provide two indices:


>> A = [1 2 3;4 5 6;7 8 9]A =

1 2 34 5 67 8 9

>> a(3,2)ans =ans

8>> A(2:3,3)ans =

69

>> A(2,:)ans = The last two examples use the

l b l i d hi h ans

4 5 6>> A(:,3)ans =

3

colon symbol as an index, which matlab interprets as the entire row or column.

369


If a matrix is addressed using a single index, matlab counts the index down successive columns:

>> A(4)ans =2>> A(8)ans =63 8 End as a subscript3.8 End as a subscript

To access the last element of a matrix along a given dimension, use end as a subscript (MATLAB version 5 or later). This allows you to go to the final element without knowing in advance how big the matrix is. Forexample:

>> Q = 4:10>> Q 4:10Q =

4 5 6 7 8 9 10


>> Q(end)>> Q(end)ans =

10>> Q(end-4:end)ans =

6 7 8 9 10>> Q(end-2:end)ans =ans

8 9 10

>> Q = [spiral(3) [10;20;30]]Q =Q =

7 8 9 106 1 2 205 4 3 30This technique works

f t di i l >> Q(end,end)ans =30>> Q(2,end-1:end)

for two-dimensional matrices as well:

Q(2,end 1:end)ans =2 20


>> Q(end-2:end,end-1:end)ans =

9 102 202 203 30

>> Q(end-1,:)ans =

6 1 2 20

3.9 Deleting Rows or Columns

To get rid of a row or column set it equal to the empty matrix [].

>> A = [1 2 3;4 5 6;7 8 9]A =

1 2 34 5 67 8 97 8 9


>> A(:,2) = [ ]A =

1 31 34 67 9

3.10 Transpose

To convert rows into columns use the transpose symbol ’ :

>> A’ans =ans =

1 4 73 6 9


>>B= [[1 2 3]’ [4 5 6]’]B =

1 42 52 53 6

Be careful when taking the transpose of complex matrices. The transpose operator takes the complex conjugate transpose. p p p j g p

If z is the matrix:1 0− i0 + 2i 1 + i0 + 2i 1 + i

then z’ is:1 0− 2i0 + i 1 − i .

To take the transpose without conjugating the complex elements, use the ’ operator In this case z ’ is:the . operator. In this case z. is:1 0 + 2i

0 − i 1 + i .


4. Graphics in MATLAB

0 . 5

1

0 1 2 3 4 5 6 7 8 9 1 0-1

-0 . 5

0

0 1 2 3 4 5 6 7 8 9 1 0

5

P e a k s

-3 -2 -1 0 1 2 3

-3-2

-10

12

3

-5

0

xy


figure Create a new figure

4.1 Main functions

subplot Create many axis

grid Display a grid

axis Define the limits of axis

hold Keep the plots

close Close figures

title Insert a title in the graphic

xlabelylabel Label the axisylabelzlabel

Label the axis

text, gtext Insert comment

legend Display a legend

To put mathematics in labels you can use matlab’s backslashnotation (familiar to users of the TEX typesetting system)


4.2 2D Graphics

PLOT(X Y) PLOT(X1 Y1 X2 Y2 X3 Y3 )

plot Sketch curves or clouds of points

semilogx Plot semi-logarithmic curves

PLOT(X,Y) or PLOT(X1,Y1,X2,Y2,X3,Y3,...)

semilogy

loglog Plot semi-logarithmic curves

polar Plot graphs in polar coordinates

plotyy Plot two curves in the same graph with their own axis systemplotyy Plot two curves in the same graph with their own axis system

ezplot Plot functions

ezpolar Plot functions in polar coordinates

zoom Graphic zoomzoom Graphic zoom

Plot symbols and colors may be obtained when we use one of the 4 first previous commands, by adding a string S in those commands. first previous commands, by adding a string S in those commands.

PLOT(X,Y,S) or PLOT(X1,Y1,S1,X2,Y2,S2,X3,Y3,S3,...)


