By Muhammad Rizwan I060388 For Section A&B C&D

INTRODUCTION TO MATLAB

INTRODUCTION TO MATLAB

MATLAB It stands for MATrix LABoratory It is developed by The Mathworks, Inc . (http://www.mathworks.com) It is widely used in mathematical computation Numerical Computation Linear Algebra Matrix Computations Simple Calculations Scripting Graphing

It stands for MATrix LABoratory

It is developed by The Mathworks, Inc . (http://www.mathworks.com)

It is widely used in mathematical computation

Numerical Computation

Linear Algebra

Matrix Computations

Simple Calculations

Scripting

Graphing

Typical Uses • Math and computation • Algorithm development • Modeling, simulation, and prototyping • Data analysis, exploration, and visualization • Scientific and engineering graphics • Application development, including graphical user interface building

• Math and computation

• Algorithm development

• Modeling, simulation, and prototyping

• Data analysis, exploration, and visualization

• Scientific and engineering graphics

• Application development, including graphical user interface building

Starting MATLAB To start MATLAB, double-click the MATLAB shortcut or Click on “Start” and then on “Run” and write ‘matlab’ and then press OK It will take some seconds and then matlab starts

To start MATLAB, double-click the MATLAB shortcut

or

Click on “Start” and then on “Run” and write ‘matlab’ and then press OK

It will take some seconds and then matlab starts

Quitting MATLAB To end your MATLAB session, select Exit MATLAB from the File menu. or type quit or exit in the Command Window. There are different type of windows Command Window Editor Window (M-File) Figure Window GUI (Graphical User Interface)

To end your MATLAB session, select Exit MATLAB from the File menu.

or type quit or exit in the Command Window.

There are different type of windows

Command Window

Editor Window (M-File)

Figure Window

GUI (Graphical User Interface)

Operations Performed A+B A-B A*B C’ B=C A ,B ,C are variables

A+B

A-B

A*B

C’

B=C

A ,B ,C are variables

MATLAB Variables Scalar A = 4 Vector A = [2 3 4] Matrices A=

Scalar

A = 4

Vector

A = [2 3 4]

Matrices

A=

Numbers & Formats Matlab recognizes several dierent kinds of numbers

Matlab recognizes several dierent kinds of numbers

Format Set display format for output

Format Syntax format type format('type') Both types can be used for same purpose To see current format write get(0,'format')

Syntax

format type

format('type')

Both types can be used for same purpose

To see current format write get(0,'format')

Some Basics Can act as a calculator x = 3-2^4 Variable names Legal names consist of any combination of letters and digits, starting with a letter. These are allowable: NetCost, Left2Pay, x3, X3, z25c5 These are not allowable: Net-Cost, 2pay, %x, @sign

Can act as a calculator

x = 3-2^4

Variable names

Legal names consist of any combination of letters and digits, starting with a letter.

These are allowable:

NetCost, Left2Pay, x3, X3, z25c5

These are not allowable:

Net-Cost, 2pay, %x, @sign

Input and Output (Contd) V=[1 1/2 1/6 1/12] [1 3 5] row vector [1 3 5]’ [1;3;5] column vector [1;3;5]’ [1 3 5;7 8 4] Matrix

V=[1 1/2 1/6 1/12]

[1 3 5] row vector

[1 3 5]’

[1;3;5] column vector

[1;3;5]’

[1 3 5;7 8 4] Matrix

Input and Output size(A) //return size of a matrix Seeing a matrix A(2,3) //returns element at 2,3 position A(2,:) // returns 2 nd row A(:,3) //returns 3 rd coloumn

size(A) //return size of a matrix

Seeing a matrix

A(2,3) //returns element at 2,3 position

A(2,:) // returns 2 nd row

A(:,3) //returns 3 rd coloumn

Matrix Operations A+B A-B A*B b*A // b is a vector either row or column vector Transpose of a matrix C’ B=C’

A+B

A-B

A*B

b*A // b is a vector either row or column vector

Transpose of a matrix

C’

B=C’

Matrix Operations (Contd) Augmented matrix [B b] [A;C] [C A;A C] Diagonal matrix D=diag([1 2 3]) // create diagonal matrix Diag(D) // return diagonal diag(diag(D)) what it can do?

