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Lecture 6 Sept 15, 09

- Goals:
- two-dimensional arrays
- matrix operations
- circuit analysis using Matlab
- image processing – simple examples

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.

Matrix addition, multiplication, inverse, determinant etc.

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

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

Example:

Example:

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

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.

Saving images in different formats

- Image formats:
- jpeg, bmp, png etc.
- >> imwrite(I, ‘king.bmp’)
- will save I in bmp format.

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

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

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

Exercise 4.1

- Write statements to do the following operations on a vector x:
- Return the odd indexed elements.

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

2) Return the first half of x.

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

3) Return the vector in the reverse order.

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

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

- 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

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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