0 . 8

1

>> x=linspace(1,10,20);>> y=sin(x);z=cos(x);>> plot(x,y,’-.',x,z,'r')- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

>> plot(x,y, . ,x,z, r )

1 2 3 4 5 6 7 8 9 1 0- 1

- 0 . 8

- 0 . 6

0

0 . 5

1

0

0 . 5

1

>> t = 0: 1:2*pi;

- 1 - 0 . 5 0 0 . 5 1- 1

- 0 . 5

- 1 - 0 . 5 0 0 . 5 1- 1

- 0 . 5

0 . 5

1

0 . 5

1

>> t = 0:.1:2*pi;>> subplot(2,2,1)>> plot(cos(t),sin(t))>> subplot(2,2,2)>> plot(cos(t),sin(2*t))

- 1 - 0 . 5 0 0 . 5 1- 1

- 0 . 5

0

- 1 - 0 . 5 0 0 . 5 1- 1

- 0 . 5

0>> subplot(2,2,3)>> plot(cos(t),sin(3*t))>> subplot(2,2,4)>> plot(cos(t),sin(4*t))


Symbol Color Symbol marker

4.3 Graphic symbols

y

y yellow

m magenta

c cyan

r red

+ plus

º circle

* star

· pointr red

g green

b blue

w white

k black

p

x X-mark

s square

d diamond

^ triangle upk black

Symbol Style

― solid

triangle up

v triangle down

> Triangle right

< Triangle left

p pentagramso d

: dotted

― · dashpot

― ― dashed

none no line

p pentagram

H hexagram

none no marker

none no line


4.4 Clearing the Figure Window

You can clear the plot window by typing clf, which stands for ‘clearYou can clear the plot window by typing clf, which stands for clearfigure’. To get rid of a figure window entirely, type close. To get rid ofall the figure windows, type close all. New figure windows can becreated by typing figure.

So far we have allowed matlab to choose the axes for our plots. You can change the axes in many ways:

4.5 Axes

axis([xmin xmax ymin ymax ]) sets the axes’ minimum and maximum values.

• axis square makes the axes the same length• axis equal makes the axes the same scale• axis tight sets the axes limits to the range of the data• axis auto allows matlab to choose axes limits• axis auto allows matlab to choose axes limits• axis off removes the axes leaving only the plotted data• axis on puts the axes back again


4.6 3D Graphics

1. Elementary commands (using matrix)plot3 Sketch linear curves and clouds of points

mesh Sketch a matrix under a meshed curve

surf Sketch a matrix under a surfaced curve

2. Elementary commands (math functions)ezplot3 Sketch 2D functions and parametric functions

h Sk t h 2D f ti d t i f ti d h d ezmesh Sketch 2D functions and parametric functions under a meshed curve

ezsurf Sketch 2D functions and parametric functions under a surfaced curve

3 Tools commands3. Tools commandshidden Transparent meshing

shading Color smoothing

light lightinglight lighting

colorbar Add a bar of color

colormap Table of color


Examples:

>> t=0:.1:2*pi;>>plot3(cos(3*t),sin(3*t),t)

>> [X,Y]=meshgrid(-10:10);>> Z=sqrt(X.^2+Y.^2);>> mesh(X,Y,Z)


An interesting function: peaks function

222222 )1(53)1(2 1)1(10)1(3 yxyxyx eeyxxexz −+−−−+−− −−−−−=3

)5

()( y

>> [X Y Z]=peaks;>> [X,Y,Z]=peaks;>> mesh(X,Y,Z)

>> [X Y Z]=peaks;>> [X,Y,Z]=peaks;>> surf(X,Y,Z)


h di i t>> shading interp

>> axis tight;

>> colorbar;


>> [X,Y,Z]=peaks;>> contour(X,Y,Z)

>> [X,Y,Z]=peaks;>> plot3(X,Y,Z)

>> [X,Y,Z]=peaks;>> surfc(X,Y,Z);( , , );>> shading flat;


Suppose we have the set of (X,Y) coordinates 1,1 1,2 1,3 1, 42,1 2,2 2,3 2, 4

( , )3 1 3 2 3 3 3 4

X Y

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟

( , )3,1 3, 2 3,3 3,44,1 4,2 4,3 4, 4⎜ ⎟⎜ ⎟⎝ ⎠

The (x,y) can be split into two matrices

⎛ ⎞ ⎛ ⎞1 2 3 41 2 3 41 2 3 4

X

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟

1 1 1 12 2 2 23 3 3 3

Y

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟1 2 3 4

1 2 3 4⎜ ⎟⎜ ⎟⎝ ⎠

3 3 3 34 4 4 4⎜ ⎟⎜ ⎟⎝ ⎠

This is meshgrid principle

>> x=[1:4];y=[1:4]; x [1:4];y [1:4];

>> [X,Y]=meshgrid(x,y)


4.7 Color Maps

• Matlab uses a matrix called colormap to color surfacesor images. or images. • The colormap is a list of triplets corresponding To the intensities between 0 and 1of the red, green and blue.