Augmented matrix

[B b]

[A;C]

[C A;A C]

Diagonal matrix

D=diag([1 2 3]) // create diagonal matrix

Diag(D) // return diagonal

diag(diag(D)) what it can do?

Matrix Powers Product of A with itself k If A is square matrix and k is positive integer >>A^k Displaying an Identity Matrix having the same size as A >>A^0 Identity Matrix >>eye(3) >>t=10; eye(t) >>eye(size(A)) display an Identity Matrix the same size as A

Product of A with itself k

If A is square matrix and k is positive integer

>>A^k

Displaying an Identity Matrix having the same size as A

>>A^0

Identity Matrix

>>eye(3)

>>t=10; eye(t)

>>eye(size(A)) display an Identity Matrix the same size as A

Some Basics (Contd) shortcut for producing row vectors: 1:4 1:3:20 Plotting a graph x = linspace (0,1,10); // from 0 to 1 divide in 10 parts y = sin(3*pi*x); plot(x,y)

shortcut for producing row vectors:

1:4

1:3:20

Plotting a graph

x = linspace (0,1,10); // from 0 to 1 divide in 10 parts

y = sin(3*pi*x);

plot(x,y)

Script M-Files typing at the Matlab becomes tedious, when number of commands increases, want to change the value of one or more variables, re evaluate a number of commands, typing at the Matlab becomes tedious.

typing at the Matlab becomes tedious, when

number of commands increases,

want to change the value of one or more variables,

re evaluate a number of commands,

typing at the Matlab becomes tedious.

Script M-Files Script File: Group of Matlab commands placed in a text file with a text editor. Matlab can open and execute the commands exactly as if they were entered at the Matlab prompt. The term “script” indicates that Matlab reads from the “script” found in the file. Also called “M-files,” as the filenames must end with the extension ‘.m’, e.g. example1.m.

Script File: Group of Matlab commands placed in a text file with a text editor.

Matlab can open and execute the commands exactly as if they were entered at the Matlab prompt.

The term “script” indicates that Matlab reads from the “script” found in the file. Also called “M-files,” as the filenames must end with the extension ‘.m’, e.g. example1.m.

Script M-Files choosing New from the File menu in the Matlab Command window and selecting M-file . Create the file named add.m in your present working directory using a text editor:

choosing New from the File menu in the Matlab Command window and selecting M-file .

Create the file named add.m in your present working directory using a text editor:

Add.m % comments a=1 b=2 d=a-b; c=a+b

% comments

a=1

b=2

d=a-b;

c=a+b

add.m Save as add.m To execute the script M-file, simply type the name of the script file add at the Matlab prompt: • % allows a comment to be added Open your script file Why result of d is not in the screen ? c Compute and display add

Save as add.m

To execute the script M-file, simply type the name of the script file add at the Matlab prompt:

• % allows a comment to be added

Open your script file

Why result of d is not in the screen ?

c Compute and display add

Matlab functions useful in M-files: Take input from user and show result disp(ans) Display results without identifying variable names input(’prompt’) Prompt user with text in quotes, accept input until “Enter” is typed

Take input from user and show result

disp(ans) Display results without identifying variable names

input(’prompt’) Prompt user with text in quotes, accept input until “Enter” is typed

Matlab functions useful in M-files: The input command is used for user input of data in a script and it is used in the form of an assignment statement. For example: a = input(‘Enter quadratic coefficient a: ‘); disp('Value of first quadratic root: ')

The input command is used for user input of data in a script and it is used in the form of an assignment statement. For example:

a = input(‘Enter quadratic coefficient a: ‘);

disp('Value of first quadratic root: ')

M-Files M-files can be either scripts or functions. Scripts are simply files containing a sequence of MATLAB statements. Functions make use of their own local variables and accept input arguments.

