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CS 177

Lists and Matrices

Week 8

Announcements Project 2 due on 7th March, 2015 at 11.59 pm

Table of Contents

Lists

Matrices

Traversing a Matrix

Construction of Matrices

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1D arrayJust a list of numbers

1D arrayYou can create an empty list

- This breaks because my_array is an empty list so you can’t set an

element of an empty list

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

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

Matrices

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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.

Matrices

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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.

a0,0 a0,1 a0,2

a1,0

a2,0

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.

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Matrix - index

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Traversing a Matrix

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Example- Matrix

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Example- Matrix Contd..

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Construction of Matrices

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In this case we create a 5 × 4 matrix populated

with 0s.

Construction of Matrices

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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

Example 2 - Construction

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What should be the output after the following loop:

Example 2 - Construction

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What should be the output after the following loop:

Sum of Diagonal

2 3 1 2

6 5 7 2

2 1 1 5

3 4 5 3

0 1 2 3

0

1

2

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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.

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Sum of Diagonal

2 3 1 2

6 5 7 2

2 1 1 5

3 4 5 3

0 1 2 3

0

1

2

3

Exercise 1: Given a matrix A.

Write a nested for loop that will calculate the sum of diagonal.

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Sum = 0for i in range(len(A)):

for j in range (len(A[0])):if (i==j):

Sum = Sum + A[i][j]

Sum of Rows

2 3 1 2

6 5 7 2

2 1 1 5

3 4 5 3

0 1 2 3

0

1

2

3

Exercise 2:

Write a nested for loop that will calculate the sum of each row

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Sum of Rows

2 3 1 2

6 5 7 2

2 1 1 5

3 4 5 3

0 1 2 3

0

1

2

3

Exercise 2:

write a nested for loop that will calculate the sum of each row

sumRow = 0for i in range(len(A)):

for j in range (len(A[0])):sumRow = sumRow + A[i][j]

print (sumRow)sumRow = 0

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Compare Codes

Exercise 3:

Are these two codes the same?

sumRow = 0for i in range(len(A)):

for j in range (len(A[0])):sumRow = sumRow + A[i][j]

print (sumRow)sumRow = 0

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for i in range(len(A)):sumRow = 0for j in range (len(A[0])):

sumRow = sumRow + A[i][j]print (sumRow)

A = [[2, 3, 1, 2], [6, 5, 7, 2], [2, 1, 1, 5], [3, 4, 5, 3]]

1 2

Compare Codes

Exercise 3:

Are these two codes the same?

sumRow = 0for i in range(len(A)):

for j in range (len(A[0])):sumRow = sumRow + A[i][j]

print (sumRow)sumRow = 0

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for i in range(len(A)):sumRow = 0for j in range (len(A[0])):

sumRow = sumRow + A[i][j]print (sumRow)

A = [[2, 3, 1, 2], [6, 5, 7, 2], [2, 1, 1, 5], [3, 4, 5, 3]]

1 2

YES

Sum of Columns

2 3 1 2 1

6 5 7 2 1

2 1 1 5 1

3 4 5 3 1

0 1 2 3

0

1

2

3

Exercise 5:

Write a nested for loop that will calculate the sum of each column

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4

Sum of Columns

2 3 1 2 1

6 5 7 2 1

2 1 1 5 1

3 4 5 3 1

0 1 2 3

0

1

2

3

Exercise 5:

Write a nested for loop that will calculate the sum of each column

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for i in range(len(A[0])):sumCol = 0for j in range (len(A)):

sumCol = sumCol + A[j][i]print (sumCol)

Sum of two matrices

A[0][0]+B[0][0]

A[0][1]+B[0][1]

…A[0][2]+B[0][2]

…

…

A[3][0]+B[3][0]

A[3][1]+B[3][1]

…A[3][3]+B[3][3]

= +C A B2 3 1 2

6 5 7 2

2 1 1 5

3 4 5 3

5 5 5 5

1 1 1 1

3 3 3 3

4 4 4 4

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Exercise 6:

Write a nested for loop that will calculate the sum of two matrices

Sum of two matrices

A[0][0]+B[0][0]

A[0][1]+B[0][1]

…A[0][2]+B[0][2]

…

…

A[3][0]+B[3][0]

A[3][1]+B[3][1]

…A[3][3]+B[3][3]

= +C A B2 3 1 2

6 5 7 2

2 1 1 5

3 4 5 3

5 5 5 5

1 1 1 1

3 3 3 3

4 4 4 4

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Exercise 6:

Write a nested for loop that will calculate the sum of two matrices

for i in range(len(A)):for j in range (len(A[0])):

C[i][j] = A[i][j]+B[i][j]

Max Element

2 3 1 2 1

6 5 7 2 8

2 1 1 5 3

3 4 5 3 1

0 1 2 3

0

1

2

3

Exercise 7 :

Write a nested for loop that will find the max element in the matrix

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Max Element

2 3 1 2 1

6 5 7 2 8

2 1 1 5 3

3 4 5 3 1

0 1 2 3

0

1

2

3

Exercise 7 :

Write a nested for loop that will find the max element in the matrix

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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)

More Exercises

Given the following code to find the Max of a Matrix:

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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

Min in Matrix

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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

Min in each Row

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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

Min in each column

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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

Min in Matrix

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