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Lecture 6 Sept 15, 09 Goals:PowerPoint Presentation

Lecture 6 Sept 15, 09 Goals:

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- Lecture 6 Sept 15, 09
- Goals:
- two-dimensional arrays
- matrix operations
- circuit analysis using Matlab
- image processing – simple examples

4.2. Matrices Sept 15, 09

Example: The following 2 x 3 matrix (matA) can be created in Matlab as follows:

Dimension of a matrix can be accessed by function called size.

Accessing and modifying array elements Sept 15, 09

Accessing and modifying array elements Sept 15, 09

Accessing and modifying array elements Sept 15, 09

Matrix operations Sept 15, 09

Matrix addition, multiplication, inverse, determinant etc.

Matrix operations Sept 15, 09

Matrix addition, multiplication, inverse, determinant, transpose etc.

Logical indexing in 2-dim matrices Sept 15, 09

Exercise: Solve a linear system of equations: Sept 15, 09

3x + 5y – 6z= 11

4x – 6y + z = 9

-2x + 3y + 5z = –13

Example 2 Sept 15, 09

Sum, max, min, size etc. Sept 15, 09

4.3. Mixed Data Types Sept 15, 09

Structure is variable that can hold a group of data (of different types).

Example:

Array of structures Sept 15, 09

Example:

Cell arrays Sept 15, 09

A cell array is like a vector, except that each member need not be all of the same type.

Images as arrays Sept 15, 09

Images as arrays Sept 15, 09

Numerical representation of

array (gray scale image)

Visual representation

Reading and opening an image Sept 15, 09

Selecting a subimage Sept 15, 09

Just like we can copy a part of an array into another array, we can copy a part of one image and create a new image.

Changing some pixel values in an image Sept 15, 09

- Saving images in different formats Sept 15, 09
- Image formats:
- jpeg, bmp, png etc.
- >> imwrite(I, ‘king.bmp’)
- will save I in bmp format.

image rotation Sept 15, 09

Exercise: Write a one-line statement in Matlab that will rotate an image by 180 degrees.

image rotation Sept 15, 09

Exercise: Write a one-line statement in Matlab that will rotate an image by 180 degrees.

image rotation Sept 15, 09

Exercise: Write a one-line statement in Matlab that will rotate an image by 180 degrees.

>> J = I(size(I,1):-1:1, :, :);

Discussions and exercises, Chapter 4 Sept 15, 09

Exercise 4.1

- Exercise 4.2 Sept 15, 09
- Write statements to do the following operations on a vector x:
- Return the odd indexed elements.

Exercise 4.2 Sept 15, 09

Write statements to do the following operations on a vector x:

2) Return the first half of x.

Exercise 4.2 Sept 15, 09

Write statements to do the following operations on a vector x:

3) Return the vector in the reverse order.

Exercise 4.3 Sept 15, 09

Given a vector v, and a vector k of indices, write a one or two statement code in Matlab that removes the elements of v in positions specified by k.

Example:

>> v = [1, 3, 5, 7, 11, 9, 19]

>> k = [2, 4, 5]

>> < your code here>

>> v

ans =

1, 5, 9, 19

Exercise 4.3 Sept 15, 09

Given a vector v, and a vector k of indices, write a one or two statement code in Matlab that removes the elements of v in positions specified by k.

Exercise 4.5. (This is a bit tricky, especially without using a loop construct like while or for.)

Write a statement to return the elements of a vector randomly shuffled.

Hint provided is a useful one.

First understand how sort function works.

Reshaping Arrays using a loop construct like

- Arrays are actually stored in column order in Matlab. So internally, a 2 × 3 array is stored as a column vector:A(1,1)
A(2,1)

A(1,2)

A(2,2)

A(1,3)

A(2,3)

- Any n × m array can be reshaped into any p × q array as long as n*m = p*q using the reshape function.

Summary using a loop construct like

This chapter introduced you to vectors and arrays. For each collection, you saw how to:

■ Create them by concatenation and a variety of special-purpose functions

■ Access and remove elements, rows, or columns

■ Perform mathematical and logical operations on them

■ Apply library functions, including those that summarize whole columns or rows

■ Move arbitrary selected rows and columns from one array to another

■ image – how to create them, open them, change etc.

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