M-files can be either

scripts or

functions.

Scripts are simply files containing a sequence of MATLAB statements.

Functions make use of their own local variables and accept input arguments.

Functions Format function [x, y] = myfun(a, b, c) % Function definition a , b , c are input parameters and x , y are output parameters

function [x, y] = myfun(a, b, c) % Function definition

a , b , c are input parameters and x , y are output parameters

Functions function [output_parameter_list] = function_name(input_parameter_list) The first word must always be ``function''. Following that, the (optional) output parameters are enclosed in square brackets [ ]. If the function has no output_parameter_list the square brackets and the equal sign are also omitted. The function_name is a character string that will be used to call the function. The function_name must also be the same as the file name (without the ``.m'') in which the function is stored. In other words the MATLAB function, ``foo'', must be stored in the file, ``foo.m''.

function [output_parameter_list] = function_name(input_parameter_list)

The first word must always be ``function''.

Following that, the (optional) output parameters are enclosed in square brackets [ ].

If the function has no output_parameter_list the square brackets and the equal sign are also omitted.

The function_name is a character string that will be used to call the function.

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

In other words the MATLAB function, ``foo'', must be stored in the file, ``foo.m''.

addtwo.m // without output parameters function addtwo(x,y) % addtwo(x,y) Adds two numbers, vectors, whatever, and % print the result = x + y x+y

addtwo.m // without output parameters

function addtwo(x,y)

% addtwo(x,y) Adds two numbers, vectors, whatever, and

% print the result = x + y

x+y

Elementary Math Functions >> abs(x) % absolute value of x >> exp(x) % e to the x-th power >> fix(x) % rounds x to integer towards 0 >> log10(x) % common logarithm of x to the base 10 >> rem(x,y) % remainder of x/y >> sqrt(x) % square root of x >> sin(x) % sine of x; x in radians >> acoth(x) % inversion hyperbolic cotangent of x >> help elfun % get a list of all available elementary functions

>> abs(x) % absolute value of x

>> exp(x) % e to the x-th power

>> fix(x) % rounds x to integer towards 0

>> log10(x) % common logarithm of x to the base 10

>> rem(x,y) % remainder of x/y

>> sqrt(x) % square root of x

>> sin(x) % sine of x; x in radians

>> acoth(x) % inversion hyperbolic cotangent of x

>> help elfun % get a list of all available elementary functions

Flow Control If Conditionally execute statements Syntax: if expression statements end expression is a MATLAB expression, usually consisting of variables or smaller expressions joined by relational operators (e.g., count < limit), or logical functions (e.g., isreal(A)). statements is one or more MATLAB statements to be executed only if the expression is true or nonzero.

If

Conditionally execute statements

Syntax:

if expression

statements

end

expression is a MATLAB expression, usually consisting of variables or smaller expressions joined by relational operators (e.g., count < limit), or logical functions (e.g., isreal(A)).

statements is one or more MATLAB statements to be executed only if the expression is true or nonzero.

Logical comparisons

MATLAB supports these variants of the ``if'' construct if ... end if ... else ... end if ... elseif ... else ... end

MATLAB supports these variants of the ``if'' construct

if ... end

if ... else ... end

if ... elseif ... else ... end

if ... end >> d = b^2 - 4*a*c; >> if d<0 >> disp('warning: discriminant is negative, roots are imaginary'); >> end

>> d = b^2 - 4*a*c;

>> if d<0

>> disp('warning: discriminant is

negative, roots are imaginary');

>> end

if ... else ... end >> d = b^2 - 4*a*c; >> if d<0 >> disp('warning: discriminant is negative, roots are imaginary'); >> else >> disp('OK: roots are real, but may be repeated'); >> end

>> d = b^2 - 4*a*c;

>> if d<0

>> disp('warning: discriminant is

negative, roots are imaginary');

>> else

>> disp('OK: roots are real, but may be

repeated');