Red Green Blue Color0 0 0 Black

1 1 1 White

1 0 0 Red

0 1 0 Green

0 0 1 Blue

1 1 0 Yellow

1 0 1 Magenta

0 1 1 Cyan

G.5 .5 .5 Gray

.5 0 0 Dark red

1 .62 .4 Dark orange

You can create your own color maps or use any Matlab predefined color mapshsv hot gray bone copper pink white flag lines colorcube jet

prism cool autumn spring winter summer


Carry out the following commands and observe

>> peaks;>> Colormap(gray(8))

>> m=gray(8);>> Imagesc(Colormap(m))


4.8 Specialized graphs

Bars and surfacesbar vertical barsbar vertical bars

barh Horizontal bars

bar3 3D vertical bars

bar3h 3D Horizontal bars

area display surfaces

piespie Display a pie

pie3 Display a 3D pie

histogramshist Display an histogram of a certain distribution

Discrete datastem Display a sequence of discrete values

stem3 3D display

stairs Display stairs, echelons


vectorscompass Display vectors centered at 0

feather Display equally spaced vectors along an axis

quiver Display vectors in a plane

quiver3 Display vectors in a space

Level linesclabel Display level lines labels

contour Display level lines in a plane

3 Di l 3D l l licontour3 Display 3D level lines

contourf Display level lines by filling the spaces

61Introduction to MatlabIntroduction to Matlab>> t=[-2:2]’;>> y=[5 2 1;8 7 3; 9 8 7; 5 5 5; 4 3 2];

>> bar(t,y) >> bar(t,y,’stack’)

>> bar3(t,y) >> area(t,y)

>> pie([31 15 8]) >> hist(randn(1000,3))


5. Complement on Matrix manipulation

5.1 Relational operations Example

< > Less than/greater than

<= Less than or equal to

5.1 Relational operations >> A=rand(4,3)>> B=(A>.2)&(A<0.8)>> C=A.*B>> D=(A~=A(1 1))

>= Greater than or equal to

== Equal to

~= Not equal to

>> D=(A =A(1,1))

q

5.2 Logical operations

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

| or : Returns 1 for every element location that is true (nonzero) in either one or the other, or both arrays, and 0 for all other elements.

~ Not : Complements each element of the input arrayp p y

xor or (exclusif) : Returns 1 for every element location that is true (nonzero) in only one array, and 0 for all other elements.


5.3 Operator Precedence

• You can build expressions that use any combination of arithmetic, relational, and logicaloperators.p

• Precedence levels determine the order in which MATLAB evaluates an expression. Withineach precedence level, operators have equal precedence and are evaluated from left to right.

• The precedence rules for MATLAB operators are shown in this list, ordered from highestprecedence level to lowest precedence level:p p

1. Parentheses ()2. Transpose (.'), power (.^), complex conjugate transpose ('), matrix

power (^) power (^) 3. Unary plus (+), unary minus (-), logical negation (~)4. Multiplication (.*), right division (./), left division(.\), matrix

multiplication (*), matrix right division (/), matrix left division (\)p ( ), g (/), (\)

5. Addition (+), subtraction (-)6. Colon operator (:)7. Less than (<), less than or equal to (<=), greater than (>), greater than

or equal to (>=), equal to (==), not equal to (~=)8. Element-wise AND (&)9. Element-wise OR (|)


>> a|b&c is similar to >> a|(b&c) Built-in functions

>> A = [3 9 5];>> B = [2 1 5];>> C = A./B.^2C =

and(A,B) equivalent to A & Bor(A,B) equivalent to A | Bnot(A) equivalent to ~A

C 0.7500 9.0000 0.2000

>> C = (A./B).^2C C =

2.2500 81.0000 1.0000Returns 1 for a vector where all elements of the vector are true (nonzero), and 0 if all elements are not trueallReturns 1 for a vector where any element of the vector is true (nonzero), and 0 if no elements are true.anyand 0 if all elements are not true

Find indices and values of nonzero elementsfind

Note The all and any functions ignore any NaN values in the input arrays

Sort array elements in ascending or descending ordersort

Find indices and values of nonzero elementsfind


>> X = [1 0 4 3 0 0 0 8 6];>> X = [1 0 4 -3 0 0 0 8 6];>> indices = find(X)>> find(X > 2)>> find(X == 0)

