CS 177. Lists and Matrices. Week 8

Transcription

1 CS 177 Lists and Matrices Week 8 1

2 Announcements Project 2 due on 7 th March, 2015 at pm

3 Table of Contents Lists Matrices Traversing a Matrix Construction of Matrices 3

4 Just a list of numbers 1D array

5 You can create an empty list 1D array - This breaks because my_array is an empty list so you can t set an element of an empty list

6 1D array So to add to an empty list you would have to append

7 1D array You can also use a list comprehension to initialize an array This basically just creates an element 0 however many times the for loop runs

8 Matrices Matrices in mathematics are simply arrays of numbers or variables arranged in both rows and columns. Each number or variable contained within the matrix can be uniquely identified by its position in the row and column. 8

9 Matrices Each element of the matrix has a unique position determined by a row index i and a column index j. In the matrix below: the number 1, is defined to be in position 0,0 (located in row 0 and column 0) M = number of rows. N = number of columns. a 0,0 a 0,1 a 0,2 a 1,0 a 2,0 9

10 Encoding a Matrix We will consider a List to encode a Matrix. Although the List below does not visibly look like the matrix on the right, it does contain the same data. 10

11 Matrix - index 11

12 Traversing a Matrix 12

13 Example- Matrix 13

14 Example- Matrix Contd.. 14

15 Construction of Matrices In this case we create a 5 4 matrix populated with 0s. 15

16 Construction of Matrices The loop is traversing the entire matrix, but it only assigns the value 1 if the row index i is equal to the column index j 16

17 Example 2 - Construction What should be the output after the following loop: 17

18 Example 2 - Construction What should be the output after the following loop: 18

19 Sum of Diagonal Exercise 1: Given a matrix A = [[2, 3, 1, 2], [6, 5, 7, 2], [2, 1, 1, 5], [3, 4, 5, 3]] Write a nested for loop that will calculate the sum of diagonal

20 Sum of Diagonal Exercise 1: Given a matrix A. Write a nested for loop that will calculate the sum of diagonal. Sum = 0 for i in range(len(a)): for j in range (len(a[0])): if (i==j): Sum = Sum + A[i][j]

21 Sum of Rows Exercise 2: Write a nested for loop that will calculate the sum of each row

22 Sum of Rows Exercise 2: write a nested for loop that will calculate the sum of each row sumrow = 0 for i in range(len(a)): for j in range (len(a[0])): sumrow = sumrow + A[i][j] print (sumrow) sumrow =

23 Compare Codes Exercise 3: Are these two codes the same? A = [[2, 3, 1, 2], [6, 5, 7, 2], [2, 1, 1, 5], [3, 4, 5, 3]] sumrow = 0 for i in range(len(a)): for j in range (len(a[0])): sumrow = sumrow + A[i][j] print (sumrow) sumrow = 0 for i in range(len(a)): sumrow = 0 for j in range (len(a[0])): sumrow = sumrow + A[i][j] print (sumrow)

24 Compare Codes Exercise 3: Are these two codes the same? A = [[2, 3, 1, 2], [6, 5, 7, 2], [2, 1, 1, 5], [3, 4, 5, 3]] sumrow = 0 for i in range(len(a)): for j in range (len(a[0])): sumrow = sumrow + A[i][j] print (sumrow) sumrow = 0 for i in range(len(a)): sumrow = 0 for j in range (len(a[0])): sumrow = sumrow + A[i][j] print (sumrow) 1 2 YES 24

25 Sum of Columns Exercise 5: Write a nested for loop that will calculate the sum of each column

26 Sum of Columns Exercise 5: Write a nested for loop that will calculate the sum of each column for i in range(len(a[0])): sumcol = 0 for j in range (len(a)): sumcol = sumcol + A[j][i] print (sumcol)

27 Sum of two matrices Exercise 6: Write a nested for loop that will calculate the sum of two matrices A[0][0]+ B[0][0] A[3][0]+ B[3][0] A[0][1]+ B[0][1] A[3][1]+ B[3][1] C = A + B A[0][2]+ B[0][2] A[3][3]+ B[3][3]

28 Sum of two matrices Exercise 6: Write a nested for loop that will calculate the sum of two matrices A[0][0]+ B[0][0] A[3][0]+ B[3][0] A[0][1]+ B[0][1] A[3][1]+ B[3][1] C = A + B A[0][2]+ B[0][2] A[3][3]+ B[3][3] for i in range(len(a)): for j in range (len(a[0])): C[i][j] = A[i][j]+B[i][j] 28

29 Max Element Exercise 7 : Write a nested for loop that will find the max element in the matrix

30 Max Element Exercise 7 : Write a nested for loop that will find the max element in the matrix maxelement = A[0][0] for i in range(len(a)): for j in range(len(a[0])): if (maxelement < A[i][j]): maxelement = A[i][j] print(maxelement)

31 More Exercises Given the following code to find the Max of a Matrix: 1. maxelement = A[0][0] 2. for i in range(len(a)): 3. for j in range(len(a[0])): 4. if (maxelement < A[i][j]): 5. maxelement = A[i][j] 6. print(maxelement) Modify the code to find: Exercise 8: The Minimum in the Matrix Exercise 9: The Minimum of each row Exercise 10: The Minimum of each column 31

32 Min in Matrix minelement = A[0][0] for i in range(len(a)): for j in range(len(a[0])): if (minelement > A[i][j]): minelement = A[i][j] print(minelement) Exercise 8: The Minimum in the Matrix 32

33 Min in each Row for i in range(len(a)): minelement = A[i][0] for j in range(len(a[0])): if (minelement > A[i][j]): minelement = A[i][j] print(minelement) Exercise 9: Find the Minimum of each row 33

34 Min in each column for i in range(len(a[0])): minelement = A[0][i] for j in range(len(a)): if (minelement > A[j][i]): minelement = A[j][i] print(minelement) Exercise 10: The Minimum of each column 34

35 Min in Matrix 35