Lecture 6                                                   Sept 15, 09
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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 Example: The following 2 x 3 matrix (matA) can be created in Matlab as follows:.

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Lecture 6 sept 15 09 goals

  • Lecture 6 Sept 15, 09

  • Goals:

  • two-dimensional arrays

  • matrix operations

  • circuit analysis using Matlab

  • image processing – simple examples


Lecture 6 sept 15 09 goals

4.2. Matrices

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.


Lecture 6 sept 15 09 goals

Accessing and modifying array elements


Lecture 6 sept 15 09 goals

Accessing and modifying array elements


Lecture 6 sept 15 09 goals

Accessing and modifying array elements


Lecture 6 sept 15 09 goals

Matrix operations

Matrix addition, multiplication, inverse, determinant etc.


Lecture 6 sept 15 09 goals

Matrix operations

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


Lecture 6 sept 15 09 goals

Logical indexing in 2-dim matrices


Lecture 6 sept 15 09 goals

Exercise: Solve a linear system of equations:

3x + 5y – 6z= 11

4x – 6y + z = 9

-2x + 3y + 5z = –13


Lecture 6 sept 15 09 goals

Example 2


Lecture 6 sept 15 09 goals

Sum, max, min, size etc.


Lecture 6 sept 15 09 goals

4.3. Mixed Data Types

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

Example:


Lecture 6 sept 15 09 goals

Array of structures

Example:


Lecture 6 sept 15 09 goals

Cell arrays

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


Lecture 6 sept 15 09 goals

Images as arrays


Lecture 6 sept 15 09 goals

Images as arrays

Numerical representation of

array (gray scale image)

Visual representation


Lecture 6 sept 15 09 goals

Reading and opening an image


Lecture 6 sept 15 09 goals

Selecting a subimage

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.


Lecture 6 sept 15 09 goals

Changing some pixel values in an image


Lecture 6 sept 15 09 goals

  • Saving images in different formats

  • Image formats:

  • jpeg, bmp, png etc.

  • >> imwrite(I, ‘king.bmp’)

  • will save I in bmp format.


Lecture 6 sept 15 09 goals

image rotation

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


Lecture 6 sept 15 09 goals

image rotation

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


Lecture 6 sept 15 09 goals

image rotation

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

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


Lecture 6 sept 15 09 goals

Discussions and exercises, Chapter 4

Exercise 4.1


Lecture 6 sept 15 09 goals

  • Exercise 4.2

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

  • Return the odd indexed elements.


Lecture 6 sept 15 09 goals

Exercise 4.2

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

2) Return the first half of x.


Lecture 6 sept 15 09 goals

Exercise 4.2

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

3) Return the vector in the reverse order.


Lecture 6 sept 15 09 goals

Exercise 4.3

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


Lecture 6 sept 15 09 goals

Exercise 4.3

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.


Lecture 6 sept 15 09 goals

Exercise 4.4 what does Matlab output for the following commands?

1) 6 ~= 1 : 10

2) (6 ~= 1) : 10


Lecture 6 sept 15 09 goals

Exercise 4.4 what does Matlab output for the following commands?

1) 6 ~= 1 : 10

2) (6 ~= 1) : 10


Lecture 6 sept 15 09 goals

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

Reshaping Arrays

  • 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

Summary

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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