5.4 some functions

mean Returns the mean values of the elements along different dimensions of an array

max, min Returns the largest (smallest) element along different dimensions of an array,

sum Return the sum of the elements along different dimensions of an array

diff Calculates differences between adjacent elements of a vector.diff

prod Returns the products of the elements

cumsum Returns the cumulative sum along different dimensions of an array.

cumprod Returns the cumulative product along different dimensions of an array.


examples

>> a=rand(1,5)>> max(a)

>> sort(a)>> sort(A)

examples

>> A=rand(3,6)>> max(A)>> max(max(A))

>> mean(a)>> mean(A)>> max(A)>> max(max(A))>> max(max(A))

d t( b) t th l d t f th t d bdot(a,b) returns the scalar product of the vectors a and b

Cross(a,b) returns the cross product of the vectors a and b.

>> a = [1 2 3]; b = [4 5 6];>> c = cross(a,b)>> d = dot(a b)>> d = dot(a,b)


The format Function : controls the numeric format of the valuesdisplayed by MATLAB. The function affects only how numbers are

5.4 Format functions

displayed by MATLAB. The function affects only how numbers aredisplayed, not how MATLAB computes or saves them.

>> x = [4/3 1.2345e-6]

format short 1.3333 0.0000

format short e 1.3333e+000 1.2345e-006

format short g 1.3333 1.2345e-006

format long 1.33333333333333 0.00000123450000

format long e 1.333333333333333e+000 1.234500000000000e-00

format long g 1.33333333333333 1.2345e-006

format bank 1.33 0.00

format rat 4/3 1/810045

Special Characters % : Insert comment line into code

>> x=[1:5] %create an row vector from 1 to 5 increment 1


6. M-Files

It is used for solving complicated problems. There are two different kinds of M-files: • Script M-files • Function M-files.

M files are ordinary text files containing MATLAB commands You can M-files are ordinary text files containing MATLAB commands. You can create and modify them using any text editor or word processor that is capable of saving files as plain ASCII text. (Such text editors include notepad in Windows or emacs, winedit, and vi in UNIX.) More p , , )conveniently, you can use the built-in Editor/Debugger, which you can start by typing edit, either by itself (to edit a new file) or followed by the name of an existing M-file in the current working directory. You can also use the File menu or the two leftmost buttons on the tool bar to start use the File menu or the two leftmost buttons on the tool bar to start the Editor/Debugger, either to create a new file or to open an existing file. Double-clicking on an M-file in the Current Directory browser will also open it in the Editor/Debugger


All Matlab commands, functions and operations can be done in an editortext file. To open an editor text file you click on the menu FILE/New oruse that matlab command >>edit

Once you have finished to type your commands you have to save it by giving it a name under extension .m

Matlab save all files in the default repertory C:\MATLAB7\work

>> Edit trial1.m % edit a Matlab file named trial1

Then type the following commands in this text editorx=[1:0.1:10];y=sin(x);plot(x,y,'r-.') and save the file trial1.m

To run a file in Matlab command window prompt we have to type thep p ypname of the file without its extension (Matlab recognize it)

Type in the Matlab window prompt>> trial


A sequence of instructions in a file is called a SCRIPT

(For the commentaries use % character)

If you want to see the command during the script carrying out you have to use the command

h / ff >> echo on/off

Exercise:

Type echo on on the MATLAB prompt and run the file trial1.m


A practical example :

Open a new file and call it Peaks1.mE t th f ll i d d th filEnter the following commands and run the file.subplot(2,1,1)rv=linspace(.3,1,50);thv=linspace(pi/4,5*pi/4,50);p (p / , p / , );[r,th]=meshgrid(rv,thv);x=r.*cos(th); y=r.*sin(th);plot(x,y,’.’)

Reopen the file Peaks1.m. Go to the end of the file and enter the following commandsubplot(2,1,2)

mesh(x,y,peaks(50)+10*x)

Carry out the fileCarry out the file.


Another example:

Create the file task1.m that contains the following script and execute it

echo on

% Turn on 15 digit display

format longformat long

x = [0.1, 0.01, 0.001];

y = sin(x)./x

% These values illustrate the fact that the limit of

% sin(x)/x as x approaches 0 is 1.

echo off

>> task1

If you use echo on in a script M-file, then MATLAB will also echo the comments, so they will appear in the Command Window.


7 F ti M fil7. Functions M-files

•Functions are m-files that can be used to extend the MATLAB language.

