Lecture 7 Sept 19, 11 Goals: two-dimensional arrays (continued) matrix operations circuit analysis using Matlab image processing – simple examples Chapter 4 exercises

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.

Exercise: Write a code segment in Matlab to create a 10 by 10 identity matrix.

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

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

Logical indexing in 2-dim matrices

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

Sum, max, min, size etc.

Example 2

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

Array of structures Example:

Images as arrays

Numerical representation of array (gray scale image) Visual representation

Reading and opening an image

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.

Changing some pixel values in an image

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

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

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

Discussions and exercises, Chapter 4 Exercise 4.1

Exercise 4.2 Write statements to do the following operations on a vector x: 1)Return the odd indexed elements.

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

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

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] >> >> v ans = 1, 5, 9, 19

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.

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

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

Exercise 4.5. (This is quite 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.

Exercise 4.5. (This is quite 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. Solution: r = rand(length(x)); [rsort, indices] = sort(x); x(indices)

Exercise 4.6. Write a statement in Matlab to perform the following operations on a vector x: return the odd indexed elements of x followed by even indexed elements of x. Exercise 4.7. x = reshape(0:2:71, 3, 12). Find the index of 52.

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 ■ Reshape arrays ■ read an image, modify the array representation, view, save an image etc. ■ use Matlab to solve circuit analysis problems.