matab no2

M-files and Matrix operations

Designed by : Dawar [email protected]

March – July 2012CECOS College of Engineering and IT

Lab No.02


Matrices

MATLAB treats every thing as a matrix (check the Workspace)

1-by-1 matrices are interpreted as scalars

Matrices with only one row or one column are known as vectors

A matrix is a rectangular array of numbers.

1 9 2 6

7 8 3 5

1 8 2 4

A matrix with 3 rows, 4 columns, and 12 elements


Defining matrices

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

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

and

>> A = [ 1 2 3

4 5 6

7 8 9 ];

Defines A =

1 2 3

4 5 6

7 8 9


Accessing matrix elements

The matrix element located in the i-th row and j-th column of

“A” is referred to as, A(i,j)

Try the following instruction and observe the change in “A”

>> A(2,3) = 10


Some Built-in matrix functions

Function Description

diag : returns diagonal elements as vectoreye : identity matrixmagic : magic squareones : matrix of onesrand : randomly generated matrixtriu : upper triangular part of a matrixtril : lower triangular part of a matrixzeros : matrix of zerossize : Number of rows and columns in a matrixlength : Length of an array find : find indices of some elements in array


Matrix functions : Examples>> a=[1 2 3;4 5 6;7 8 9]

a =

1 2 34 5 67 8 9

>> triu(a)

ans =

1 2 30 5 60 0 9

>> tril(a)

ans =

1 0 04 5 07 8 9

>> size(a)

ans =

3 3

>> length(a)

ans =

3

>> diag(a)

ans =

159


Matrix functions : Examples

>> eye(3)

ans =

1 0 00 1 00 0 1

>> magic(3)

ans =

8 1 63 5 74 9 2

>> ones(3)

ans =

1 1 11 1 11 1 1

>> ones(3,2)

ans =

1 11 11 1

>> rand(3)

ans =

0.8147 0.9134 0.27850.9058 0.6324 0.54690.1270 0.0975 0.9575

>> zeros(3)

ans =

0 0 00 0 00 0 0

>> zeros(3,2)

ans =

0 00 00 0


Matrix functions : Examples

>> rand(3,2)

ans =

0.9649 0.95720.1576 0.48540.9706 0.8003


Matrix operations

+ => Addition - => Subtraction * => Multiplication ^ => Power' => Conjugate transpose/ => Division

To perform index by index operation, use dot (.) notation

./ => Index by index division

.* => Index by index multiplication

.^ => Index by index power

. ' => Non conjugate transpose


Dot notation

Observe the change in result due to the “dot”


Examples/Exercise

A+B, A’, A*B, 2*A, A/2, A/B, A./B, C/D, C./D, C*D, C.*D, C^2, C.^2

A =

1 2 34 5 67 8 9

B =

1 1 12 2 23 3 3

C =

1 2 1 2

D =

2 1 2 1

Practice the following matrix operations


Colon notation


M - files

M-files are script/text files containing MATLAB commands

Script M-file

Function M-file

To make a script M-file, you need to open a file using the built-in

MATLAB editor.

There are two ways to accomplish it:

1. From file menu, click NEW

2. Type edit on command line


M - files

To save the M-file go to the “file” menu and click on “save”.

The name should not contain spaces, should not start with a number and should not

be same as any built-in function.

The extension of this file should be “.m”


M - files

This code can now be executed in two ways

1. Write the name of file on command window

(excluding “.m”)

2. Under the “debug” menu, click “Run”

The variables used in the M-file will be maintained in the workspace

and hence accessible from the command window.


M - files

Code written in M-file to calculate various parameters of a circle

Check the values of the variables after running the M-file


Comments

While writing any code, it’s a good practice to write proper comments

against each instruction.

In MATLAB, any thing written after “%” is treated as a comment and is

ignored by the compiler.


Function M-files

User defined functions

These M-files start with a keyword, “function”

The first line of these files should look like

function[output variables]=functionName(input variables)

These files are saved with the funtionName.m as file name.

An example:


Function M-files

Calling this function from command window


Function M-files

Any comments after the first line becomes the help for that function

Command window


Tasks

1- Generate a vector of 50 elements having random values between 0

and 50.

2- Generate a vector, containing all the odd numbers between 0 and

100.

3- Create a function M-file that accepts two numbers and generates

there sum, product and difference as output.

4- Use Cramer's rule to solve the following set of equations.

3x1 - 1x2 + 0x3 = 11x1 + 4x2 - 2x3 = 50x1 - 2x2 + 8x3 = 6

matab no2

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