F i i d d•Functions can accept input arguments and produce output arguments.

•Many of MATLAB’s own commands are implemented as m-files;

Try typing >> type mean to see how MATLAB calculates the mean.Try typing type mean to see how MATLAB calculates the mean.

•Functions use variables that are local to themselves and do not appear

in the main workspace.

•Always the m-file has the name of the function

Syntax: function [u,v,…]=FunctionName(x,y,…)

output input


A l f f i

function x = quadratic(a,b,c)

An example of a function:

inputoutput

% QUADRATIC Find roots of a quadratic equation.%% X = QUADRATIC(A,B,C) returns the two roots of the% d ti ti A* ^2 + B* + Cn

taries

% quadratic equation y = A*x^2 + B*x + C.%% The roots are contained in X = [X1 X2].

Com

men

% S. MZIOU, October 2007

delta = 4*a*c;denom = 2*a;n

s denom = 2*a;rootdisc = sqrt(b.^2 - delta); % Root of the discriminantx1 = (-b + rootdisc)./denom;x2 = (-b - rootdisc)./denom;st

ruct

ion

x = [x1 x2];In


Function m-files must start with the word function, followed by theoutput variable(s), an equals sign, the name of the function, and theinput variable(s).

Functions do not have to have input or output arguments. If there ismore than one input or output argument they must be separated bymore than one input or output argument, they must be separated bycommas. If there are one or more input arguments, they must beenclosed in round brackets, and if there are two or more outputarguments, they must be enclosed in square brackets. The followingillustrate these points (they are all valid function definition lines):

f1. function [xx,yy,zz] = sphere(n)

2. function fancyplot

3. function a = lists(x,y,z,t)3. function a lists(x,y,z,t)


Function names must follow the same rules as variable names.

The file name is the function name with “.m” appended.

If the file name and the function name are different, MATLAB uses the

file name and ignores the function name file name and ignores the function name.

You should use the same name for both the function and the file to avoid

confusion.

Following the function definition line you should put comment lines

that explain how to use the function. These comment lines are printed in

th d i d h t h l f ll d b th fil the command window when you type help followed by the m-file name

at the prompt:


>> help quadratic

QUADRATIC Find roots of a quadratic equationQUADRATIC Find roots of a quadratic equation.X = QUADRATIC(A,B,C) returns the two roots of the quadratic equationy = A*x^2 + B*x + C.The roots are contained in X = [X1 X2]

MATLAB only echoes the comment lines that are contiguous; the firstno comment line, in this case the blank line before the signature, tellsMATLAB that the help comments have ended. The first line of the helpcomments is searched and if successful displayed when you type acomments is searched and, if successful, displayed when you type alookfor command.

Comment lines can appear anywhere in the body of an m-file.Comments can be put at the end of a line of code: For instance

rootdisc = sqrt(b.^2 - delta); % Root of the discriminant

Blank lines can appear anywhere in the body of an m-file Apart fromBlank lines can appear anywhere in the body of an m-file. Apart fromending the help comment lines in a function, blank lines are ignored.


d l f ( )/ h b f l lwe computed some values of sin(x)/x with x = 10−b for several values of b. Suppose, in addition, that you want to find the smallest value of b for which sin(10−b)/(10−b) and 1 agree to 15 digits. Here is a function M-file called sinelimit.m designed to solve that problem:M file called sinelimit.m designed to solve that problem:

function y = sinelimit(c)% SINELIMIT computes sin(x)/x for x = 10ˆ(-b),% h b 1 % where b = 1, ..., c.format longb = 1:c;x = 10.ˆ(-b);( );y = (sin(x)./x)’;


8. Flow Control

MATLAB has four kinds of statements you can use to control the flowthrough your code:

If, else, elseif, end : execute statements based on a logical test

Switch, case, otherwise, end: execute groups of statements based

on a logical test

While, end: execute statements an indefinite number of times, based

l i l t ton a logical test

For, end: execute statements a fixed number of times


If, Else, Elseif, end

The general form is:

The basic form is

if testStatements

if test1Statements1

elseif test2statements2Statements

endstatements2

elsedefault statements

end

The test is an expression that is either 1 (true) or 0 (false). Thestatements between the if and end statements are executed if the test istrue. If the test is false the statements will be ignored and execution willresume at the line after the end statement. The test expression can be avector or matrix, in which case all the elements must be equal to 1 forthe statements to be executed. Further tests can be made using theelseif and else statementselseif and else statements.


