Lecture 6 Sept 15, 09 Goals:

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

2. 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.

3. Accessing and modifying array elements

4. Accessing and modifying array elements

5. Accessing and modifying array elements

6. Matrix operations Matrix addition, multiplication, inverse, determinant etc.

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

8. Logical indexing in 2-dim matrices

10. Exercise: Solve a linear system of equations: 3x + 5y – 6z= 11 4x – 6y + z = 9 -2x + 3y + 5z = –13

11. Example 2

13. Sum, max, min, size etc.

14. 4.3. Mixed Data Types Structure is variable that can hold a group of data (of different types). Example:

15. Array of structures Example:

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

17. Images as arrays

18. Images as arrays Numerical representation of array (gray scale image) Visual representation

19. Reading and opening an image

20. 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.

21. Changing some pixel values in an image

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

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

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

25. 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, :, :);

26. Discussions and exercises, Chapter 4 Exercise 4.1

28. Exercise 4.2 • Write statements to do the following operations on a vector x: • Return the odd indexed elements.

29. Exercise 4.2 Write statements to do the following operations on a vector x: 2) Return the first half of x.

30. Exercise 4.2 Write statements to do the following operations on a vector x: 3) Return the vector in the reverse order.

31. 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

32. 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.

33. Exercise 4.4 what does Matlab output for the following commands? 1) 6 ~= 1 : 10 2) (6 ~= 1) : 10

34. Exercise 4.4 what does Matlab output for the following commands? 1) 6 ~= 1 : 10 2) (6 ~= 1) : 10

35. 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.

36. 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.

37. 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.