Udayan Das; Aubrey Lawson; Chris Mayfield; Narges Norouzi

Learning objectives

By the end of this section you should be able to

Demonstrate the use of a list-of-lists to structure data.
Demonstrate individual element addressing using multi-dimensional indexing.
Use nested loops to iterate a list-of-lists.

List-of-lists

Lists can be made of any type of element. A list element can also be a list. Ex: [2, [3, 5], 17] is a valid list with the list [3, 5] being the element at index 1.

When a list is an element inside a larger list, it is called a nested list. Nested lists are useful for expressing multidimensional data. When each of the elements of a larger list is a smaller list, the larger list is called a list-of-lists.

Ex: A table can be stored as a two-dimensional list-of-lists, where each row of data is a list in the list-of-lists.

Checkpoint

List-of-lists

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Concepts in Practice

Lists

For each of the questions below, consider the following matrix:

mat A = [\begin{matrix} 7 & 4 & 5 \\ 3 & 9 & 6 \\ 1 & 2 & 8 \end{matrix}]

1.

What would be the correct way to represent matA in Python?

```
[[7, 4, 5], [3, 9, 6], [1, 2, 8]]
```
```
[7, 4, 5
3, 9, 6
1, 2, 8]
```
```
[[7, 3, 1], [4, 9, 2], [1, 2, 8]
```

2.

What would be the correct index for the number 6 in the above list?

[5]
[2][1]
[1][2]

3.

What would be the result of the following code:

  print(matA[0])

Error
7
[7, 4, 5]

Using nested loops to iterate nested lists

A nested loop structure can be used to iterate a list-of-lists. For a two-dimensional list-of-lists, an outer for loop can be used for rows, and an inner for loop can be used for columns.

Example 9.4

Iterating a list-of-lists

The code below demonstrates how to iterate a list-of-lists.

The outer loop on line 9 goes element by element for the larger list. Each element in the larger list is a list. The inner loop on line 10 iterates through each element in each nested list.

1	"""Iterating a list-of-lists."""
2
3	# Create a list of numbers
4	list1 = [[1, 2, 3],
5	[1, 4, 9],
6	[1, 8, 27]]
7
8	# Iterating the list-of-lists
9	for row in list1:
10	for num in row:
11	print(num, end=" ")
12	print()

The above code's output is:

    1 2 3
    1 4 9
    1 8 27

Concepts in Practice

Iterating a list-of-lists

For each question below, consider the following list:

my_list = [[7, 4, 5, 12],
          [24, 3, 9, 16],
          [12, 8, 91, -5]]

4.

Which code prints each number in my_list starting from 7, then 4, and so on ending with -5?

for row in my_list:
  for elem in row:
    print(elem)

for elem in my_list:
    print(elem)

5.

The range() function can also be used to iterate a list-of-lists. Which code prints each number in my_list starting from 7, then 4, and so on, ending with -5, using counting for loops?

for column_index in range(0, len(my_list[0])):
  for row_index in range (0, len(my_list)):
    print(my_list[row_index][column_index])

for row_index in range(0, len(my_list)):
  for column_index in range (0, len(my_list)):
    print(my_list[row_index][column_index])
  print()

for row_index in range(0, len(my_list)):
  for column_index in range (0, len(my_list[0])):
    print(my_list[row_index][column_index])

Try It

Matrix multiplication

Write a program that calculates the matrix multiplication product of the matrices matW and matZ below and prints the result. The expected result is shown.

mat W = [\begin{matrix} 13 & 4 & 5 \\ 2 & - 9 & 7 \\ 7 & 3 & 19 \end{matrix}] mat Z = [\begin{matrix} 2 & 1 & 5 \\ 3 & 7 & 9 \\ - 1 & 13 & 19 \end{matrix}]

result = [\begin{matrix} 33 & 106 & 196 \\ - 30 & 30 & 62 \\ 4 & 275 & 423 \end{matrix}]

In the result matrix, each element is calculated according to the position of the element. The result at position [i][j] is calculated using row i from the first matrix, W, and column j from the second matrix, Z.

Ex:

result[1][2] = (row 1 in W) times (column 2 in Z)

result [1] [2] = [\begin{matrix} 2 & -9 & 7 \end{matrix}] * [\begin{matrix} 5 \\ 9 \\ 19 \end{matrix}]

result [1] [2] = 2 * 5 + (-9) * 9 + 7 * 19 = 10 - 81 + 133 = 62

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9.4 Nested lists

Learning objectives

List-of-lists

List-of-lists

Lists

Using nested loops to iterate nested lists

Iterating a list-of-lists

Iterating a list-of-lists

Matrix multiplication