Examples

If (x>=0)z=x;

Elsez=-x


Switch

The basic form of a switch statement is:The basic form of a switch statement is:switch testcase result1

statementscase result2

statements. The respective statements are executed if the

value of test is equal to the respective results...otherwise

statementsd

q pIf none of the cases are true, the otherwisestatements are done. Only the first matchingcase is carried out. If you want the samestatements to be done for different cases youend statements to be done for different cases, youcan enclose the several results in curlybrackets:


Example:

switch xcase 1disp(’x is 1’)case {2 3 4}case {2,3,4}disp(’x is 2, 3 or 4’)case 5disp(’x is 5’)otherwisedisp(’x is not 1, 2, 3, 4 or 5’)end


While

The basic form of a while loop iswhile test

statementsend

The statements are executed repeatedly while the value of test isequal to 1. For example, to find the first integer n for which 1+2+…+nis greater than 1000:

n = 1;while sum(1:n)<=1000while sum(1:n)< 1000n = n+1;end


For

The basic form of a for loop is:

for index = start:increment:stopstatements

endend

You can omit the increment, in which case an increment of 1 is assumed.ou ca o t t e c e e t, c case a c e e t o s assu edThe increment can be positive or negative. During the first pass throughthe loop the index will have the value start . The index will be increased by increment during each successive pass until the indexexceeds the value stop exceeds the value stop .


The following example produces views of thepeaks function from many angles:

clfcolormap(gray)plotnum = 1;z = peaks(20);for az = 0:10:350subplot(6,6,plotnum)subplot(6,6,plotnum)surfl(z),shading flatview(az,30)axis tight

i ffaxis offplotnum = plotnum + 1;end


Vectorised Code

MATLAB is a matrix language, and many of its algorithms are optimisedfor matrices. MATLAB code can often be accelerated by replacing forand while loops with operations on matrices.

In the following example, we calculate the factorial of the numbers from 1 to 500 using a for loop. Create a script m-file called factorialloop.mthat contains thefollowing code:

for number = 1:500fact = 1;fact 1;for i = 2:numberfact = fact*i;end( b ) f ty(number) = fact;

end


We can time how long this program takes to run by using the stopwatchWe can time how long this program takes to run by using the stopwatchfunctions tic and toc:

>> tic;factorialloop;toc

elapsed_time =4.6332 Which is the time in seconds.

The same calculation can be done in much less time by replacing the internal for loop by the prod function. Create an m-file called factorialvect.m:

for number = 1:500y(number) = prod(1:number);

end

This version takes about a tenth of the time:

>> clear>> clear>> tic;factorialvect;tocelapsed_time =0.4331


Further increases in speed can be achieved by pre-allocating the outputmatrix y. If we have an m-file called factorialpre.m:

y = zeros (1,500);for number = 1:500y(number) = prod(1:number);y(number) = prod(1:number);end

the execution time is about 10% faster:

>> clear>> tic;factorialpre;tocelapsed time =elapsed_time0.3752


Graphics objects are the basic drawing elements used by MATLAB to

#. The notion of object

p j g ydisplay data. Each instance (figures, axis, lines, texts,…) of an object isassociated with a unique identifier called a handle. Using this handle, youcan manipulate the characteristics (called object properties) of anexisting graphics object You can also specify values for properties whenexisting graphics object. You can also specify values for properties whenyou create a graphics object.

•Two main functions

set: Find out about state of the objectt Ch th ti f th bj tget: Change the properties of the object

The basic syntax for setting the value of a property on an existing object is set(object_handle,'PropertyName','NewPropertyValue')

To query the current value of a specific object's property, use a statement like returned_value = get(object_handle,'PropertyName');


•Three major object_handle

gcf : get current figuregca: get current axisgco: get current object

>> t=linspace(0,10,50)>> t linspace(0,10,50)>> plot(t,sint)

Assume that we want to plot the points themselves aswell as the line joining them.a) One solution is to clear the figure and to type thefollowing command:>> plot(t,sint,’-o’)

b) Another solution is to to handle all elements of the figure as objects>> h=get(gca,’children’)>> set(h,’marker’,’o’)

Basics on MATLABsamymziouimamcourses.weebly.com/uploads/2/7/8/4/... · MATLAB has excellent...

Documents

Transcript of Basics on MATLABsamymziouimamcourses.weebly.com/uploads/2/7/8/4/... · MATLAB has excellent...