>> end

if ... elseif ... else ... end >> d = b^2 - 4*a*c; >> if d<0 >> disp('warning: discriminant is negative, roots are imaginary'); >> elseif d==0 >> disp('discriminant is zero, roots are repeated'); >> else >> disp('OK: roots are real and distinct'); >> end

>> d = b^2 - 4*a*c;

>> if d<0

>> disp('warning: discriminant is negative,

roots are imaginary');

>> elseif d==0

>> disp('discriminant is zero, roots are

repeated');

>> else

>> disp('OK: roots are real and distinct');

>> end

for for variable = expression statement ... statement End Example for i = 1:m for j = 1:n H(i,j) = 1/(i+j); end end

for variable = expression

statement

...

statement

End

Example

for i = 1:m

for j = 1:n

H(i,j) = 1/(i+j);

end

end

Note no semicolon is needed to suppress output at the end of lines containing if, else, elseif or endif elseif has no space between ``else'' and ``if'' the end statement is required the ``is equal to'' operator has two equals signs Indentation of ``if'' blocks is not required, but considered good style.

no semicolon is needed to suppress output at the end of lines containing if, else, elseif or endif

elseif has no space between ``else'' and ``if''

the end statement is required

the ``is equal to'' operator has two equals signs

Indentation of ``if'' blocks is not required, but considered good style.

while constructs Repeat statements an indefinite number of times Syntax: while expression do something end where ``expression'' is a logical expression. The ``do something'' block of code is repeated until the expression in the while statement becomes false.

Repeat statements an indefinite number of times

Syntax:

while expression

do something

end

where ``expression'' is a logical expression. The ``do something'' block of code is repeated until the expression in the while statement becomes false.

Example while i = 2; while i<8 i = i + 2 end Output: i = 4 i = 6 i = 8

i = 2;

while i<8

i = i + 2

end

Output:

i = 4

i = 6

i = 8

Graphics MATLAB is an interactive environment in which you can program as well as visualize your computations. It includes a set of high-level graphical functions for: Line plots (plot, plot3, polar) Bar graphs (bar, barh, bar3, bar3h, hist, rose, pie, pie3) Surface plots (surf, surfc) Mesh plots (mesh, meshc, meshgrid) Contour plots (contour, contourc, contourf) Animation (moviein, movie)

MATLAB is an interactive environment in which you can program as well as visualize your computations.

It includes a set of high-level graphical functions for: Line plots (plot, plot3, polar)

Bar graphs (bar, barh, bar3, bar3h, hist, rose, pie, pie3) Surface plots (surf, surfc)

Mesh plots (mesh, meshc, meshgrid)

Contour plots (contour, contourc, contourf)

Animation (moviein, movie)

Line Plots Note: You can also set properties means line size, color, text show ,grid , axis etc. For this I will place some reference code observe it >> t = 0:pi/100:2*pi; >> y = sin(t); >> plot(t,y)

Note:

You can also set properties means line size, color, text show ,grid , axis etc.

For this I will place some reference code observe it

>> t = 0:pi/100:2*pi;

>> y = sin(t); >>

plot(t,y)

Bar Graphs >> x = magic(3) // creat 3x3 matrix >>x = 8 1 6 3 5 7 4 9 2 >> bar(x) >> grid

>> x = magic(3) // creat 3x3 matrix

>>x = 8 1 6 3 5 7 4 9 2

>> bar(x)

>> grid

Surface Plots >> Z = peaks; // already implemented function >> surf(Z)

>> Z = peaks; // already implemented function

>> surf(Z)

Explore it yourself

See Mat lab libraries in C:Program FilesMATLABR2006b oolbox See Help Menu

Thanks for your patience

Write a script file which have any mathematical function and write an other script file in which you use this function and apply Newton-Raphson method on it , also draw it.

Write a script file which have any mathematical function and write an other script file in which you use this function and apply Newton-Raphson method on it , also draw it.

Write a script file which have any mathematical function and write an other script file in which you use this function and apply Regula-falsi method on it , also draw it.

Write a script file which have any mathematical function and write an other script file in which you use this function and apply Regula-falsi method on it , also draw it.