Ch.5. Loops. (a.k.a. repetition or iteration)

Transcription

1

2 Ch.5 Loops (a.k.a. repetition or iteration)

3 5.1 The FOR loop End of for loop End of function

4 5.1 The FOR loop What is the answer for 100?

5 QUIZ

6 Modify the code to calculate the factorial of N: N!

7 Modify the code to calculate the factorial of N: N!

8

9 Vectors and for loops go hand-in-hand

10 Vectors and for loops go hand-in-hand

11 Vectors and for loops go hand-in-hand Write a script that uses a loop to find the product of all values stored in a vector.

12 Vectors and for loops go hand-in-hand Write a script that uses a loop to find the product of all values stored in a vector.

13 Vectors and for loops go hand-in-hand Write a script that uses a loop to find the maximum value stored in a vector.

14 What does this script do?

15 Here s a better way to do it

16 Exercise 5 Prompt the user for an integer n and print I love this stuff! n times.

17 Straight from the horse s mouth Source:

18 Straight from the horse s mouth Source:

19 Source: QUIZ

20 QUIZ Calculate the sum of all prime numbers between 0 and 15, using a for loop. Source:

21 What does this code do? numvec = []; for iv = 1:n inputnum = input( Enter a number: ); numvec(iv) = inputnum;

22 What does this code do? numvec = []; for iv = 1:n inputnum = input( Enter a number: ); numvec(iv) = inputnum; Because of the repeated extension operations, this code is inefficient!

23 Code efficiency: PREALLOCATION This runs a lot faster!

24 Remember cumulative sums and products

25 What does this code do?

26 Use preallocation!

27

28 To do for next time: Read pp of text Solve in notebook: end-of-chapter 2, 3

29 Exercise 7

30 Exercise 8

31 QUIZ: preallocation Write your own function my_cumprod to emulate the cumprod function. The argument is a vector vec, already initialized.

32 5.2 Nested for loops

33 Nested for loops Modify the script to print a triangle : * ** *** **** *****

34 Nested for loops

35 Matrices and nested for loops go hand-in-hand Print a 10x10 multiplication table

36 Print a 10x10 multiplication table Yes, it s OK for functions to return matrices!

37 More practice: Also print row and column labels for the table!

38 Matrices and nested for loops go hand-in-hand Write a script that calculates the sum of all the elements in a matrix. Initialize the matrix with random integers in the range

39 Matrices and nested for loops go hand-in-hand Write a script that calculates the sum of all the elements in a matrix. Create a 50x50 matrix Initialize the matrix with random integers in the range M = randi([-10 10], 50, 50, 'int8');

40 What does this code do?

41

42 QUIZ: How can we obtain the sum of each row instead?

43 QUIZ: Modify this code to output the sum of each row instead

44 The while loop

45 Exercise 23

46 It is possible to use more complex conditions: while x >= 42 && x <100 while x >= 42 ~found

47 What does this code do? Programming concept: sentinel

48 Another example of a sentinel

49 What else does this program do?

50 To do for next time: Read pp of text Solve in notebook: end-of-chapter 17

51 QUIZ: Based on this example

52 More complex error checking

53 5.4 Vectorizing We ve used loops to manipulate vectors and matrices

54 5.4 Vectorizing and we ve seen that all the usual operations can also be performed by built-in MATLAB functions!

55 Vectorizing sums and products >> v = v * 3 >> v = v / 2 >> v3 = v1 + v2 >> M = M + 42 >> M3 = M2 M1 >> v2 = v1.* v2 >> M2 = M1.^2 >> mata = matb./3 Notice the dot for *, /, and ^ Achtung! Array operators operate term-by-term!

56 QUIZ: What is printed here? >> M = [2:3; 4:5] >> M1 = [1,2; 3,4] >> M.* M1 >> M.^ 2

57 QUIZ

58

59 mat = mat.* 2;?

60 Vectorizing loops w/if statements Idea: Use vectorized logical functions!

61 Example: Vectorize this code using the function find() Hint: find the index of the sentinel!

62 Vectorize this code from Ch.4 using the function find()

63 Examples of vectorized logical ops. >> v = [ ] >> isgr = vec > 5 isgr = >> sum(isgr) ans = 3 >> isgr + 5 ans = 3

64 Examples of vectorized logical ops. >> v = [ ] >> isgr = vec > 5 isgr = >> vec(isgr) ans =

65 Why doesn t this work? >> v = [ ] >> isgr = vec > 5 isgr = >> vec(isgr) ans = >> vec([ ]) How do we fix it?

66 Why doesn t this work? >> v = [ ] >> vec(logical([ ])) ans =

67 Other vectorized logical functions >> false(2) ans = >> true(1,5) ans =

68 Other vectorized logical functions >> v = [ ]; >> any(v) ans = 1 >> all(v) ans = 0

69 Other vectorized logical functions >> v = [ ]; >> v1 = [ ]; >> find(v<3) ans = >> find(v==3) ans = 4 find() returns the index/indices of the elements that satisfy the condition

70

71 Exercise 29

72 Exercise 30

73 Can we use find() with matrices? Yes, but find() uses linear indexing! >> M=[1 2 3;4 5 6;7:9]; >> find(m > 5) ans =????

74 Other vectorized logical functions >> v = [ ]; >> v1 = [ ]; >> find(v<3) ans = >> find(v==3) ans = 4 >> isequal(v,v1) ans = 1

75 Other vectorized logical functions >> v1 = [ ]; >> v2 = [ ]; >> v1 & v2 ans = >> v1 v2 ans =

76 >> v1 = [ ]; >> v2 = [ ]; Print: --the values where v1 and v2 are equal --the positions where v1 and v2 are equal --the numbers of elements that are equal

77 Homework for Ch.5 End-of-chapter: 18, 19, 21, 28, 32, 34 Due: Friday, Oct.10 before exam